the case of the large planets Jupiter and Saturn (cf. chapter vii., § 144). It was, however, proved by Newton that in any system of bodies, such as the solar system, moving about in any way under the influence of their mutual attractions, there is a particular point, called the centre of gravity, which can always be treated as at rest; the sun moves relatively to this point, but so little that the distance between the centre of the sun and the centre of gravity can never be much more than the diameter of the sun.
It is perhaps rather curious that this result was not seized upon by some of the supporters of the Church in the condemnation of Galilei, now rather more than half a century old; for if it was far from supporting the view that the earth is at the centre of the world, it at any rate negatived that part of the doctrine of Coppernicus and Galilei which asserted the sun to be at rest in the centre of the world. Probably no one who was capable of understanding Newton's book was a serious supporter of any anti-Coppernican system, though some still professed themselves obedient to the papal decrees on the subject.
- Throughout the Coppernican controversy up to Newton's time it had been generally assumed, both by Coppernicans and by their opponents, that there was some meaning in speaking of a body simply as being "at rest" or "in motion," without any reference to any other body. But all that we can really observe is the motion of one body relative to one or more others. Astronomical observation tells us, for example, of a certain motion relative to one another of the earth and sun; and this motion was expressed in two quite different ways by Ptolemy and by Coppernicus. From a modern standpoint the question ultimately involved was whether the motions of the various bodies of the solar system relatively to the earth or relatively to the sun were the simpler to express. If it is found convenient to express them—as Coppernicus and Galilei did—in relation to the sun, some simplicity of statement is gained by speaking of the sun as "fixed" and omitting the qualification "relative to the sun" in speaking of any other body. The same motions might have been expressed relatively to any other body chosen at will: e.g. to one of the hands of a watch carried by a man walking up and down on the deck of a ship on a rough sea; in this case it is clear that the motions of the other bodies of the solar system relative to this body would be excessively complicated; and it would therefore be highly inconvenient though still possible to treat this particular body as "fixed."
A new aspect of the problem presents itself, however, when an attempt—like Newton's—is made to explain the motions of bodies of the solar system as the result of forces exerted on one another by