273 



Let r be the radius of a spherical and solid celestial body, 

 and g the velocity at the end of the first second of a weight 

 falh'ng on the surface of this body ; then the greatest velocity 

 which this weight can obtain by its fall towards the celestial 

 body, or the velocity with which it will arrive at its surface 

 after a fall from an infinite height, is \/2gr in one second. 

 This number, wherein g and r are expressed in metres, we 

 shall call G. 



For our globe the value of g is 9*8164 . . and that of r 

 6,369,800 ; and consequently on our earth 



G = 47(2 x 9*8164X6,369,800) = 11,183. 



The solar radius is 112*05 times that of the earth, and the 

 velocity produced by gravity on the sun's surface is 28*36 

 times greater than the same velocity on the surface of our 

 globe ; the greatest velocity therefore which a body could ob- 

 tain in consequence of the solar attraction, or 



G= |/(28*36X 112*05) X 11,183 = 630,400; 

 that is, this maximum velocity is equal to 630,400 metres, or 

 85 geographical miles in one second. 



By the help of this constant number, which may be called 

 the characteristic of the solar system, the velocity of a body 

 in central motion may easily be determined at any point of its 

 orbit. Let a be the mean distance of the planetary body from 

 the centre of gravity of the sun, or the greater semidiameter 

 of its orbit (the radius of the sun being taken as unity) ; and 

 let h be the distance of the same body at any point of its orbit 

 from the centre of gravity of the sun ; then the velocity, 

 expressed in metres, of the planet at the distance h is 



'2o^A 

 GX 



At the moment the planet comes in contact with the solar sur- 

 face, h is equal to 1, and its velocity is therefore 



12* 



