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Rhett Allain

The Greatest Physics Demo of All Time Happened on the Moon

Stuff falls all the time. Maybe you’ve dropped a ball. Perhaps that cup of coffee slipped out of your hands. The mostly likely situation is that a cat decided to knock an object off a table—because that's what cats do.

And for as long as things have been falling, people have had questions about what is going on (and about the cat's motivation). Does a falling object move at a constant speed, or does it speed up? If you drop a heavy object and a light one at the same time, which will fall faster?

The great thing about these two questions is that you can ask pretty much anyone and they will have an answer—even if they are actually wrong. The even greater thing is that it's fairly simple to determine the answers experimentally. All you have to do is drop some stuff.

Some of the earliest explanations for what happens when you drop things go all the way back to Aristotle (around 350 BC), who was interested in explaining how the world works. Aristotle's answers were quite simple: If you let go of something, it will fall toward the ground. It will fall at a constant speed. If you drop two objects at the same time, the heavier one will move downward with a greater speed than the lighter one. That's it. And really, this seems like it could be true. I mean, if I drop a rock and a feather, it seems clear that the rock will hit the ground first.

But there is a problem. There's not an experiment to check if this is correct. Aristotle was a philosopher, not a scientist, and like most of the other Greek philosophers of his time, he was into thought experiments, not science experiments. (The Greeks knew that there couldn't be a perfect experiment, because some error would always be introduced into the data. They thought that seeking imperfect real-world evidence would just push them off the path of determining the ultimate truths of the universe through logic and reasoning.)

Aristotle's reasoning for this kind of motion actually makes sense. We can all agree that if you push something, it will move. The greater the pushing force, the more it will move—that means it would go faster. That makes sense, right? And if you hold a rock and a feather, the gravitational force on the rock is clearly greater. You can just feel that force when you lift the two objects up to compare them. There's no mystery there. So if the rock has a greater downward-pulling force, then it will have a greater downward falling velocity. If you drop a rock and a feather, the rock will hit the ground first. See? Physics isn't that hard.

Well, even though this explanation makes sense, it is indeed wrong. Really, the only thing that is correct is that normally a rock will hit the ground before a feather.

To understand why, let's start with the most basic idea—the relationship between force and motion. Most people call this Newton's second law, but if you go with “force-motion model,” that would be cool too. For movement in one dimension (like with a falling object), we can write this as:

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This says that the total force on an object (F net ) is equal to the product of the object's mass (m) and the acceleration (a).

But what is the acceleration? In short, this is a value that describes how the velocity changes. So, an acceleration of 0 meters per second per second means that the velocity won't change. An acceleration of 10 m/s 2 means that in 1 second, the object's velocity will increase by 10 meters per second. The important thing is that forces change the velocity of an object. If something has a greater force, it doesn't move faster. It changes more . Change is the key.

There's a small problem, though. When you drop a rock from shoulder height above the ground, it will only take about half a second to fall. That's not very much time—certainly not enough for a person to determine that it's speeding up. It just looks like it falls very fast. In fact, the human eye is pretty good at detecting if something moves, but not so great at judging changes in speed. (Check out this awesome video from Veritasium on how humans track objects.) So it's hard to fault anyone (like Aristotle) for saying things fall at a constant speed. It really does look that way to the naked eye.

OK, but what about dropping a rock and feather—doesn't the rock hit first? Usually, the answer is yes. But let's replace the rock with a hammer and then just take a change of scenery and move the experiment to the moon. This is exactly what happened during the Apollo 15 lunar mission in 1971 . Commander David Scott took a hammer and an eagle feather and dropped them onto the lunar regolith. Here's what happened:

The feather and the hammer hit the ground at the same time.

Why did it happen? First, it is indeed true that even on the moon there is a greater gravitational force on the hammer than the feather. We can calculate this gravitational force as the product of mass (m in kilograms) and the gravitational field (g in newtons per kilogram). On the surface of the moon, the gravitational field has a value of 1.6 N/kg. If you put this expression in for the net force on a falling object, it looks like this:

Since both the gravitational force and the acceleration depend on the same mass, it's on both sides of the equation and cancels. That leaves an acceleration of -g. The hammer and the feather fall down with identical motions and hit the ground at the same time. Honestly, I'm just a little sad that the astronauts didn't use one of the higher-quality film cameras instead of a TV camera—but that's just me.

So, what's different about dropping something on the moon versus on Earth? Yes, there is a different gravitational weight on the moon—but that's not the issue. It's the lack of air that makes the difference. Remember that Newton's second law is a relationship between the net force and the acceleration. If you drop a feather on the surface of the Earth, there are two forces acting on it. First, there is the downward-pulling gravitational force that is equal to the product of mass and the gravitational field. Second, there is an upward-pushing force due to the interaction with the air, which we often call air drag . This air drag force depends on several things, but the important ones are the object's speed and the size of the object.

Let's look at a simple example. Suppose the feather has a mass of 0.01 kilograms. This would give it a downward gravitational force of 0.098 newtons. Now imagine the feather is moving downward with a velocity of 1 meter per second, and this produces an upward air drag force of 0.04 newtons. This means that the net force would be 0.04 N - 0.098 N = -0.058 N. That would give a downward acceleration of 5.8 m/s 2 compared to an object without air resistance, which would have an acceleration of 9.8 m/s 2 .

Yes, a falling rock also has an upward-pushing air drag force. If it was the same size as the feather and moving at the same speed, it would have the same upward drag force of 0.04 N. However, if it has a mass of 1 kilogram, then its downward gravitational force would be 9.8 newtons. The net force would be 9.4 N, to produce an acceleration of 9.4 m/s 2 . Because of the rock's larger mass, it would have a much greater acceleration and it would hit the ground first—at least on Earth.

Do heavier objects always hit the ground before lighter ones? Nope. Here are some simple experiments you can do at home to show that Aristotle was wrong. (Bonus: You don't even need to go to the moon to do them.)

The first experiment uses two sheets of paper—just plain paper that you can get from your printer. If the pieces are identical, then they have the same mass and the same downward gravitational force. Now take just one of those sheets and crumple it up into a ball. This decreases the size of the object, but not its mass. When you drop the normal paper and the crumpled paper, which one will hit the ground first?

Oh, you don't have any paper with you? Fine, here is what that looks like:

You can see that the crumpled paper hits first—even though the two pieces have the exact same mass. Right there, Aristotle is busted.

But wait, here’s another experiment. This one requires more complicated objects. See if you can get something with a large surface area but a low mass. For example, I have a piece of cardboard and a tiny piece of chalk. The cardboard is indeed more massive (100 grams vs. 1 gram for the chalk). But if I drop them, which will hit the ground first? Let's find out.

Check that out. Thanks to air resistance, the more massive cardboard hits after the chalk.

Again, Aristotle was wrong. (And if you repeated both of those comparison drops on the moon, where there isn't air resistance, the objects would hit the surface at the same time.)

Did we really have to go all the way to the moon to show how things fall? Of course not. But it's still one of the coolest physics demos I've ever seen. I can't wait for a repeat the next time there's an astronaut on the moon . Hopefully, this time they will use a better video camera.

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Newton's reasoning for the orbit of the Moon

Newton's Lunar Theory

By michael nauenberg, nicholas kollerstrom, newton's forgotten lunar theory: his contribution to the quest for longitude}, (green lion press, santa fe, 2000).

What Really Happened with the Apple?

Sir isaac's most excellent idea, the center of mass for a binary system, two limiting cases, circular velocity and geosynchronous orbit, v circ = (gm/r) 1/2, open and closed orbits, escape velocity, v es = (2gm/r) 1/2, weight and the gravitational force, mass and weight, newton's derivation of kepler's laws, v circ = (gm/r) 1/2 = (2 pi r)/ p, (gm) p 2 = 4 pi 2 r 3, newton's interpretation of kepler's laws, g(m s + m p ) p 2 = 4 pi 2 r 3, g m s p 2 = 4 pi 2 r 3.

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The Apple and the Moon Video Tutorial

The The Apple and the Moon Video Tutorial explains how Newton derived his argument that gravity was the force that holds the moon in orbit. The inverse square law is introduced and the idea of the universal nature of gravity is emphasized. Numerous examples, illustrations, and animations assist in the explanations. The video lesson answers the following questions:

• How did Isaac Newton develop the idea of the universal law of gravitation?
• What is meant by the saying gravity is universal?

View Video Tutorial

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Moonbeams Shine on Einstein, Galileo and Newton

Thirty-five years after Moon-walking astronauts placed special reflectors on the lunar surface, scientists have used these devices to test Albert Einstein's general theory of relativity to unprecedented accuracy.

The research was conducted under NASA's Astronomy and Physics Research and Analysis program, part of the agency's Science Mission Directorate, Washington, D.C. JPL, is a division of the California Institute of Technology, Pasadena.

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4 4 Unification and the Moon‐Test (Propositions 3 and 4 Book 3)

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It reviews Newton’s argument for the claim that the moon is maintained in its orbit by an inverse-square force directed toward the earth. It introduces Newton’s moon-test argument for identifying the force that maintains the moon in its orbit with terrestrial gravity. Newton shows that inverse-square adjusting the centripetal acceleration exhibited by the lunar orbit agrees with Huygens’ measurement of the strength of terrestrial gravity at the surface of the earth. This chapter includes a somewhat detailed account of Newton’s moon-test calculation, including his dubious precession correction. It discusses his first two Rules for reasoning in natural philosophy, and his two-body correction. It examines the informative moon-test argument presented in Newton’s scholium to proposition 4. It argues that the agreement between the moon-test measurements and the pendulum measurements of the strength of terrestrial gravity is an example of empirical success. It also reviews the lunar precession problem.

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How the Moon Falls Toward the Earth (but Keeps Missing It)

• First Online: 01 January 2012

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• Douglas W. MacDougal 2  

Part of the book series: Undergraduate Lecture Notes in Physics ((ULNP))

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Galileo had shown by experimentation and theory how things fall, and documented his findings in his 1638 Dialog Concerning Two New Sciences . He asked simple questions about everyday phenomena and tested them with experiment until he understood the general laws behind the phenomena of motion. Isaac Newton (1642–1727) applied Galileo’s and Kepler’s laws of motion to the moon and planets and their satellites, and, with brilliant and subtle geometrical reasoning, developed the universal theory of gravitation that united earthly and heavenly phenomena. This he laid out with astonishing rigor in the first part of Newton’s Mathematical Principles of Natural Philosophy (first published in Latin in 1687, and commonly known today by the first word of its Latin title, the Principia ), perhaps the greatest masterwork of human thought in the history of science. Newton showed that the same force (gravitation) that caused the fall of an apple from a tree caused Jupiter’s moons to orbit Jupiter, Earth’s Moon to orbit Earth, and all the planets and moons together to orbit the Sun.

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Sir Isaac Newton [ 1 ]. (Short title) Principia. Book I (On the Motion of Bodies) and Book III (The System of the World) treat the motions of bodies and the consequences of gravitation. Book II of the Principia , however, deals with the motion of bodies in resisting mediums, of little concern in contemporary celestial mechanics. It may have been written chiefly to rebut Descartes theory of vortices. See, for example, the last Scholium in Book II, after Proposition LIII: “Hence it is manifest that the planets are not carried round in corporeal vortices; for, according to the Copernican hypothesis, the planets going round the sun revolve in ellipses, having the sun in their common focus…But the parts of a vortex can never revolve with such a motion.” From Sir Isaac Newton [ 1 ]. All excerpts from the Principia discussed here are drawn from this translation.

Being at “rest” in space was shown by Einstein in 1905 to be an entirely relative concept. For now we will use the terms “rest” and “motion” in the sense of absolute rest and motion relative to an absolute frame of reference, as Newton intended.

Principia , 13.

Principia , Book III, 551–52.

Principia , Axioms, or Laws of Motion, 13.

If the Moon’s orbit were perfectly circular, its velocity at all points would be constant. It is assumed so for our instructional purposes, but any object in an elliptical orbit will move with velocities that vary depending on the nature of the ellipse, as it draws nearer or farther from the body orbited; its mean motion, however, will be constant. In the case of the Moon, too, the irregularities in the distribution of the mass of the Earth, the effects of the Sun’s gravity, etc . all influence the shape of its orbit.

A “change of motion” in Law II is a change in [mass × velocity]. In dealing with fixed masses, as is the case with most classical problems of celestial mechanics, Law II means that force = mass × change in velocity. Since a change in velocity is acceleration, then force = mass × acceleration. It can be said that the measure of mass is the force required to accelerate it. The equation also suits those situations where mass does change, such as in rockets whose expenditures of fuel continually reduce the mass of the rocket as it ascends.

Sometimes acceleration and force will appear to be used interchangeably; this is because acceleration is force per unit mass.

Principia , Definition V, 2.

Principia , Book I, Proposition I, Corollary 4, 42.

While we cannot now take to time to prove this corollary to the proposition, it is an important one. It holds even for non-circular orbits. Newton creates parallelograms on the arcs of each orbit, with the chords forming the long axis of each parallelogram. For large arcs that are not circular, the line on each from A to the center of force may not be congruent (not match up) with the bisector of the chord. But as we take smaller and smaller units of time, the arcs too are diminished, the bisector lines converge with the force lines, and both point to the center of force. Thus, as we imagine the increments of time approaching zero (as Δ t  → 0) the direction of the force vectors in each orbit ultimately coincide with the lines bisecting the chords.

The Moon’s orbit is not too far from circular, and so revolves around the Earth at a fairly constant velocity, running through its phases predictably in a cycle of a little more than 27 days. If an object is moving uniformly in a circular orbit, it will journey equal distances along any arc in equal times. It will also, according to Newton’s very first proposition (and consistent with Kepler’s Second Law discussed in Chap. 4 ), sweep out equal areas in equal times:

The areas which revolving bodies describe by radii drawn to an immovable centre of force, do lie in the same immovable planes, and are proportional to the times in which they are described. ( Principia , Book I, Proposition I, Theorem I.)

This too makes intuitive sense. Visualize each orbit composed of little triangles drawn from the center, where the sides are the radii and the bases are the distances traveled by the object in equal times. The length of each base thus depends on the velocity of the body. Since the area of each triangle is proportional to its base times height, where height – the radius – is constant, the areas of all triangles in a given orbit will be the same. The areas, too, will be proportional to the velocity, since, as we said, the object’s motion is uniform along the arc. Now increase the number of triangles by making them smaller and smaller, until the triangles effectively merge into a circle, and the bases merge into the arc, and the conclusion is the same. In Newton’s words: “Now let the number of those triangles be augmented, and their breadth be diminished ad infinitum ; and… their ultimate perimeter …will be a curved line: and therefore the centripetal force, by which the body is continually drawn back from the tangent to this curve, will act continually…” ( Principia , Book I, Proposition I, Theorem I, 41.) This line of argument is how Newton demonstrated his first proposition.

Principia , Book I, Proposition IV, 45.

Ibid., Corollary 1.

We use the symbol f to represent centripetal acceleration. We will maintain the reference here to forces, as Newton did, in describing the proportions, since acceleration is force per unit mass.

Principia , Book I, Proposition IV, Corollary 9, 46.

For example, if s = .01, then s 2  = .0001; if s = .0001, then s 2  = .0000001.

The phrase centrifugal force appears to have originated with Christiaan Huygens who stated his Theorems on Centrifugal Force Arising from Circular Motion as early as 1659, having developed them even earlier. He did not publish them, however, until 1673, where they appeared appended to his book on pendulums. See Pendulum Clock , 176–8.

John Herival [ 2 ].

Newton developed this concept in the Scholium to his Proposition IV. Principia , Book I, Proposition IV, 47.

Newton I (1949) Mathematical principles of natural philosophy (trans: Motte A, 1729, revised by Cajori F). University of California Press, Berkeley, p 395

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Herival J (1965) The background to Newton’s principia, vol 7. Oxford University Press, London

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MacDougal, D.W. (2012). How the Moon Falls Toward the Earth (but Keeps Missing It). In: Newton's Gravity. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5444-1_5

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DOI : https://doi.org/10.1007/978-1-4614-5444-1_5

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Newton’s Cannon

This interactive HTML5 simulation is based on a thought experiment and illustration from Isaac Newton's A Treatise of the System of the World . It was specifically inspired by this Java version by Michael Fowler and Drew Dolgert. The simulated experiment shows how the motion of a familiar projectile like a cannon ball is fundamentally the same as the orbit of a celestial body like the moon.

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The Moon’s orbit has a radius of about 384,000 km (239,000 miles; approximately 60 Earth radii), and its period is 27.3 days (its synodic period , or period measured in terms of lunar phases, is about 29.5 days). Newton found the Moon’s inward acceleration in its orbit to be 0.0027 metre per second per second, the same as (1/60) 2 of the acceleration of a falling object at the surface of Earth.

In Newton’s theory every least particle of matter attracts every other particle gravitationally, and on that basis he showed that the attraction of a finite body with spherical symmetry is the same as that of the whole mass at the centre of the body. More generally, the attraction of any body at a sufficiently great distance is equal to that of the whole mass at the centre of mass. He could thus relate the two accelerations, that of the Moon and that of a body falling freely on Earth, to a common interaction, a gravitational force between bodies that diminishes as the inverse square of the distance between them. Thus, if the distance between the bodies is doubled, the force on them is reduced to a fourth of the original.

The constant G is a quantity with the physical dimensions (length) 3 /(mass)(time) 2 ; its numerical value depends on the physical units of length, mass, and time used. ( G is discussed more fully in subsequent sections.)

The weight W of a body can be measured by the equal and opposite force necessary to prevent the downward acceleration; that is M g . The same body placed on the surface of the Moon has the same mass, but, as the Moon has a mass of about 1 / 81 times that of Earth and a radius of just 0.27 that of Earth, the body on the lunar surface has a weight of only 1 / 6 its Earth weight, as the Apollo program astronauts demonstrated. Passengers and instruments in orbiting satellites are in free fall. They experience weightless conditions even though their masses remain the same as on Earth.

Kepler’s very important second law depends only on the fact that the force between two bodies is along the line joining them.

The motions of the moons of Jupiter (discovered by Galileo) around Jupiter obey Kepler’s laws just as the planets do around the Sun. Thus, Newton calculated that Jupiter, with a radius 11 times larger than Earth’s, was 318 times more massive than Earth but only 1 / 4 as dense .

Isaac Newton: Who He Was, Why Apples Are Falling

Sir Isaac Newton was born especially tiny but grew into a massive intellect and still looms large, thanks to his findings on gravity, light, motion, mathematics, and more.

Mathematics, Physics

Isaac Newton Kneller Painting

Far more than just discovering the laws of gravity, Sir Isaac Newton was also responsible for working out many of the principles of visible light and the laws of motion, and contributing to calculus.

Photograph of Sir Godfrey Kneller painting by Science Source

Legend has it that Isaac Newton formulated gravitational theory in 1665 or 1666 after watching an apple fall and asking why the apple fell straight down, rather than sideways or even upward. "He showed that the force that makes the apple fall and that holds us on the ground is the same as the force that keeps the moon and planets in their orbits," said Martin Rees, a former president of Britain's Royal Society, the United Kingdom's national academy of science, which was once headed by Newton himself. "His theory of gravity wouldn't have got us global positioning satellites," said Jeremy Gray, a mathematical historian at the Milton Keynes, U.K.-based Open University. "But it was enough to develop space travel." Isaac Newton, Underachiever? Born two to three months prematurely on January 4, 1643, in a hamlet in Lincolnshire, England, Isaac Newton was a tiny baby who, according to his mother, could have fit inside a quart mug. A practical child, he enjoyed constructing models, including a tiny mill that actually ground flour—powered by a mouse running in a wheel. Admitted to the University of Cambridge on 1661, Newton at first failed to shine as a student. In 1665 the school temporarily closed because of a bubonic plague epidemic and Newton returned home to Lincolnshire for two years. It was then that the apple-falling brainstorm occurred, and he described his years on hiatus as "the prime of my age for invention." Despite his apparent affinity for private study, Newton returned to Cambridge in 1667 and served as a mathematics professor and in other capacities until 1696. Isaac Newton: More than Master of Gravity Decoding gravity was only part of Newton's contribution to mathematics and science. His other major mathematical preoccupation was calculus, and along with German mathematician Gottfried Leibniz, Newton developed differentiation and integration —techniques that remain fundamental to mathematicians and scientists. Meanwhile, his interest in optics led him to propose, correctly, that white light is actually the combination of light of all the colors of the rainbow. This, in turn, made plain the cause of chromatic aberration—inaccurate color reproduction—in the telescopes of the day. To solve the problem, Newton designed a telescope that used mirrors rather than just glass lenses, which allowed the new apparatus to focus all the colors on a single point—resulting in a crisper, more accurate image. To this day, reflecting telescopes, including the Hubble Space Telescope, are mainstays of astronomy. Following his apple insight, Newton developed the three laws of motion, which are, in his own words:

• Newton's Law of Inertia : Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed upon it.
• Newton's Law of Acceleration : Force is equal to the change in momentum (mV) per change in time. For a constant mass, force equals mass times acceleration [expressed in the famous equation F = ma].
• Newton's Law of Action and Reaction: For every action, there is an equal and opposite reaction.

Newton published his findings in 1687 in a book called Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) commonly known as the Principia . "Newton's Principia made him famous—few people read it, and even fewer understood it, but everyone knew that it was a great work, rather like Einstein's Theory of Relativity over two hundred years later," writes mathematician Robert Wilson of the Open University in an article on a university website . Isaac Newton's "Unattractive Personality" Despite his wealth of discoveries, Isaac Newton wasn't well liked, particularly in old age, when he served as the head of Britain's Royal Mint, served in Parliament, and wrote on religion, among other things. "As a personality, Newton was unattractive—solitary and reclusive when young, vain and vindictive in his later years, when he tyrannized the Royal Society and vigorously sabotaged his rivals," the Royal Society's Rees said. Sir David Wallace, director of the Isaac Newton Institute for Mathematical Sciences in Cambridge, U.K., added, "He was a complex character, who also pursued alchemy"—the search for a method to turn base metals into gold—"and, as Master of the Mint, showed no clemency towards coiners [counterfeiters] sentenced to death." In 1727, at 84, Sir Isaac Newton died in his sleep and was buried with pomp and ceremony in Westminster Abbey in London.

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Newton’s Views on Space, Time, and Motion

Isaac Newton founded classical mechanics on the view that space is distinct from body and that time passes uniformly without regard to whether anything happens in the world. For this reason he spoke of absolute space and absolute time , so as to distinguish these entities from the various ways by which we measure them (which he called relative spaces and relative times ). From antiquity into the eighteenth century, contrary views which denied that space and time are real entities maintained that the world is necessarily a material plenum. Concerning space, they held that the idea of empty space is a conceptual impossibility. Space is nothing but an abstraction we use to compare different arrangements of the bodies constituting the plenum. Concerning time, they insisted, there can be no lapse of time without change occurring somewhere. Time is merely a measure of cycles of change within the world.

Associated with these issues about the ontological status of space and time was the question of the nature of true motion. Newton defined the true motion of a body to be its motion through absolute space. Those who, before or shortly after Newton, rejected the reality of space, did not necessarily deny that there is a fact of the matter as to the state of true motion of any given body. They thought rather that the concept of true motion could be analyzed in terms of the specifics of the relative motions or the causes thereof. The difficulty (or, as Newton alleged, the impossibility) of so doing constituted for Newton a strong argument for the existence of absolute space.

In recent literature, Newton's theses regarding the ontology of space and time have come to be called substantivalism in contrast to relationism . It should be emphasized, though, that Newton did not regard space and time as genuine substances (as are, paradigmatically, bodies and minds), but rather as real entities with their own manner of existence as necessitated by God's existence (more specifically, his omnipresence and eternality).

1. Overview of the Scholium

2.1 the void, 2.2 aristotle's doctrines, 2.3 sixteenth-century innovations, 2.4 charleton and the seventeenth-century revival of atomism, 3. descartes' innovation.

• 4. Newton's Manuscript: De Gravitatione …

5.1 Arguments for Absolute Time

5.2 direct arguments for absolute space, 5.3 the arguments from properties, causes, and effects, 5.4 discriminating in practice between absolute and apparent motion, 6.1 what the major impediments are, 6.2 why they are indeed impediments, 7. newton's legacy, other internet resources, related entries.

Today, Newton is best known as a physicist whose greatest single contribution was the formulation of classical mechanics and gravitational theory as set out in his Philosophae Naturalis Principia Mathematica ( Mathematical Principles of Natural Philosophy ), first published in 1687, and now usually referred to simply as “Newton's Principia ”. Newton's views on space, time, and motion not only provided the kinematical basis for this monumental work and thus for the whole of classical physics up until the early twentieth century, but also played an integral role in Newton's general system of philosophy and theology (largely developed prior to the Principia ). Because Newton never drafted a treatise on, or even a digest of, this general system, his stature as one of the great philosophers of the seventeenth century, indeed, of all time, is no longer widely appreciated.

A “Scholium” at the beginning of the Principia , inserted between the “Definitions” and the “Laws of Motion”, lays out Newton's views on time, space, place, and motion. He begins by saying that, since in common life these quantities are conceived of in terms of their relations to sensible bodies, it is incumbent to distinguish between, on the one hand, the relative, apparent, common conception of them, and, on the other, the absolute, true, mathematical quantities themselves. To paraphrase:

• Absolute, true, and mathematical time , from its own nature, passes equably without relation to anything external, and thus without reference to any change or way of measuring of time (e.g., the hour, day, month, or year).
• Absolute, true, and mathematical space remains similar and immovable without relation to anything external. (The specific meaning of this will become clearer below from the way it contrasts with Descartes' concept of space.) Relative spaces are measures of absolute space defined with reference to some system of bodies or another, and thus a relative space may, and likely will, be in motion.
• The place of a body is the space which it occupies, and may be absolute or relative according to whether the space is absolute or relative.
• Absolute motion is the translation of a body from one absolute place to another; relative motion the translation from one relative place to another.

Newton devotes the bulk of the Scholium to arguing that the distinction between the true quantities and their relative measures is necessary and justified.

It is evident from these characterizations that, according to Newton:

• space is something distinct from body and exists independently of the existence of bodies,
• there is a fact of the matter whether a given body moves and what its true quantity of motion is, and
• the true motion of a body does not consist of, or cannot be defined in terms of, its motion relative to other bodies.

The first of these theses was a point of major contention in 17th-century natural philosophy and one assailed by Newton's critics such as Leibniz, Huygens, and Berkeley. The second was not in general dispute. Descartes, Leibniz, and Berkeley all believed that, to put it in somewhat scholastic terms, the predicate ‘ x is in true motion’ is a complete predicate in the sense that it holds or fails to hold for any given body. (Huygens, at least in his post- Principia views, constitutes a special case.) Thus, for those who denied the first thesis, it was necessary to secure a definition, or an analysis, of what it means for a body be in true motion (and what determines the quantity of that motion), so as to be as adequate to the facts as Newton's characterization of true motion. The figures mentioned above all deemed that motion relative to other bodies is a necessary condition for true motion, although not, by itself, a sufficient condition.

Over the course of years, the consensus in the 17th and early 18th Centuries on thesis (2) was lost sight of, and it became common to characterize Newton's opponents as denying that there is a fact of the matter as to whether a body is in true motion and maintaining instead that all motion is merely relative motion . Thus, modern readers expect that Newton's Scholium on space, time, and motion should be read as arguing not only thesis (1) above, but also thesis (2), that all motion is not merely relative motion, but that some motions are true and absolute. Newton's arguments concerning motion, however, are designed to show, not that true motion is distinct from merely relative motion (which is granted by all), but rather that the only feasible analysis of true motion requires reference to absolute places, and thus the existence of absolute space.

In particular it has been assumed that Newton's so-called “rotating bucket experiment”, together with the later example of a pair of globes connected by a chord and revolving about their center of gravity, is supposed to argue, or provide evidence for, the existence of true, or absolute, motion. Not only is this false, but the two cases have distinct purposes in the framework of the Scholium. The rotating bucket experiment is the last of five arguments from the “properties, causes, and effects of motion” designed to show cumulatively that an adequate analysis of true motion must involve reference to absolute space. In contrast, the example of the revolving globes is intended to illustrate how it is that, despite the fact that absolute space is invisible to the senses, it is nonetheless possible to infer the quantity of absolute motion of individual bodies in various cases.

2. The Legacy from Antiquity

The most important question shaping 17th-century views on the nature of space, time and motion is whether or not a true void or vacuum is possible, i.e., a place devoid of body of any sort (including rarified substances such as air). Ancient atomism, dating back at least to the pre-Socratic philosopher Democritus (5th century, B. C.), held that not only is such possible, but in fact actually exists among the interstices of the smallest, indivisible parts of matter and extends without bound infinitely. Following Plato, Aristotle rejected the possibility of a void, claiming that, by definition, a void is nothing, and what is nothing cannot exist.

According to Aristotle, the universe is a material plenum, finite in extent, bounded by the outermost sphere of the fixed stars. Beyond that there is no void, i.e., empty places, since, as Aristotle defines ‘place’, the place of something is the outermost of “the innermost motionless boundary of what contains it.” Hence, since there are no boundaries outside the outermost celestial sphere, there are no places or space outside of it.

Time, according to Aristotle, is just the measure of motion, where by ‘motion’ he means change of any sort, including qualitative change. In order to define the uniformity of time, that is, the notion of equal intervals of time, Aristotle was guided by astronomical practice, which in antiquity provided the most practical and accurate measures of time. He identified uniform motion with the rate of motion of the fixed stars, a choice for which he found a dynamical justification in his celestial physics.

“Local” motion is but one species of motion, viz., change of place. Motion, in general, he defined as the actualization of potentiality, a notion commonly held in the 17th century to be so obscure as to be either useless or meaningless. However, as far as local motion is concerned, there is no difficulty as to what constitutes the true or absolute motion of a body in a finite geocentric universe. Indeed, elementary substances in the sub-lunar realm (earth, air, fire, and water) move of their own accord either up or down, i.e., toward the center or away from the center by their very nature. The celestial realm, beginning with the orbit of the moon, consists of an interlocking network of celestial spheres composed of a fifth element (aether), which by its nature is disposed to circular motion about the center of the of universe (i.e., the center of the earth). If the motion of this substance is taken to be the measure of time, the celestial spheres necessarily rotate uniformly. Since the net motion of an embedded sphere is the sum of its natural motion superimposed on the natural motions of the spheres in which it is embedded, and since the axes of rotation are in general set at slightly different angles in order to account for why the sun does not move on the celestial equator and the planets and the moon do not move strictly on the ecliptic (i.e., the path of the sun against the fixed stars), the motions of the moon, planets, and even the sun are not necessarily uniform. However, since the sphere of the fixed stars is embedded in no other celestial sphere in motion, the motion of the fixed stars is de facto the measure of all motion.

The motions spoken of so far are all natural motions of the substances in questions, motions induced by the body being the very substance that it is. In contrast, other motions, in which the cause of the motion is external rather that internal to the body, Aristotle subsumed under the concept of violent motion. Violent motion required for its continuation the constant application of an external cause.

Although Aristotle's views dominated medieval scholasticism, there occurred a renewed interest in atomism in the early 17th Century. Apart from general factors such as the Renaissance, Humanism, and the Reformation, specific innovations of the 16th Century made it attractive. Although Copernicus' introduction of a helio-static system was motivated by a strict adherence to Aristotle's dynamics of celestial spheres, it brought into question his terrestial physics. Galileo's telescopic observations of the surface of the moon and his discovery of moons orbiting about Jupiter brought into question the very distinction between the terrestial and the celestial. Moreover, the visibility of an abundance of new stars, apparently without end, suggested that the universe may in fact be without bound.

An important representative of the revival of atomism and its concomitant views concerning the void is Walter Charleton's Physiologia Epicuro-Gassendo-Charltoniana: Or a Fabrick of Science Natural, upon the Hypothesis of Atoms, “Founded by Epicurus, Repaired by Petrus Gassendus, Augmented by Walter Charleton” , which appeared in English in 1654, twelve years after Newton's birth. It is a text with which Newton became familiar as an undergraduate, and some of the core theses concerning time and space later put forth in the Principia and various unpublished manuscripts in Newton's hand can be found in Charleton. These include:

• that time and space are real entities even though they fit neither of the traditional categories of substance or accident (i.e., property of a substance),
• that time “flow[s] on eternally in the same calm and equal tenor,” while the motion of all bodies is subject to “acceleration, retardation, or suspension”,
• that time is distinct from any measure of it, e.g., celestial motion or the solar day,
• that space is “absolutely immoveable” and incorporeal,
• that bodies, or “Corporeal Dimensions” are everywhere “Coexistent and Compatient” with the “Dimensions” of the parts of space they occupy,
• that space distinct from body existed before God created the world and that God's omnipresence is his literal presence everywhere, and
• that motion is the translation or migration of body from one place, as an immovable part of space, to another.

Charleton's arguments for his views concerning time have much the same tenor as those given by Newton in the Principia . In marked contrast, though, those for empty, immense, and immutable space are quite different. Charleton appeals to the explanation of such phenomena as rarefaction and condensation, the differences in “degrees of Gravity” of bodies, and the numerous ways in which bodies can interpenetrate at the micro-level in terms of solubility, absorption, calefaction, and diverse chemical reactions. However, Charleton does not introduce the terminology of “relative” time, “relative” spaces, or “relative” places, and nowhere raises concerns regarding true (absolute) motion versus merely relative motion. Oddly enough, although Charleton occasionlly mentions and criticizes Descartes with regard to other matters, no note of the fact is made that Descartes, a decade earlier, had proposed explanations, in detail or in outline, for just these sorts phenomena according to a system of nature in which the world is completely filled with matter and in which space distinct from body cannot exist. Descartes, it can be justly said, is the founder of the other main school of the “mechancal philosophy” of the 17th Century, which stood in direct opposition to atomism on the issue of the possibility of a vacuum and which adapted the Aristotelian doctrines on the nature of time, space, and motion to the new world view.

Although avowedly anti-Aristotelian in many regards, particularly on the view, shared with atomists, that all qualitative change on the macroscopic scale is reducible to the rearrangement and/or motion of matter on the microscopic scale, it was Descartes' ambition to carry out this program by retaining what is essentially Aristotle's notion of Prime Matter. The pure elements (earth, air, fire, and water) of Aristotle's physics could mutate into one another by alteration of the fundamental qualities definitive of them. These were the four haptic qualities of hot, cold, wet, and dry. Because of this, there had to be something distinguishable, at least in thought, from qualities that persist during elemental alteration. This quality-less substratum is what Aristotle referred to simply as matter, or as it is often called, Prime Matter, in order to avoid confusion with the macroscopically identifiable, quality-laden, homogenous portions of everyday objects. Unlike atomists, who attributed at least the quality of hardness (impenetrability) to the ultimate particles of matter, Descartes argued that matter, or synonymously, body [corpus] has no qualities whatsoever, but only quantity, i.e., extension. In other words, body and extension are literally one and the same [res extensa]. An immediate corollary is that there can be no vacuum, for that would require an extended region devoid of body --- a manifest contradiction. The task, then, was to show how all apparent qualities can be explained in terms of the infinite divisibility and rearrangement of extension with respect to itself. The task was grand indeed, for its goal was to develop a unified celestial and terrestrial physics that could account equally for the ductility of metals, magnetic attraction, the tides, the mechanism of gravity, the motion of the planets, the appearance and disappearance of comets, and the birth and death of stars (supernovae).

Descartes published his system of the world in 1644 as the Principles of Philosophy ( Principia Philosophae ). Part II of the Principles lays out the thesis of the identity of space (extension) and matter, develops a definition of motion in the “true, or philosophical sense”, and sets out the fundamental dynamical laws of his system. Motion, according to “the truth of the matter”, is defined to be “the translation of one part of matter, or one body, from the vicinity of those bodies, which are immediately contiguous to it and are viewed as if at rest, to the vicinity of others.” In consequence, Descartes points out, each body has a single motion proper to it (in contrast to the numerous relative motions that can be ascribed to it depending on which other bodies are selected in order to determine its place). It is this single proper motion that figures in his laws of motion. Of particular importance for Descartes' entire system, is that a body in circular motion has an endeavor [conatus] to recede from the center of rotation.

4. Newton's Manuscript De Gravitatione …

This fact, together with Descartes' contention that a body also participates in the motion of a body of which it is a part, makes it difficult to reconcile Descartes' system of the world with his definition of proper motion. Newton concluded that the doctrine is in fact self-refuting and that, where Descartes needed to, he had surreptitiously helped himself to a notion of space independent of body, particularly in order to assign the desired degree of centrifugal conatus to the planets and their satellites as they are swept about by celestial vortices of “subtle” matter.

The untitled and unfinished manuscript which begins “De Gravitatione et aequipondio fluidorum et solidorum …”, written perhaps a decade or more before the Principia , consists for the most part of an extensive and scathing critique of Descartes' doctrine of motion. The document, published for the first time in (Hall and Hall, 1962), is well worth the study for a glimpse at the development of Newton's thinking at a relatively young age. It manifestly embraces the doctrines of space and time later codified in the Principia . Notable, as well, is that each of the five arguments from the properties, causes and effects of motion advanced in the Scholium has a clearly identifiable antecedent in De Gravitatione . (See Rynasiewicz 1995 for details.) This makes it clear the extent to which the Scholium is concerned to argue specifically against the Cartesian system (as pointed out by Stein 1967), which Newton perceived to be the only other viable contender at the time.

5. Newton's Scholium on Time, Space, Place and Motion

The Scholium has a clearly discernible structure. Four paragraphs marked by Roman numerals I–IV follow the opening paragraph, giving Newton's characterizations of time, space, place and motion, respectively, as summarized in the third paragraph of Section 1 above. If we were to extend Newton's enumeration to the remaining paragraphs, then paragraphs V–XII constitute a sustained defense of the distinctions as characterized in I–IV. Paragraph XIII then states the general conclusion that the relative quantities are genuinely distinct from the respective absolute quantities and makes comments on the semantic issue of the meanings of these terms in the Bible. There follows one remaining, and quite extensive paragraph [XIV], which takes up the question how in practice one can ascertain the true motions of bodies and concludes: “But how we are to obtain the true motions from their causes, effects and apparent differences, and vice-versa, will be explained at length in the treatise that follows. For that is the end to which I composed it.”

In what follows, links have been inserted to the text of the Scholium according to the extended enumeration suggested above. Clicking on a link will open a new window in such a way that the reader can navigate back and forth between a given paragraph of the text and the commentary elucidating that paragraph.

Paragraph V appeals to the fact that astronomy distinguishes between absolute and relative time in its use of the so-called equation of time. This serves to correct for inequalities in the commonly adopted standard of time, the solar day, which most people mistakenly believe to be uniform. The solar day, defined as the period of time it takes the sun to return to zenith, varies by as much as 20 minutes over the course of a year. The standard of correction in the equation of time used in Ptolemaic astronomy was based upon the assumption that the sidereal day—the period of time it takes a fixed star to return to zenith—is constant, because the celestial sphere on which the fixed stars are located should not be assumed to speed up and slow down. With the demise of the Ptolemaic system and Aristotelian cosmology, this rationale was no longer compelling, and at least some astronomers, most notably Kepler, called into doubt whether the rate of rotation of the earth remained constant over the course of the year. (Kepler considered that its rotation would be faster when closer to the sun due to an excitatory effect of the sun.) Thus, the issue of the correct measure of time occupied considerable attention in 17th Century astronomy, especially because the ability to measure the rate of rotation of the earth is equivalent to the problem of determining longitude, which, for sea-faring nations, was critical for navigation (and hence military and economic dominance). Huygens' pendulum clock provided the first terrestrial candidate for a decently accurate measure of uniform time. Newton mentions this, as well as the eclipses of the moons of Jupiter, an alternative method based on Kepler's period law.

The invocation of the need for an equation of time in astronomy is not just an appeal to a well entrenched scientific practice. In the course of his discussion, Newton explains why he thinks the need is justified. Although he will argue in Book III of the Principia that the diurnal rotation of the earth is uniform, this is a contingent fact. It could have been otherwise. Indeed, it could have been that there are no uniform motions to serve as accurate measures of time. The reason is that all motion is subject to being accelerated or retarded (by the application of external forces). In contrast, absolute time (which is nothing other than duration or the perseverance of the existence of things) remains the same, whether the motions be be swift, slow, or null.

Paragraph VI defends the thesis of the immobility of (absolute) space, which against the backdrop of Descartes, clearly means that the parts of space, just as the parts of time, do not change their relation with respect to one another. Newton argues that the parts of space are their own places, and for a place to be moved out of itself is absurd. A more expansive antecedent of this argument occurs in De Gravitatione , applied specifically to time: if yesterday and tomorrow were to interchange their temporal relations with respect to the remainder of time, then yesterday would become today, and today yesterday. Thus, Newton held an interestingly holistic identity criterion for the parts of space and time.

Newton devotes five full paragraphs to justifying his characterization of the distinction between absolute and relative motion. The first three present arguments from properties of absolute motion and rest, the next presents an argument from their causes, and the final an argument from their effects. The force of these has confused modern commentators for a combination of reasons which, historically, are difficult to untangle. Since only those not already prejudiced by those commentaries, directly or indirectly, will find what follows unusual, it is best to defer an autopsy of those reasons until Section 6, after an exposition of the arguments.

Suffice it to say for the moment that it is a common misunderstanding that in these arguments Newton intends to develop empirical criteria for distinguishing cases of absolute motion from merely apparent motion and thereby to disprove the thesis that all motion is merely relative motion. To the contrary, the arguments take as their point of departure the assumption, common to Cartesian and Aristotelian philosophy, that each body has a unique state of true motion (or rest). Throughout the arguments, the terms ‘true motion’ and ‘absolute motion’ are treated synonymously. At issue is whether true motion (and rest) can be reduced to some special instance of relative motion (or rest) with respect to other bodies. In announcing at the outset of these arguments that “absolute and relative rest and motion are distinguished by by their properties, causes, and effects”, Newton indicates his intent to show that they cannot, at least if true motion and rest are to have those features we generally associate, or ought to associate, with them.

Argument 1 from Properties [ Paragraph VIII ] Property : Bodies that are truly at rest are at rest with respect to one another. Conclusion : True rest cannot be defined simply in terms of position relative to other bodies in the local vicinity.

Reasoning : Suppose there were a body somewhere in the universe absolutely at rest, say far away, in the region of the fixed stars, or even farther. (Whether or not that body might ever be observed doesn't enter into what follows.) Clearly it is impossible to know just from considering the positions of bodies in our region relative to one another whether any of these latter bodies maintains a fixed position with respect to that hypothetical distant body. To amplify, let B be one of the local bodies, C the relative configuration over time of the set of local bodies, and A the far distant body at absolute rest. The specification of C alone fails to establish the position of B relative to A over time. In particular, C fails to establish whether B is relatively at rest with respect A, which, by the property stated above, is a necessary condition for B to be absolutely at rest. Hence, specification of the local configuration C underdetermines whether or not B is at absolute rest. Thus the conclusion: it is impossible to define what it is for a body such as B to be at absolute rest [i.e., to give necessary and sufficient conditions for when it is that B is at rest] simply in terms of how B fits into the local configuration C.

Argument 2 from Properties [ Paragraph IX ] Property : If a part of a body maintains a fixed position with respect to the body as a whole, then it participates in the motion of the whole body. Conclusion : True and absolute motion cannot be defined as a translation from the vicinity of (the immediately surrounding) bodies, viewing the latter as if they were at rest.

Reasoning : Newton first introduces two considerations that can be taken either to support, or to illustrate, or to amplify upon the import of the stated property. The first is that if a part of a rotating body is at rest relative to the body as a whole, it endeavors to recede from the axis of rotation. The second is that the impetus of a body to move forward arises from the combination of the impetus of its parts.

From the property it follows that if those bodies surrounding a given body move (either rotationally or progressively forward as a fixed configuration) while the surrounded body is at rest relative to the surrounding ones, then the surrounded body partakes in the (true) motion of the group of surrounding bodies. Hence, if the surrounding bodies move truly, then so does the surrounded body. But according to the (Cartesian) definition of motion—which identifies the true motion of a body with its transference from the vicinity of immediately surrounding bodies, regarding the surrounding bodies to be as though they are at rest—it would have to be said (wrongly) that the surrounded body is truly at rest. Hence that definition is untenable.

Argument 3 from Properties [ Paragraph X ] Property : Anything put in a moving place moves along with that place, and hence a body participates in the motion of its place when it moves [relatively] away from that place. Conclusion : The complete and absolute motion of a body cannot be defined except by means of stationary places.

Reasoning : From the property, the [relative] motion of a body out of a given place is only part of the motion of the body if the place in question is itself in motion. The complete and true motion of the body consists of its motion relative to the moving place added vectorially to whatever motion the place may have. Should the place be moving relative to a place which is in turn moving, then the motion of that place must be added, and so on. Barring infinite regress, the sum must terminate with a motion relative to a stationary place.

Addended Argument : After deriving this conclusion, Newton amplifies upon the consequences. The only places that are stationary are all of those that that stay in fixed positions with respect to one another from infinity to infinity, and since these always remain stationary, they make up what Newton calls immobile absolute space.

The Argument from Causes [ Paragraph XI ] Causes : the forces impressed upon bodies. The major premise is that application of a [non-zero net] force on a body is both a necessary and sufficient condition for either generating or altering its true motion. More specifically: (A) Impressed force is a necessary condition for generating or altering true motion (but not, as remains to be shown, merely relative motion). (B) Application of a [non-zero net] force is a sufficient condition for the generation or alteration of true motion (but not, as will be shown subsequently, merely relative motion). Conclusion : The true motion of an individual body cannot be defined as any particular sub-instance of its motion relative to other bodies.

Reasoning : Newton seeks to establish that application of a positive net force to a body is neither a necessary not a sufficient condition for the generation of motion relative to other bodies. The two lines of reasoning are given separately, call them ‘Prong A’ and ‘Prong B’, respectively.

Prong A : To be established is that, although an impressed force is necessary for the generation or alteration of true motion in a body, it is not necessary for the generation of motion relative to other bodies. The reasoning is quite simple: pick a given body and merely apply the same [accelerative] force to all other bodies in question. These other bodies will then remain in the same relative configuration with respect to one another, but a relative motion with respect to the original body [to which no force has been applied] will either be generated or altered.

Prong B : To be established is that, although an impressed force is sufficient for the generation or alteration of true motion in a body, it is not sufficient for the generation of motion relative to other bodies. Again, the line of reasoning is quite straightforward. Consider an arbitrarily given body amongst a system of bodies and simply apply the same [accelerative] force to all bodies in question. Then, despite the fact that a force has been impressed upon the originally given body, there is neither generation nor alteration of relative motion with respect to the remaining bodies.

The Argument from Effects [ Paragraph XII ] Effects : the forces of receding from the axis of rotational motion [centrifugal endeavor]. The major premise is that the centrifugal endeavor of bodies [or parts of bodies] to recede from the axis of rotation is directly proportional to the quantity of the true circular motion. Conclusion : True rotational motion cannot be defined as relative rotation with respect to the surrounding bodies.

Reasoning : The line of reasoning is in fact parallel to the preceding argument from causes, although this may not be completely perspicuous due to the fact that the correlates of the two prongs above are here stages of a single on-going experimental situation, the so-called “rotating bucket” experiment, which, Newton intimates, he actually performed. In order to set up this experiment, one suspends a bucket using a long cord and by turning the bucket repeatedly, winds up the cord until it is strongly twisted, then fills the bucket with water. During the course of the experiment, the degree to which the water tries to climb up the sides of the bucket is used as a measure of its centrifugal endeavor to recede from the center. Newton uses the experiment to establish that centrifugal endeavor is neither a necessary condition nor a sufficient condition for the existence of relative circular motion [of the water] with respect to its surroundings [the bucket].

Stage 1 : When the bucket is first released, it rotates rapidly with respect to the rest frame of the experimenter while the water remains at rest with respect to the experimenter. In other words, there is rapid relative motion of the water with respect to the bucket. However, the surface of the water remains flat, indicating that it has no tendency to recede from the axis of relative rotation. Thus, the existence of centrifugal endeavor in the parts of a body is not a necessary condition for the body to be rotating relative to its surroundings. That is, such relative rotation with respect to immediately adjacent bodies need not produce any centrifugal endeavor in the parts of the body to recede from the axis of relative rotation.

In the further course of the experiment, as the bucket continues to rotate, the water gradually begins to rotate with it, and as it does so, begins to climb up the sides of the bucket. Eventually, according to Newton, the water acquires the same rotation of the bucket relative to the lab frame, at which point we have the following situation.

Stage 2 : The water and the bucket are at relative rest, yet the water has achieved its highest ascent up the sides of the bucket, indicating a maximum centrifugal endeavor to recede from the axis of common rotation. Hence, the existence of centrifugal endeavor is not a sufficient condition for the presence of relative circular motion between a body and its surroundings, i.e., if a body, or rather its parts, have a centrifugal endeavor to recede from a central axis, it does not follow that there is a relative circular motion of the body with respect to its immediate surroundings.

Astrophysical Application . After deriving the conclusion, Newton uses the premises of the first two arguments from properties, together with the premise of the argument from effects, to critique the vortex theory of planetary motion. According to that theory, each of the planets (and most notably the earth) is relatively at rest with respect to the “subtle” matter of the celestial vortex of our own sun. Hence, according to Descartes' own definition of true motion (as well as his explicit insistence), they have no true motion. However, it is manifest that they do not maintain fixed positions with respect to one another. So, according to the property invoked in the first argument, they cannot [all] be truly at rest. Moreover, from the property invoked in the second argument, they partake in the circular motion of the solar vortex [assuming that motion to be true motion, as Descartes implicitly assumed]. Finally, because they would accordingly participate in the true circular motion of this hypothetical vortex, they should have an endeavor to recede from the axis of its rotation.

This completes the sequence of arguments from the properties, causes, and effects of motion. The next paragraph [ XIII ] states the cumulative conclusions of the arguments marshalled beginning with the arguments for absolute time in paragraph V: “Hence relative quantities are not the quantities themselves, whose names they bear, but are only sensible measures of them (either accurate or inaccurate), which are commonly used in place of the quantities they measure.” Having made his case, Newton comments on the ordinary language meaning of the terms for these quantities in order to address contemporary issues of dogma and heresy.

Galileo's condemnation by the Catholic Church for asserting that the earth is in motion was still recent history at the time Newton composed the Principia . Descartes, who lived in reach of Papal authority and feared similar fate, had found a clever way of espousing Copernicanism without falling prey to accusation of heresy. According to his definition of motion “properly speaking”, he contends, the earth is truly at rest.

In Newton's system of the world as set out in Book III of the Principia , the earth patently moves absolutely. In anticipation, Newton indicates how to reconcile this with scripture by observing that, if usage determines the meanings of words, then in ordinary discourse (including the Bible) the terms ‘time’, ‘space’, ‘place’, and ‘motion‘ are properly understood to signify the relative quantities; only in specialized and mathematical contexts do they denote the absolute quantities. (Keep in mind Newton's title, The Mathematical Principles of Natural Philosophy .) He proceeds to chastise Descartes on two counts, first for doing violence to the scriptures by taking them to refer to the absolute quantities, and second, for confusing the true quantities with their relative measures.

Having argued his case that true motion consists in motion with respect to absolute space, and thus having dealt to his satisfaction with the metaphysics of motion, Newton turns in the final paragraph of the Scholium to epistemological strategies available on his account. On an Aristotelian or Cartesian account, one can directly observe the allegedly absolute motion of a body if both it and its immediate surroundings are visible. In contrast, because the parts of absolute space are not directly accessible to the senses, it is very difficult, Newton confesses, to ascertain the true motion of individual bodies and to discriminate them in practice from the apparent motions. “Nevertheless,” he remarks in a rare moment of wit, “the situation is not entirely desperate.” Evidence is available in part from apparent motions, which are the differences of true motions, and in part from the forces, which are the causes and effects of true motions.

Newton illustrates with an example. Imagine a pair of globes, connected by a cord, revolving about their common center of gravity. The endeavor of the globes to recede from the axis of motion is revealed by the tension in the cord, from which the quantity of circular motion can be estimated. Furthermore, whether the direction of their revolution is clockwise or counterclockwise can be detected by applying forces to opposite faces of the globes to see whether the tension in the cord increases or decreases. All this can be done in empty space where no other bodies are present to serve as points of reference.

Suppose now that, in addition to the globes, there is second system of bodies maintaining fixed positions with respect to one another (for example, the fixed stars). If the two systems are in a state of relative rotation, one cannot gauge from just the relative rotation, which, if either, is at rest. However, from the tension in the cord connecting globes, one can establish whether the relative rotation is due entirely to the absolute rotation of the system of globes. Supposing so, the second system of bodies can then be exploited to provide an alternative technique for determining whether the globes revolve in a clockwise or counterclockwise direction—one simply consults the direction of rotation relative to the stationary system.

At this point Newton cuts off the Scholium, explaining that the whole point of having written the treatise to follow is to show how to infer the true motions from their causes, effects, and apparent differences, and conversely the causes and effects from either the true or the apparent motions.

6. Common Impediments to Understanding the Scholium

As remarked in Section 5.3 above, the purpose of the arguments from properties, causes, and effects has been widely misunderstood in both the historical and philosophical literature, and as a consequence, so too the relation of these to the example of the revolving globes in the final paragraph. Some diagnosis as to why may help those readers already steeped in tradition to overcome certain prejudices they bring to the Scholium and may also serve to further illuminate the framework in which Newton and his contemporaries struggle with the problem of motion.

(1) Newton's stated intention in the Scholium is to maintain that absolute space, time, and motion are genuinely distinct from their relative counterparts. For the case of space, this clearly amounts to arguing the existence of an entity distinct from body in which bodies are located—something denied by relationists. Similarly, for the case of time, this involves arguing the existence of an entity distinct from the succession of particular events in which the events are located—again, something denied by relationists. It may seem then as a matter of course that, for the case of motion, Newton should argue for existence of something denied by relationists, presumably, absolute motion.

(2) It would amount to a virtual petitio principii were Newton to rest a case for absolute motion on the existence of absolute space. Hence, one would expect him to appeal to various physical phenomena that might provide independent warrant. Now it is well known that Newton's laws satisfy the principle of Galilean relativity, according to which there can be no experimental test to determine whether a system is at rest or in a state of uniform rectilinear motion. However, Newton's laws do support a distinction between inertial and non-inertial motion in that they predict, in non-inertial frames, the appearance of so-called “fictitious forces,” for instance, centrifugal forces in rotating frames, resulting in a tendency for bodies to recede from the axis of rotation. Since this is exactly the effect involved in the rotating bucket experiment, it is tempting to interpret Newton as marshaling it as a case in which this phenomenon suggests independent warrant for the existence of absolute motion.

(3) Moreover, since the same effect is operative in the example of the revolving globes, it is hard to see why that example does not serve the very same purpose. In fact, in his famous critique of Newton in the Science of Mechanics , Ernst Mach, in quoting from the Principia , cut out all of the intervening text to make it appear as though the two are but variant examples in the development of a single argument.

(4) Finally, the choice of language in Motte's 1729 translation, which is the basis for the most widely available twentieth century English translation by Cajori, tends to reinforce the presumption that the arguments from properties, causes, and effects seek to identify phenomena that empirically distinguish absolute from (merely) apparent motion. In the Cajori version, the conclusions of the first three arguments, the arguments from the properties of motion and rest, read:

• … it follows that absolute rest cannot be determined from the position of bodies in our regions. [ Paragraph VIII ]
• …the true and absolute motion of a body cannot be determined by the translation of it from those which only seem to rest; [ Paragraph IX ]
• Wherefore, entire and absolute motions can be no otherwise determined than by immovable places; [ Paragraph X ]

Thus, it is tempting to assume that both the argument from causes and the argument from effects are likewise concerned to identify an empirical signature of absolute motion by which it can be distinguished from (merely) apparent motion. (Reading the arguments in this fashion, only the argument from effects, which deals with the centrifugal effects of circular motion, appears to help Newton's cause—a commonly registered complaint.)

It will be more illuminating to respond to these in reverse order.

(Ad 4) It is an artifact of Motte's translation that the Latin verb definiri (passive infinitive) is rendered occasionally as ‘be determined’ rather than as ‘be defined’. According to seventeenth-century English usage, either choice is acceptable. In appropriate contexts, the two function as synonyms, as in the Euclidean axiom, “Two points determine a line.” Motte's practice conforms with this. The conclusion of the argument from effects, ‘definiri’ is translated as ‘be defined’:

And therefore this endeavor does not depend upon any translation of the water in respect of the ambient bodies, nor can true circular motion be defined by such translation. [ Paragraph XII ]

If one now goes back and substitutes ‘be defined’ for ‘be determined’ into the conclusions from the arguments from properties quoted above, they take on, to the modern ear, a different meaning. They make claims as to what constitutes an adequate definition of the concepts of true, or absolute, motion and rest.

(Ad 3) We have already seen how paragraph XIII signals the conclusion, not just of the arguments from properties, causes, and effects, but the direct arguments for absolute time and absolute space as well, which, altogether, Newton takes establish the ontological distinction between the absolute and the relative quantities. That the next paragraph, in which the globes are introduced, concerns a different, epistemological issue would be apparent were it not for another artifact of the Motte translation, this time involving the Latin verb ‘distinguere’. Newton uses the word again and again, almost thematically, in characterizing and arguing for the ontological distinction between the absolute and the relative quantities; and Motte renders it in English as ‘to distinguish’. Unfortunately, the English verb appears in the Motte translation one more time at the start of the final paragraph:

It is indeed a matter of great difficulty to discover, and effectually to distinguish, the true motions of particular bodies from the apparent;

But in the Latin, the word ‘distinguere’ is nowhere to be found. Rather, the sentence reads:

Motus quidem veros corporum singulorum cognoscere, & ab apparentibus actu discriminare , difficillimum est;

Thus, to the Latin reader, it is clear that Newton is moving on to a different consideration.

(Ad 2) What has been said in connection with (4) suffices against the false expectations developed in (2). However, there may remain some sense that, even on a proper reading, Newton tried to bluff his way past the principle of Galilean relativity. Newton indeed acknowledges the principle, though not by name, in Corollary V to the laws of motion:

The motions of bodies in a given [relative] space are the same among themselves whether that space is at rest or moves uniformly in a straight line without uniform motion.

And there is no reason to think that he did not appreciate the limitation it poses for experimentally differentiating between absolute rest and uniform motion in a straight line. A particular instance of Corollary V is the solar system as a whole. Assuming the absence of external forces, it follows (from Corollary IV to the laws) that the center of gravity of the solar system is either at rest or moves uniformly in a straight line. But which? Because of Corollary V, when Newton wishes to attribute a definite state of motion to the center of mass of the solar system in Book III, he must introduce the hypothesis that “The center of the system of the world is at rest.” Should this not be some source of embarrassment?

Apparently not. Immediately following the hypothesis, he writes:

This is conceded by everyone, although some contend it is the earth, others the sun, that is at rest in the center. Let us see what follows from this.

According to Newton, the attribution of a state of absolute rest to one or the other of these bodies is universally taken for granted. What does confound all conventional wisdom in what follows is that neither the earth nor the sun is at rest, but rather the center of gravity of the solar system.

(Ad 1) Although arguing that absolute space and absolute time are distinct from any relative spaces and relative times involves, in each case, arguing for the existence of an additional entity, it does not follow that, in arguing that absolute motion is distinct from relative motion, Newton is obliged to argue yet another existence claim. Unfortunately, the term ‘absolute motion’ is prone to be read in two distinct ways. On one reading, it means, as a matter of stipulative definition, ‘change of absolute place’. In this sense of ‘absolute motion’, the existence of absolute motion (or more precisely, the possibility of the existence of absolute motion) follows immediately from the existence of absolute space and absolute time. As indicated before, nothing further needs to be said. On the other reading, ‘absolute motion’ is synonymous with ‘true motion’. And as we have just seen, Newton finds no reason to doubt that his audience does not grant that a body is either truly at rest or truly in motion. The venerable tradition that takes motion and rest to be contraries has yet to be questioned. So it is not incumbent on Newton make a case for the reality of absolute motion in the sense of true motion. What is incumbent is for him to argue that true motion just is change of absolute place. And that is the purpose of the arguments from properties, causes, and effects.

Newton's views on space, time, and motion dominated physics from the 17th Century until the advent of the theory of relativity in the 20th Century. Nonetheless, these views have been subjected to frequent criticism, beginning with contemporaries, such as Leibniz and Berkeley, and continuing on to the close of the 19th Century, most notably with Ernst Mach, whose writings influenced Einstein. In the early twentieth century, Newton tended to be cast as a metaphysical dogmatist by the early philosophical interpreters of relativity, in particular Hans Reichenbach. Unfortunately, that stigma has tended to linger.

More recent scholarship reveals a more sober picture of why Newton felt fully justified in positing absolute space, absolute time, and absolute motion. Moreover, the novel feature of special relativity, the rejection of absolute simultaneity—something that never occurred to any of Newton's earlier critics—necessitated only that absolute space and absolute time be replaced with an absolute space-time (Minkowski spacetime). And although Einstein's development of general relativity was in large part motivated by a desire to implement a general principle of relativity, to wit that all motion is relative motion, that it succeeds in doing so was questioned shortly after the theory was introduced. As for the question of the absoluteness of space-time in general relativity, it no longer has the character of something which acts without being acted upon, as Einstein himself pointed out. The space-time metric tensor not only encodes for spatiotemporal structure, but also represents the gravitational potentials, and thus gravitational energy. By Einstein's famous equation for the equivalence of energy and mass, it follows that the gravitational field possesses mass. Only, since gravitational energy can not be localized in terms of an energy density tensor, but is possessed by the field holistically, neither can this mass be localized. Thus, philosophical controversy as to whether space-time can exist without matter becomes tendentious according whether one counts the gravitation field as something material or not.

Thus, the question whether the revolution in our views about space and time in the last century vindicates Newton's critics as more philosophically astute becomes a misplaced one. The distinction between what counts as matter in contrast to empty space presupposed in the earlier debates has been eclipsed by possibilities undreamt of before the introduction of modern field theory and relativity. [ 1 ]

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• Nerlich, Graham, 2005, “Can Parts of Space Move? On Paragraph Six of Newton’s Scholium,” Erkenntnis , 62: 119–135.
• Palter, Robert, 1987, “Saving the Text: Documents, Readers, and the Ways of the World,” Studies in History and Philosophy of Science , 18: 385–439.
• Pemberton, Henry, 1728, A View of Sir Isaac Newton’s Philosophy , London: S. Palmer.
• Popper, K. R., 1953, “A Note on Berkeley as Precursor of Mach,” British Journal for the Philsophy of Science , 4: 26–36.
• Power, J. E., 1970, “Henry More and Isaac Newton on Absolute Space,” Journal of the History of Ideas , 31: 289–296.
• Ray, C., 1987, The Evolution of Relativity . Bristol: Adam Hilger, 3–12.
• Reichenbach, H., 1958, The Philosophy of Space and Time . New York: Dover Publications, 210–218.
• Shapin, S., 1981, “Of Gods and Kings: Natural Philosophy and Politics in the Leibniz-Clarke Disputes,” Isis , 72: 187–215.
• Sklar, L., 1974, Space, Time and Space-Time . Berkeley, CA: University of California Press, 161–193.
• Slowik, Ed, 2009, “Newton's Metaphysics of Space: A ` Tertium Quid ' betwixt Substantivalism and Relationism, or merely A `God of The (Rational Mechanical) Gaps'?” Perspectives on Science 17: 429–456.
• Stein, Howard, 1967, “Newtonian Space-Time,” in Robert Palter (ed.), The Annus Mirabilis of Sir Isaac Newton 1666-1966 . Cambridge, MA: MIT Press, 174–200.
• –––, 1977, “Some Philosophical Prehistory of General Relativity,” in Minnesota Studies in the Philosophy of Science , vol. VIII, J. Earman, C. Glymour, and J. Stachel (eds.), Minneapolis: University of Minnesota Press, 3–49.
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How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

• The Newton Project
• The Newton Project — Canada
• The Isaac Newton Institute for Mathematical Sciences
• Biographical Sketch of Newton (School of Mathematics and Statistics, University of St Andrews, Scotland)
• Fontenelle's Biographical Sketch of Newton (1728) (David R. Wilkins, Trinity College, Dublin)
• Papers of Isaac Newton (Cambridge University Library)
• Andrew Motte's 1729 translation of the Principia
• Voltaire on Descartes and Newton

Aristotle, Special Topics: natural philosophy | Clarke, Samuel | Descartes, René: life and works | Newton, Isaac | Newton, Isaac: Philosophiae Naturalis Principia Mathematica | Newton, Isaac: philosophy | space and time: absolute and relational space and motion, post-Newtonian theories | space and time: the hole argument

Acknowledgments

I'd like to thank John Norton for observations which led to many improvements.

Copyright © 2011 by Robert Rynasiewicz < ryno @ lorentz . phl . jhu . edu >

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Newton’s Cannonball

To learn about how Newton's cannonball experiment explains the circular orbit of the moon around the earth without it falling into the earth, read this article.

Issac Newton was on a quest to explain two aspects of the moon orbiting around the earth. Firstly, the moon should crash to the ground if all objects accelerate towards the earth’s centre. Secondly, what makes the moon move in circular orbits rather than a straight line even though, according to Galileo Galilei, objects tend to move in the same direction and speed until an external force acts upon them. 

Hence, to understand the orbital motion of objects, Newton proposed a thought experiment in 1968 called Newton’s cannonball experiment, which was mentioned in Principia Mathematica.

Newton’s cannonball

Newton’s cannonball experiment was based on a ‘thought experiment’ conceived to understand the orbital motion of objects. In the experiment, a sphere having a uniform density is used as a model of earth. A cannonball is imagined as being fired from a high mountain cannon. Each time, the muzzle velocity of the cannonball is increased till they orbit the earth. The trajectories of the cannonballs describe the orbital tunnels.

If the air resistance is negligible, Six outcomes depend on the cannonball’s velocity. They are:

The cannonball hits the ground

Imagine a cannonball is fired parallel to the surface of the earth from a cannon at a high mountain. It will cover some distance on the horizontal axis until it hits the ground. This is the displacement of the cannonball, which depends on the initial horizontal velocity with which the cannonball was fired and the time taken by the cannonball to hit the ground from the given height. 

The cannonball exhibits orbital motion

On increasing the muzzle velocity of the cannonball, at a certain initial horizontal velocity, the cannonball will not fall back on the ground. Still, it will enter the orbit to circle the earth parallel to its surface due to the earth’s gravitational pull.

The cannonball exhibits an initial elliptical path

On increasing the initial velocity of the cannonball, the length of its elliptical path increases such that the cannonball starts orbiting the earth. This makes the upper axis of the elliptical path coincide with the lower axis of the earth’s centre.

The cannonball exhibits a circular orbit

On further increasing the velocity of the cannonball, at a certain initial horizontal velocity, the upper and lower axis of the ellipse will coincide with the centre of the earth. Hence, the cannonball moving in an elliptical path will move in circular orbits. 

Newton’s cannonball formula determines the initial velocity required to make the cannonball enter a circular orbit, 

Vc is the initial velocity in ms-1 required by the cannonball to enter a circular orbit. 

g = 9.8 ms-2 is the acceleration due to gravity.

R = 6.371 x 106 m is the radius of the earth.

Newton’s cannonball works similar to the moon orbiting in a circular path around the earth. Due to inertia, an object continues to move in a constant direction and speed until it is accelerated. The gravitational pull of the earth provides acceleration in the case of the moon.

The cannonball exhibits an elliptical orbit

On further increasing the cannonball’s initial velocity, the ellipse’s upper axis approaches the centre of the earth while its lower axis moves further away. This results in the cannonball exhibiting an elliptical orbit.

The initial velocity for a cannonball to exhibit an elliptical path should be more than that for a circular path but less than the escape velocity of the earth.

√gR < Vc < √2gR

 Where gR < Vc means that the cannonball’s velocity is more than that required for a circular path.

 Vc < √2gR means that the cannonball’s velocity is less than the escape velocity of the earth.

The cannonball flies off into space

If the velocity of the cannonball exceeds the escape velocity of the earth, it flies off into space, which is expressed as, 

The cannonball is similar to the moon in Newton’s cannonball experiment, which explains the circular orbital motion of the moon around the earth, also influencing Newton’s universal law of gravitation. The rate of fall of the moon matches the curvature of the earth, making the moon orbit around the earth in a circular path, just like Newton’s cannonball does. The moon’s orbital motion results from its tangential velocity accelerated by the gravitational pull of the earth.

Frequently asked questions

Get answers to the most common queries related to the NEET UG Examination Preparation.

What was the basis of Newton's cannonball experiment?

What is newton's cannonball formula, what makes the moon orbit around the earth, when does a cannonball fly off into space.

Ans : Newton’s cannonball is a thought experiment that tends to explain the circular orbital motion of the moon around the earth, and it’s not crashing down to earth when it gets accelerated due to the earth’s gravitational force.

Ans : Newton’s cannonball formula determines the initial velocity required by an object to exhibit circular orbital motion around the earth. It is given by,

V c is the initial velocity in ms -1 required by the cannonball to enter a circular orbit. 

g = 9.8 ms -2 is the acceleration due to gravity.

R = 6.371 x 10 6 m is the radius of the earth.

Ans : The gravitational pull of the earth accelerates the moon. The rate of fall of the moon matches the curvature of the earth, making the moon orbit around the earth in a circular path, just like Newton’s cannonball does.

Ans : If the velocity of the cannonball exceeds the escape velocity of the earth, it flies off into space, which is expressed as, 

First detection of negative ions on the Moon

The first ESA instrument to land on the Moon has detected the presence of negative ions on the lunar surface produced through interactions with the solar wind.

The European team working with the Negative Ions at the Lunar Surface (NILS) instrument confirmed the success of this scientific mission that flew to the far side of the Moon aboard the Chang’e-6 spacecraft.  

The discovery of a new component of plasma at the surface of the Moon opens a new window for space physics and for human and robotic missions in an era of renewed lunar exploration.  

Mission of firsts

The first negative ion detector on the Moon operated intermittently to collect over three hours of data – three times more than what the science teams needed for mission success. This was the first time ESA has produced scientific data at the lunar surface. 

“This was ESA’s first activity on the surface of the Moon, a world-first scientifically, and a first lunar cooperation with China. We have collected an amount and quality of data far beyond our expectations,” says Neil Melville, ESA’s technical officer for the experiment built by the Swedish Institute of Space Physics (IRF). 

Negative ions – the missing piece

The solar wind is a constant flow of radiation and particles from the Sun. Earth’s magnetic field acts as a shield. In contrast, the Moon has no magnetic field and a very tenuous atmosphere, called the exosphere. When the solar wind hits the Moon, the surface reacts, kicking up secondary particles.  

These particles may be positively or negatively charged or have no charge at all. While the positively charged particles have been measured from orbit before, measuring negative particles was a challenge.  

Negative ions are short-lived and cannot make it to orbit. This is why the European scientists needed to operate their instrument close to the lunar surface – an unprecedented mission for a particle detector.  

“These observations on the Moon will help us better understand the surface environment and act as a pathfinder to explore negative ion populations in other airless bodies in the Solar System, from planets to asteroids and other moons,” explains Martin Wieser, NILS principal investigator at IRF.  

An ecstatic science team is already working on high-level research publications to share the findings. These measurements and the instrumentation used may have applications for further investigations of the lunar environment. 

Two days on the Moon for a European experiment

Chang’e-6 landed successfully in a huge crater of the far side of the Moon known as the South Pole-Aitken Basin on 1 June 2024 at 23:23 BST (2 June 00:23 CEST).  

The NILS team analysed the parameters of the landing position (coordinates 153.99°W, 41.64 ° S), attitude, angle of the Sun and temperatures and requested to activate the instrument about four hours after touchdown.  

NILS started to collect science data 280 minutes after landing. The first data collection period lasted for 23 minutes, until the instrument reverted to low voltage. A few more rounds of data collection followed between communications blackouts and reboots.  

“We were alternating between short bursts of full-power and long cooling-off periods because the instrument was heating up. The fact that it stayed within its thermal design limits and managed to recover under extremely hot conditions is a testament to the quality of the work done by the Swedish Institute of Space Physics,” says Neil.  

NILS was switched off at 15:20 BST/16:20 CEST on 3 June 2024. 

Tracking from Earth

European ground stations are providing support to the Chang’e-6 mission on its way to the Moon and back. Shortly after the launch from China on 3 May 2024, ESA’s Kourou station in French Guiana tracked the spacecraft for several hours to confirm its orbit.

Around 25 June, ESA will catch signals from the spacecraft as it returns to Earth loaded with lunar samples using the Maspalomas station, operated by the Instituto Nacional de Técnica Aerospacial (INTA) in Gran Canaria, Spain. 

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China's Chang'e 6 spacecraft finds long-sought particles on far side of the moon

The observations help astronomers better understand the chemical makeup of the moon's regolith.

A European experiment aboard China's Chang'e 6 mission has recorded previously undetected charged particles on the moon's surface, a catalog of which enables astronomers to better probe the chemical makeup of the moon's regolith.

These particles, which are essentially gases excited by sunlight, were detected at the landing spot of the Chang'e-6 spacecraft in the southern pocket of the Apollo crater, which lies within the South Pole-Aitken Basin on the moon's far side. The ion detector was the first European Space Agency instrument to land on the moon.

"This was ESA's first activity on the surface of the moon , a world-first scientifically, and a first lunar cooperation with China," Neil Melville, ESA's technical officer for the experiment, said in a statement . "We have collected an amount and quality of data far beyond our expectations."

 While Earth is protected from solar storms thanks to its magnetic field , which repels and traps charged particles from the sun, the moon lacks its own magnetic field. So, gases in its vanishingly thin atmosphere — helium, ammonia, methane and carbon dioxide, among a handful of others — are easily ionized by sunlight and "picked up" by flowing plasma. These charged particles ferry information about the chemical makeup of the moon's regolith, where the gases originate from through different processes rife on the surface, including impacts from small asteroids .

Related: Watch China's Chang'e 6 probe land on far side of the moon in dramatic video

In 2012, a NASA moon mission named ARTEMIS (short for Acceleration, Reconnection, Turbulence and Electrodynamics of the moon's Interaction with the sun and not to be confused with the agency's modern Artemis lunar program) observed pick up ions wafting up 12,400 miles (20,000 kilometers) above the lunar surface. All of them were positive ions, meaning they contained more protons than electrons . Negative ions are short-lived and don't float far from the surface, so they were never detected prior to the Chang'e-6 experiment, scientists say.

Scientists are yet to arrive at an estimate of how many negative ions float near the moon's surface, a number that would have implications for how the moon interacts with the sun , according to the Swedish Institute for Space Physics , which built the ion detector, named Negative Ions at the Lunar Surface (NILS).

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NILS started working close to five hours after the spacecraft landed on the moon on June 1. It worked intermittently during the two-day mission, powering through low voltages, communication blackouts and reboots, ESA said. The detector collected three hours of data in total — thrice the required amount for the experiment to be considered a success.

"We were alternating between short bursts of full-power and long cooling-off periods because the instrument was heating up," Melville said in the statement. "The fact that it stayed within its thermal design limits and managed to recover under extremely hot conditions is a testament to the quality of the work done by the Swedish Institute of Space Physics."

 —   Here's what China's 1st moon landing with astronauts might look like (video)

 —   China's next moon missions get the green light

 —   China makes Chang'e 5 moon samples open to international researchers

Beyond the NILS experiment, the Chang'e 6 mission drilled the moon's surface and scooped up about  2,000 grams of material. Scientists say these samples, which are the first-ever collected from the lunar far side, could offer fresh insights into the formation and evolution of the moon and the solar system .

Once sample acquisition was complete, the robotic lander placed a wooden model of China's five-star red flag on the surface before lifting off and rendezvousing with a waiting spacecraft in orbit. 

As of Wednesday (June 12), the samples continue to circle the moon in Chang'e 6's return module, waiting for the right time to kickstart its journey back to Earth. The return capsule is scheduled to arrive on June 25 at the Siziwang Banner in north China's Inner Mongolia Autonomous Region.

Join our Space Forums to keep talking space on the latest missions, night sky and more! And if you have a news tip, correction or comment, let us know at: [email protected].

Sharmila Kuthunur is a Seattle-based science journalist covering astronomy, astrophysics and space exploration. Follow her on X @skuthunur.

NASA moon orbiter spots Chinese lander on lunar far side (photo)

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Negative Ions at the Lunar Surface (NILS).

Nils or Niels, is a male name, a Nordic short form of the name Nikolaus which is of Greek origin. Nikolaus is formed from the words Nike 'victory' and laos 'people'. The oldest evidence in Sweden is from the year 1455.

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In new experiment, scientists record Earth’s radio waves from the moon

Touch down! A NOVA-C lander named Odysseus and built by the company Intuitive Machines lands on the surface of the moon. (Credit: Intuitive Machines)

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On Feb. 22, a lunar lander named Odysseus touched down near the moon’s South Pole and popped out four antennas to record radio waves around the surface—a moment CU Boulder astrophysicist Jack Burns hails as the “dawn of radio astronomy from the moon.”

It was a major achievement for the tenacious lander, which was built by the Houston-based company Intuitive Machines and had to overcome a series of technical difficulties to make it to the lunar surface. Burns is co-investigator on the radio experiment that flew aboard Odysseus called Radio wave Observations at the Lunar Surface of the photo Electron Sheath (ROLSES). 

He’ll give an update on the ROLSES data, and will share what’s in store for future radio astronomy from the moon, this week at the 244th Meeting of the American Astronomical Society in Madison, Wisconsin. A press conference will take place Monday, June 10 at 10:15 a.m. Central Time.

“It was heroic for Intuitive Machines to land under these conditions, and to deploy our antennas, take some data and get that data back to Earth,” said Burns, professor emeritus in the Department of Astrophysical and Planetary Sciences at CU Boulder.

Natchimuthuk Gopalswamy at NASA’s Goddard Space Flight Center in Greenbelt, Maryland, led the ROLSES experiment. The instrument, which included the antennas and a device called a radio spectrometer, was designed to record a wide range of radio emissions near the moon and deep in space.

In this selfie of Odysseus, one of the ROLSES antennas sticks out into space on the far left. (Credit: Intuitive Machines)

Despite the challenges of the mission, ROLSES managed to view Earth in a unique way.

“We viewed Earth as an exoplanet, or a planet orbiting another star,” Burns said. “That enables us to ask: What would our radio emissions from Earth look like if they came from an extraterrestrial civilization on a nearby exoplanet?” 

Earth selfie

Odysseus traveled to the moon as part of NASA’s Commercial Lunar Payload Services (CLPS) program, an ambitious effort to land spacecraft built by private companies on the lunar surface. It was the first such mission to achieve what NASA calls a “soft landing,” although it tipped onto its side in the process.

But it almost didn’t happen. Among other challenges, Odysseus wasn’t able to use its laser-guided navigation system to land on the moon’s craggy surface. Instead, operators at Intuitive Machines relied entirely on the lander’s optical camera system—an impressive feat of maneuvering. 

As Odysseus was traveling to the moon, one of the ROLSES antennas slightly overheated and popped out of its housing on the lander. (A selfie from the spacecraft shows the antenna sticking out in space). It turned out to be a stroke of good luck, Burns said. 

The team used the accident to look back at Earth and record radio waves emanating from the planet for nearly an hour-and-a-half. Human technologies, including cell phones and broadcast towers, churn out radio radiation on a near constant basis. Astronomer Carl Sagan spearheaded a similar experiment from NASA’s Galileo spacecraft in the 1990s, but the ROLSES data were more exhaustive. 

Burns noted that scientists may be able to look for similar fingerprints coming from planets far away from our own—a potential sign of intelligent life. 

He and his colleagues are just getting started. NASA has already greenlit a second ROLSES experiment, which will fly on another CLPS lander, likely in 2026.

The astrophysicist is also part of a third CLPS experiment, known as the Lunar Surface Electromagnetics Experiment-Night (LuSEE-Night), scheduled to arrive at the moon in 2026. The instrument will land on the far side of the moon, a quiet spot that human radio emissions can’t reach. From there, it will gaze at radio emissions coming not from Earth but from the earliest days of the universe before the first stars formed called the Dark Ages—shedding more light on how the cosmos evolved during this crucial junction its history.

“Because NASA is going to send two or three landers to the moon every year, we have a way to upgrade our instruments and learn from what goes wrong in a way we haven’t been able to do since the early days of the space program,” Burns said.

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