PLANETS. 



ied by the cube of the 



' 



J.U 



"19614648 



tangent of the solar parallax 



Hence the masses of the Sun and Earth 

 are to each other as the numbers 

 1479560.5 and 4.436113; therefore the 



mass of the Earth is -. 0{ .. that of the 

 329809 



Sun being unity. M. de la Place calcu- 

 lated the masses of Mars and Venus from 

 the secular diminution of the obliquity of 

 the ecliptic, and from the mean accelera- 

 tion of the Moon's motion. The mass of 

 Mercury he obtained from its volume, 

 supposing the densities of that planet 

 and of the Earth reciprocally as their 

 mean distance from the Sun, a rule which 

 holds with respect to the Earth, Jupiter, 

 and Saturn. The following table exhibits 

 the masses of the different planets, that 

 of the Sun being unity : 



Mercury 



Venus 



Earth 



Mars 



Jupiter 



Saturn 



Herschel 



2025810 



1 

 383137 



1 

 329809 



1 



1846082 



1 

 1067.09 



1 

 3359.40 



1 

 19304 



The densities of bodies are proportion- 

 al to their masses divided by their bulks ; 

 and when -bodies are nearly spherical, 

 their bulks are as the cubes of their semi- 

 diameters, of course the densities in that 

 case are as the masses divided by the 

 cubes of the semi-diameters. 



PLANETS, motion of the. Each of the 

 primary planets bend their course about 

 the centre of the Sun, and are accelerat- 

 ed in their motions as they approach to 

 him, and retarded as they recede from 

 him ; so that a ray, drawn from any one 

 of them to the Sun, always describes 

 equal spaces, or areas, in equal times : 

 whence it follows that the power which 

 bends their way into a curve line, must 

 be directed to the Sun. This power is 

 no other than that of gravitation, which 

 \ve have already proved to increase, as 

 the square of the planet's distance from 

 the Sun decreases. See 



&.c. But the universality of this law still 

 further appears, by comparing the mo- 

 tions of the different planets : for the 

 power which acts on a planet near the 

 Sun is manifestly greater than that 

 which acts on a planet more remote ; 

 both because it moves with greater velo- 

 city, and because it moves in a lesser or- 

 bit, which has more curvature, and sepa- 

 rates further from its tangent, in arcs of 

 the same length, than in a greater orbit, 

 By comparing the motion of the planets, 

 the velocity of a nearer planet is found to 

 be greater than that of one more remote, 

 in the proportion of the square ro(Jt 

 of the number which expresses the great- 

 er distance, to the square root of that 

 which expresses the lesser distance ; so 

 that if one plaivet was four times further 

 from the Sun than another, the velocity 

 of the first would be half the velocity of 

 the latter ; and the nearer planet would 

 describe an arc in one minute, equal to 

 the arc described by the other planet in 

 two minutes ; and though the curvature 

 of the orbits were the same, the nearer 

 planet would describe, by its gravity, 

 four times as much space as the other 

 would describe in the same time ; so that 

 the gravity of the nearer planet would ap- 

 pear to b quadruple, from the consider- 

 ation of its greater velocity only. But be- 

 sides this, as the radius of the lesser orbit 

 is supposed to be four times less than 

 the radius of the other, the lesser orbit 

 must be four times more curved ; and the 

 extremity of a small arc of the same 

 length, will be four times further below 

 the tangent, drawn at the other extremi- 

 ty, in the lesser orbit than in the greater; 

 so that, though the velocities were equal, 

 the gravity of the nearer planet would, 

 on this account only, be found to be qua- 

 druple. Hence, on both these accounts 

 together, the greater velocity of the near- 

 er planet, and the greater curvature of 

 its orbit, its gravity towards the Sun 

 must be supposed sixteen times greater, 

 though its distance from the Sun is only 

 four times less than that of the other ; 

 that is, when the distances are as 1 to 4, 

 the gravities are reciprocally as the 

 squares of these numbers, or as 16 to 1. 

 And in the same manner as this principle 

 governs the motions of the primary plan- 

 ets of the great solar system, acts at their 

 surfaces, and keeps their parts together; 

 so it governs also the motions of the sa- 

 tellites, or secondary planets, in the les- 

 ser systems of which the greater is com- 

 posed, and is extended around them, de- 

 creasing hi the same manner as the 



