At the dawn of the modern era, Galileo discovered and described how composite bodies fall through the air (or at least the discovery is usually attributed to him).

I'm interested in whether this had been discovered earlier and how, particularly since it seems to me that there are good grounds for this result to hold true purely on the basis of continuity and symmetry.

Imagine three balls of the same size and weight, and at equal distances from each other, dropped from a tower at the same time. By symmetry, all three must hit the ground at the same time.

Now repeat the experiment, but move the left-hand ball next to the middle one. This makes no difference to the result—the three balls still hit the ground at the same time.

Now repeat the experiment once more after slightly increasing the contact area of the two adjacent balls. Again, I would expect them to hit the ground at the same time. By repeating this, the left-hand and middle balls eventually merge into a single larger ball, which will fall at the same time as the right-hand one.

Did anyone make this argument in the pre-modern literature? I'd be interested to know whether any of the ancient atomists came up with similar arguments when they considered how atoms moved under gravity. It ought to have then been a simple step via the above argument to see that composite bodies fall at the same rate.

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    $\begingroup$ I think your invocation of "gravity" in the context of pre-Galilean literature is probably anachronistic. The idea of a unified force that can be called "gravity" seems to depend on already establishing something like a constant rate of fall for all objects. The Online Etymology Dictionary traces the scientific sense of "gravity" to the 17th century. $\endgroup$ – ig0774 May 9 '12 at 17:27
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    $\begingroup$ The notion of "gravity" dates back to Aristotle, he coined the term for the "force" (he means inclination) that leads objects with a lot of "Earth" and very little "fire", "air", or "quintessence" to seek to go to the center of the universe (the center of the Earth). The opposite was the "levity" of fire, which aggragates on the sun. The splitting thought experiment into parts is due to Galileo, and seems to have been missed in ancient times. They just didn't think of it. I don't know why this is surprising, they could have invented the phonograph too, but didn't. $\endgroup$ – Ron Maimon May 10 '12 at 6:18

The closest you will find to Galileo in ancient times is one of Aristotle's successors, named Strato of Lamsacus. The Wikipedia article on him explains that he discovered that falling bodies accelerate as they fall, and one of his most convincing arguments for this is because water in a column falling down as a stream breaks into droplets after a certain distance, and this is clearly due to the increasing speed making the column of water thinner and thinner in a regular way.

Since he doesn't seem to have investigated the law of acceleration in any quantitative mathematical way, it is difficult for him to notice a mathematical regularity, even one as obvious as all objects picking up speed at the same rate in time. Galileo probably noticed the universal acceleration empirically before coming up with the thought experiment you describe, which suggests that this universality is exact.

Just because an argument is obvious in hindsight doesn't mean that people think of it. There are countless simple things the ancients could have done, but didn't. For example, Copernicus made an argument that the stars must be very far away in Earth radii, because the time of star-set is exactly 12 hours after star-rise (this is not quite right because you need to correct for atmospheric refraction, but this is also an effect that could have been measured in ancient times, if they had a pendulum clock, something they also could have, but didn't, construct. They had the required differential gearing in Archimedes' day, see Antikythera mechanism, but forgot about it later).

The ancients could have measured the positions of the planets as accurately as Brahe, but didn't. Other things that the ancients missed:

  • No slip boundary conditions for fluids are required by continuum dynamics, and are violated when you have a contact line between three bulk materials, like when a drop sticks to metal in air. The air is completely displaced where the drop hits, and this is evidence for atomism.
  • There is an upper limit to the degree to which oil spreads on water (Benjamin Franklin's early estimate of Avogadro's number). This is a convincing demonstration of atomism.
  • Parabolic mirror telescopes (discovered by Newton, available to Archimedes, since he knew the focusing properties of parabolic mirrors) One can make a perfect parabolic reflector by spinning molten metal as it cools.

It is not easy to say why people miss things. The atrocious politics of the ancient world, which put people in hereditary heirarchies of power and made slaves of the majority, might be the reason scientific discourse died, because nobilities tend to make a nobility discourse and a nobility philosophy to justify their status, and science can only proceed with slave language and common-sense slave arguments.


Aristotle dominated the physics pre Galileo and he had not sussed out gravity.

In this link is a precis of what pre-aristotelian philosophers were occupied with and there is no connection with gravity.

They did discuss and worry about the vacuum. Without a good vacuum one cannot distinguish between the fall of a feather and the fall of an iron nail experimentally.

Aristarchus did develop a heliocentric theory but did not go so far as to have a gravitational explanation.

So the answer is that at least in the western tradition everything started with the Renaissance.

  • $\begingroup$ It is not clear that Appolonius did not complete Aristarchus's theory to a full Keplerian theory of planets orbiting on conic sections with the sun at the focus. The only surviving Appolonius is a treatise on conic sections, and it is clear from Ptolmey that Appolonius developed the equant as an approximation to (at least) an off-center circle orbit in the heliocentric model. I suspect that Appolonius knew elliptical orbits, but the destruction of the books makes it impossible to be certain. What other justification is there for an astronomer to make such a detailed study of conics? $\endgroup$ – Ron Maimon May 10 '12 at 7:25
  • $\begingroup$ @RonMaimon you mean other justification than a central force? In any case the church adopted Aristotle and the geocentric and all the rest has been lost. $\endgroup$ – anna v May 10 '12 at 9:28
  • $\begingroup$ continued en.wikipedia.org/wiki/Apollonius_of_Perga .he did not seem to have a central force in mind. Just descriptive geometry from the list of all his works, no? $\endgroup$ – anna v May 10 '12 at 9:31
  • $\begingroup$ @maimon: There is an aesthetic reason for preferring the circle over the ellipse - its the simpler shape. But it doesn't take a genius to argue that an ellipse can approximate a circle very closely. I can imagine that this debate took place - but what evidence would have persuaded them that an ellipse is better? $\endgroup$ – Mozibur Ullah May 10 '12 at 9:39
  • $\begingroup$ @MoziburUllah if you read the Apolonius link I gave in my previous comment you will see that he reconciled the epicycle geometry with the heliocentric one. Certainly ellipses would come out of such a fit. $\endgroup$ – anna v May 10 '12 at 10:41

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