LECTUKE XV. 



MOTION TN AN ORBIT OF ANY INCLINATION. 



LET us consider the change in the plane of the orbit produced in 

 an indefinitely small time dt by the action of a given disturbing force. 

 Let Z be the resolved part of the disturbing force at any time in a 

 direction perpendicular to the plane in which the body is moving at the 

 instant. Imagine the force Z to act by impulses at the small intervals of 

 time dt, then Zdt will be the indefinitely small velocity generated by the 

 force Z in the time dt, in the direction perpendicular to the plane of orbit 

 at the instant. 



Let FP be the radius vector and P the position of the body at the 

 instant. Also let PT represent the velocity at the instant in magnitude 



and direction ; then if Tt be taken perpendicular to the plane FPT and 

 equal to Zdt, the velocity and its direction after the impulse will be 

 represented by Pt, and the new plane of the orbit by FPt. Draw Tm 

 perpendicular to FP and join tm ; then tmT is the angle through which 

 the plane of the orbit has been turned about the radius vector FP in 

 the indefinitely short time dt. 



