390 Dr. J. R. Mayer on Celestial Dynamics. 



must continually be arriving on the solar surface. The effect 

 produced by these masses evidently depends on their final velo- 

 city ; and, in order to determine the latter, we shall discuss some 

 of the elements of the theory of gravitation. 



The final velocity of a weight attracted by and moving towards 

 a celestial body will become greater as the height through which 

 the weight falls increases. This velocity, however, if it be only 

 produced by the fall, cannot exceed a certain magnitude ; it has 

 a maximum, the value of which depends on the volume and mass 

 of the attracting celestial body. 



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 falling on the 

 surface of this body ; then the greatest velocity which this weight 

 can obtain by its fall towards the celestial body, or the velo- 

 city 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= 4/(2 x9«8164x 6,369,800) = 11,183. 



The solar radius is ] 12*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 obtain in conse- 

 quence of the solar attraction, or 



G = • (SJfiKJg x 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 cen- 

 tral 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 



X \/ 



2a— h 



2axh 



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

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



r 2a-l 



V- 



G 



2a 



