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Consider the motion of an object in a general (attractive) central forcefield characterized by the potential energy per unit mass function . Since the forcefield
is central, it still remains true that

(299) 
is a constant of the motion. As is easily demonstrated, Equation (253)
generalizes to

(300) 
where .
Suppose, for instance, that we wish to find the potential which causes
an object to execute the spiral orbit

(301) 
Substitution of
into Equation (300) yields

(302) 
Integrating, we obtain

(303) 
or

(304) 
In other words, the spiral pattern (301) is obtained from a mixture
of an inversesquare and inversecube potential.
Next: Motion in a Nearly
Up: Planetary Motion
Previous: Kepler Problem
Richard Fitzpatrick
20110331