522 Forms of Planetary Orbits on Theory of Relativity. 



character of the orbit being set against the corresponding 

 value or interval of the parameter // : — 



m <1 



\<m<\. 



h. 











Captured. 



1 



Ji L Asymptotic circular. 



y Captured. 



Elliptic from aphelion. 



1 



h.-, Circular. 



Circular. 



Elliptic from perihelion. 



Elliptic from perihelion 



\ Parabolic. 



Parabolic. 



Hyperbolic. 



GO 



Hyperbolic. 



i<m<f 



m>±. 









j l I Captured. 



All captured. 



h 2 Circular. 





Hyperbolic. 





CO 





It appears that the circular form may be called stable only 

 for wi<-J. For§-<m<Jr it is stable only on the side of 

 increased velocity, and beyond these limits it is unstable on 

 both sides. 



Description of Diagrams. 

 The following table gives details about the curves, plotted 

 for m — \. The first and second columns give Ijli 2 and h. 

 The third,- headed " ratio," gives the ratio of the other 

 extreme distance to the initial distance, which has been 

 tahen as the unit in the above work. The a angle " column 

 gives the angular range from the initial line to capture, to 

 the other apse, or to infinity, as the case may be : — 



Fig. 



1/V. 



h. 



Ratio. 



Angle 

 (degrees). 



Orbit. 



1 



210-3 



•069 







113-1 



"I 



2 



13-29 



•271 







261-4 



I Captured. 



a 



6 



•408 







360 + 134-2 



4 



5-2503 



•43642 







4x3604-321 



J 



5 



5* 



•43644 



2 



CO 



Asymptotic circular. 



6 



51 



•438 



* 



360+1604 



Elliptic from aphelion. 



7 



5 



•447 



1 



360 



Circular. 



8 



4K 



•462 



4 

 3" 



307-5 



Elliptic from perihelion. 



9a ... 



3 



•577 



CO 



229-4 



Parabolic. 



9 6 ... 



2-64 



•616 



CO 



180 



] 



9c ... 



1 



1 



CO 



1245 



^Hyperbolic. 



9d ... 



o 



CO 



CO 



109-2 



J 



