Dr. J. R. Mayer on Celestial Bynamics. 392 



. It follows from this formula that the smaller 2a (or the major 

 axis of the orbit of a planetary body) becomes, the less will be 

 its velocity when it reaches the sun. This velocity, like the 

 major axis, has a minimum ; for so long as the planet moves 

 outside the sun, its major axis cannot be shorter than the 

 diameter of the sun, or, taking the solar radius as a unit, the 

 quantity 2a can never be less than 2. The smallest velocity 

 with which we can imagine a cosmical body to arrive on the 

 surface of the sun is consequently 



s/h 



Gxy ^= 445,750, 



or a velocity of 60 geographical miles in one second. - . . 



For this smallest value the orbit of the asteroid is circular; 

 for a larger value it becomes elliptical, until finally, with increa- 

 sing excentricity, when the value of 2a approaches infinity, the 

 orbit becomes a parabola. In this last case the velocity is 



°*a/*F-°. 



or 85 geographical miles in one second. 



If the value of the major axis become negative, or the orbit 

 assume the form of a hyperbola, the velocity may increase with- 

 out end. But this could only happen when cosmical masses 

 enter the space of the solar system with a projected velocity, or 

 when masses, having missed the sun's surface, move into the 

 universe and never return ; hence a velocity greater than G can 

 only be regarded as a rare exception, audwe shall therefore only 

 consider velocities comprised within the limits of 60 and 80 

 miles*. 



The final velocity with which a weight moving in a straight 

 line towards the centre of the sun arrives at the solar surface is 

 expressed by the formula 



c=Gx s/W 1 - 



wherein c expresses the final velocity in metres, and h the original 

 distance from the centre of the sun in terms of solar radius. If 

 this formula be compared with the foregoing, it will be seen that 

 a mass which, after moving in central motion, arrives at the sun's 

 surface ha3 the same velocity as it would possess had it fallen per- 

 pendicularly into the sun from a distance f equal to the major 



* The relative velocity also with which an asteroid reaches the solar surface 

 depends in some degree on the velocity of the sun's rotation. This, how- 

 ever, as well as the rotatory effect of the asteroid, is without moment, and 

 may be neglected. 



f This distance is to be counted from the centre of the sun, 



2D2 



