M 184186] Universal Gravitation 231 



185. One group of results of an entirely novel character 

 resulted from Newton's theory of gravitation. It became 

 for the first time possible to estimate the masses of some 

 of the celestial bodies, by comparing the attractions exerted 

 by them on other bodies with that exerted by the earth. 



The case of Jupiter may be given as an illustration. The 

 time of revolution of Jupiter's outermost satellite is known 

 to be about 16 days 16 hours, and its distance from 

 Jupiter was estimated by Newton (not very correctly) at 

 about four times the distance of the moon from the earttu 

 A calculation exactly like that of 172 or 173 shews that 

 the acceleration of the satellite due to Jupiter's attraction 

 is about ten times as great as the acceleration of the moon 

 towards the earth, and that therefore, the distance being 

 four times as great, Jupiter attracts a body with a force 

 10 x J. x 4 times as great as that with which the earth 

 attracts^ a body at the same distance ; consequently Jupiter's 

 mass is 160 times that of the earth. This process of 

 reasoning applies also to Saturn, and in a very similar way 

 a comparison of the motion of a planet, Venus for example, 

 round the sun with the motion of the moon round the 

 earth gives a relation between the masses of the sun and 

 earth. In this way Newton found the mass of the sun to 

 be 1067, 3021, and 169282 times greater than that of 

 Jupiter, Saturn, and the earth, respectively. The corre- 

 sponding figures now accepted are not far from 1047, 3530, 

 324439. The large error in the last number. is due to the 

 use of an erroneous value of the distance of the sun then 

 not at all accurately known upon which depend the other 

 distances in the solar system, except those connected with 

 the earth-moon system. As it was necessary for the em- 

 ployment of this method to be able to observe the motion 

 of some other body attracted by the planet in question, it 

 could not be applied to the other three planets (Mars, 

 Venus, and Mercury), of which no satellites were known. 



1 86. From the equality of action and reaction it follows 

 that, since the sun attracts the planets, they also attract the 

 sun, and the sun consequently is in motion, though owing 

 to the comparative smallness of the planets only to a very 

 small extent. It follows that Kepler's Third Law- is not 

 strictly accurate, deviations from it becoming sensible in 



