TOPICS
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.
--Cotes' Spiral." §4.7 in Fundamentals
of Celestial Mechanics, 2nd ed., rev. ed. Richmond, VA: Willmann-Bell, pp. 69-71,
1988.Symon, K. R. Mechanics,
3rd ed. Reading, MA: Addison-Wesley, p. 154, 1971.Whittaker,
E. T. A
Treatise on the Analytical Dynamics of Particles and Rigid Bodies: With an Introduction
to the Problem of Three Bodies. New York: Dover, p. 83, 1944.Weisstein, Eric W. "Cotes' Spiral." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CotesSpiral.html
