Ismael Bullialdus: Finder but not keeper of the Inverse Square Law of Gravitation

Looking for the origin of the idea that the Sun’s gravity diminishes as distance increases, I found this on Wikipedia:

Ismaël Boulliau known as Bullialdus was a friend of Pierre Gassendi, Christiaan Huygens, Marin Mersenne, and Blaise Pascal, and an active supporter of Galileo Galilei and Nicolaus Copernicus. It is for his astronomical and mathematical works that he is best known. Chief among them is his Astronomia philolaica, (published 1645). In this work he strongly supported Kepler‘s hypothesis that the planets travel in elliptical orbits around the Sun, but argued against the physical theory the latter had proposed to explain them.^[1] In particular, he objected to Kepler’s proposal that the strength of the force exerted on the planets by the Sun decreases in inverse proportion to their distance from it. He argued that if such a force existed it would instead have to follow an inverse-square law:^[2]

As for the power by which the Sun seizes or holds the planets, and which, being corporeal, functions in the manner of hands, it is emitted in straight lines throughout the whole extent of the world, and like the species of the Sun, it turns with the body of the Sun; now, seeing that it is corporeal, it becomes weaker and attenuated at a greater distance or interval, and the ratio of its decrease in strength is the same as in the case of light, namely, the duplicate proportion, but inversely, of the distances that is, 1/d².^[3]

Brilliant deduction, but then he dropped the ball. Wiki continues:

However, Bullialdus did not believe that any such force did in fact exist.^[2] After writing the above-quoted passage, he then went on to write:

… I say that the Sun is moved by its own form around its axis, by which form it was ignited and made light, indeed I say that no kind of motion presses upon the remaining planets … indeed [I say] that the individual planets are driven round by individual forms with which they were provided …^[3]

In his Principia Mathematica of 1687, Isaac Newton acknowledged that Bullialdus’s determination of the sizes of the planets’ orbits ranked with Kepler’s as the most accurate then available.^[4]

This seems like a sop to soothe Newton’s own conscience (if he had one).

Bullialdus was one of the earliest members of the Royal Society, London, having been elected on April 4, 1667, seven years after its founding. The Moon‘s Bullialdus crater is named in his honor.

1645 for publication and 1667 for acceptance to the Royal Society are interesting dates in relation to others who claimed primacy for their conception of the Inverse Square Law. From Wikipedia again:

Robert Hooke and Giovanni Alfonso Borelli both expounded gravitation in 1666 as an attractive force^[1] (Hooke’s lecture “On gravity” at the Royal Society, London, on 21 March; Borelli’s “Theory of the Planets”, published later in 1666). Hooke’s 1670 Gresham lecture explained that gravitation applied to “all celestiall bodys” and added the principles that the gravitating power decreases with distance and that in the absence of any such power bodies move in straight lines. By 1679, Hooke thought gravitation had inverse square dependence and communicated this in a letter to Isaac Newton. Hooke remained bitter about Newton claiming the invention of this principle, even though Newton’s “Principia” (Published in 1687) acknowledged that Hooke, along with Wren and Halley, had separately appreciated the inverse square law in the solar system,^[2] as well as giving some credit to Bullialdus. From Kepler’s third law, which states that the period of a planet’s orbit is proportional to the cube of it’s semi-major axis, Newton derived his law of gravitation:

So where in his publications did Kepler allude to the inverse proportionality as Bullialdus attests?

William Gilbert, after experimenting with magnets decided that the center of the Earth was a huge magnet. His theory led Kepler to think that a magnetic force from the Sun drove planets in their own orbits. However, according to historian of science Alexander Koyre the traditional assumption of scholastic physics was that the power of gravitational attraction remained constant with distance whenever it applied between two bodies, and such was assumed by Kepler and also by Galileo in his mistaken universal law that gravitational fall is uniformly accelerated, and also by Galileo’s student Borrelli in his 1666 celestial mechanics.

But is Koyre correct? If Bullialdus objected to Kepler’s proposal that the strength of the force exerted on the planets by the Sun decreases in inverse proportion to their distance from it then it would appear not. And if Gilbert’s magnetism of the Earth led Kepler “to think that a magnetic force from the Sun drove planets in their own orbits”, then this is more evidence he understood the concept of a diminishing force. The dropoff of the field around a magnet is far more easily observed than the change in gravitational acceleration of a free falling body at different altitudes. But perhaps there’s something subtler going on here. Could it be that Kepler wasn’t thinking of a magnetic force of gravity (how would non-magnetic items such as sheep or apples be pulled to Earth?), but a magnetic force which “drove planets in their own orbits” not towards the Sun, but around it?

Answering that question will require some source material and research, which will have to wait for a day or two, but it’s worth considering that Newtons alternative – the ‘innate force’ wouldn’t have been appealing to an earlier natural philosopher surrounded by an ‘Aether’:  Too much drag, not enough momentum. Something would have to be ‘topping up’ the planets angular velocity.

The problem of Newton’s ‘innate force’ is still with us today. Orbital energy is lost to friction, tial heating etc. Why hasn’t the system slowed down more than it has, if the only thing keeping the planets going round avoiding a Sun-dive, is the momentum they acquired at the formation of the solar system 4.5 billion years ago? Is a continual transition to lower orbits maintaining their speed? Not that we’ve been able to measure.

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