SECT. VIII. MASSES OF THE PLANETS. 55 



SECTION VIII. 



Masses of Planets that have no Satellites determined from their Perturba- 

 tions Masses of the others obtained from the Motions of their Satel- 

 lites Masses of the Sun, the Earth, of Jupiter and of the Jovial 

 System Mass of the Moon Real Diameters of Planets, how obtained 

 Size of Sun, Densities of the Heavenly Bodies Formation of Astro- 

 nomical Tables Requisite Data and Means of obtaining them. 



THE masses of such planets as have no satellites are known by 

 comparing the inequalities they produce in the motions of the 

 earth and of each other, determined theoretically, with the same 

 inequalities given by observation ; for the disturbing cause must 

 necessarily be proportional to the effect it produces. The masses 

 of the satellites themselves may also be compared with that of 

 the sun by their perturbations. Thus, it is found, from the 

 comparison of a vast number of observations with La Place's 

 theory of Jupiter's satellites, that the mass of the sun is no less 

 than 65,000,000 times greater than the least of these moons. 

 But, as the quantities of matter in any two primary planets are 

 directly as the cubes of the mean distances at which their satellites 

 revolve, and inversely as the squares of their periodic times 

 (N. 135), the mass of the sun and of any planets which have 

 satellites may be compared with the mass of the earth. In this 

 manner it is computed that the mass of the sun is 354,936 times 

 that of the earth ; whence the great perturbations of the moon, 

 and the rapid motion of the perigee and nodes of her orbit 

 (N. 136). Even Jupiter, the largest of the planets, has been 

 found by Professor Airy to be 1047*871 times less than the sun ; 

 and, indeed, the mass of the whole Jovial system is not more 

 than the 1054'4th part of that of the sun. So that the mass of 

 the satellites bears a very small proportion to that of their primary. 

 The mass of the moon is determined from several sources from 

 her action on the terrestrial equator, which occasions the nutation 

 in the axis of rotation ; from her horizontal parallax ; from an 

 inequality she produces in the sun's longitude; and from her 

 action on the tides. The three first quantities, computed from 



