Planetary Orbits on the Theory of Relativity. 



513 



For purposes of calculation it is more convenient to 

 measure 6 from aphelion and use the second form given 



under (iii.)« 



Fur. 8. 



(vi.) h~h 3 , /3=0, a= — —1. The aphelion distance 



becomes infinite and we have the analogue o£ the ordinary 

 " parabolic orbit." It does not look like a parabola (fig. ( J a), 

 for the two halves of the curve cross each other. The 

 apsidal anole now becomes the angular range of the motion 

 from the apse to infinity. Its value is 2K/(1 — 2m) , with 

 & 2 = 2m/(l — 2m), and this exceeds it. The critical velocity 

 for escape to infinity is {2mfl{\—2inf instead of (2m) . 



(vii.) h>li z , /3<Q. The region of motion is now bounded 

 by tt = instead of b} r u = j3, and the orbits may be clashed 



