A spiral that gives the solution to the central orbit problem under a radial force law
(1)
|
where
is a positive constant. There are three solution regimes,
(2)
|
where
and
are constants,
(3)
| |||
(4)
|
and is the specific angular momentum (Whittaker
1944, p. 83). The case
gives an epispiral,
while
leads to a hyperbolic spiral.