Kepler's First Steps Towards a Theory of Gravity

Reading the Introduction of Johannes Kepler's Astronomia Nova

In the history of science, Johannes Kepler is best known for the discovery of his three laws. The Wikipedia entry for Kepler's laws of planetary motion reads:

1. The orbit of a planet is an ellipse with the Sun at one of the two foci.

2. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.

3. The square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit.

Kepler first published the first two laws in the Astronomia Nova [New Astronomy¹] (1609) and the third law in the Harmonices Mundi [Harmony of the World] (1619).

The third law can be derived from Newton’s laws of motion and the universal law of gravitation, presented in 1687 in the Principia Mathematica. Because of this, it is easy to underevaluate Kepler’s rôle in the study of gravity. Consider, for example, the following NASA web page, entitled Orbits and Kepler's Laws, in which we can read:

Though Kepler hadn't known about gravitation when he came up with his three laws, they were instrumental in Isaac Newton deriving his theory of universal gravitation, which explains the unknown force behind Kepler's Third Law. [my emphasis]

But is it really true that Kepler did not know about gravitation? A quick read of the short Introduction to the Astronomia Nova is sufficient to understand that the above-mentioned web page is, in fact, incorrect.

In that Introduction, Kepler first criticizes the Aristotelian theory that a heavy body falls towards the center of the universe, which, according to that theory, happens to coincide with the center of the earth. Kepler insists that the fall of heavy objects cannot be towards a mathematical point, but, rather, towards a specific body.

A mathematical point, whether or not is is the center of the world, can neither effect the motion of heavy bodies nor act as a[n] object towards which they tend. Let the physicists prove that this force is in a point which neither is a body nor is grasped otherwise than through mere relation.

It is impossible that, in moving its body, the form of a stone see out a mathematical point (in this instance, the center of the world), without respect to the body in which this point is located. Let the physicists prove that natural things have a sympathy for that which is nothing. [pp.23-24]

Kepler then sets out some axioms for “a true theory of gravity”, which he calls a mutual attraction between kindred bodies:

The true theory of gravity rests upon the following axioms.

Every corporeal substance, to the extent that it is corporeal, has been so made as to be suited to rest in every place in which it is put by itself, outside the orb of power of a kindred body.

Gravity is a mutual corporeal disposition among kindred bodies to unite or join together; thus, the earth attracts a stone much more than the stone seeks the earth. (The magnetic faculty belongs to this order of things.)

Heavy bodies (most of all if we establish the earth in the center of the world) are not drawn towards the center of the world because it is the center of the world, but because it is the center of a kindred spherical body, namely the earth. Consequently, wherever the earth be established, or whithersoever it be carried by its animate faculty, heavy bodies are drawn to it. [p.24]

Kepler then states that were the earth not round, the attraction would be to some other part of the earth than its center:

If the earth were not round, heavy bodies would not everywhere be drawn in straight lines towards the middle point of the earth, but would be drawn towards different points from different sides. [p.25]

Furthermore, the attraction between two bodies is mutual, in the sense that with no outside influence, each would move towards the other, with the lighter body moving more than the heavier body.

If two stones were set near one another in some place in the world outside the sphere of influence of a third kindred body, these stones, like two magnetic bodies, would come together in an intermediate place, each approaching the other by an interval proportional to the bulk [moles] of the other.

If the moon and the earth were not each held back in its own circuit by an animate force or something else equally potent, the earth would ascend towards the moon by one fifty-fourth part of the interval, and the moon would descend towards the earth about fifty-three parts of the interval, and there they would be joined together; provided, that is, that the substance of each is of one and the same density. [p.25]

So, we can clearly see that Kepler definitely did make contributions to the theory of gravitation. If we consider the formula that we all learn in school, F = Gm₁m₂/r², where G is the universal gravitational constant, already Kepler had understood the importance of the masses m₁ and m₂ of the two bodies. This was, it should be remembered, in 1609, twenty-nine years before Galileo published Two New Sciences, in which the first elements of inertia are presented, and seventy-eight years before Newton published the first edition of the Principia Mathematica, in which the universal law of gravitation is presented.

Kepler then moves on to discuss the terrestrial tides, and how the motion of the moon attracting the water on earth, creates the tides. I discussed this topic in the post Sarpi and Galileo Were Wrong About the Tides.

For Kepler, the planets are not inertial bodies, and so means for making them move is necessary. He proposes that the spinning sun sends out something into space, and this something rotates as does the sun, and in so doing, carries along the planets.

Therefore, by induction extending to all the planets … it has been demonstrated that, since there are (of course) no solid orbs, as Brahe demonstrated from the paths of comets, the body of the sun is therefore the source of the power that drives all the planets around. Moreover, I have specified the manner [in which this occurs] as follows: that the sun, although it stays in one place, rotates as if on a lathe, and out of itself sends into the space of the world an immaterial species of its body, analogous to the immaterial species of its light. This species itself, as a consequence of the rotation of the solar body, also rotates like a very rapid whirlpool throughout the whole breadth of the world, and carries the bodies of the planets along with itself in a gyre, its grasp stronger or weaker according to the greater density or rarity it acquires through the law governing its diffusion. [p.34, my emphasis]

Kepler, as did most of the philosophers of his day, was looking for some explanation of the motion of the planets that did not involve action-at-a-distance. His gyre seems to be a precursor of Descartes’s vortices, Descartes having first written about these in Le Monde [The World] in 1630, some twenty years later. Newton, on the other hand, wrote down equations that imply action-at-a-distance, even if he himself was uneasy with the concept.

The topics raised in this post merit further discussion.

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1. Johannes Kepler. Astronomia Nova. New Revised Edition. Translated by William H. Donahue. Foreword by Owen Gingerich. Santa Fe, NM: Green Lion Press, 2015.