A central orbit is an orbit in which the attractive force between a central mass and test mass is a central force, i.e., is directed towards the central mass. A general central force law is therefore given by
for any function f(r), where
is the force per unit mass and
Central Force, Cotes' Spiral Orbit, Two-Body Problem
References
Danby, J. M. "Central Orbits." Ch. 4 in Fundamentals of Celestial Mechanics, 2nd ed., rev. ed. Richmond, VA: Willmann-Bell, pp. 57-87, 1988.
Goldstein, H. "The Two-Body Central Force Problem." Ch. 3 in Classical Mechanics, 2nd ed. Reading, MA: Addison-Wesley, pp. 70-127 and 580, 1980.
Legendre, A.-M. Théorie des Fonctions Elliptiques. 1895.
Nobile. Giornaile di Mat. 46, 313, 1908.
Stader, J. F. J. reine angew. Math. 46, 262, 1853.
Whittaker, E. T. "The Integrable Cases of Central Forces; Problems Soluble in Terms of Circular and Elliptic Functions." §48 in A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: With an Introduction to the Problem of Three Bodies. New York: Dover, pp. 80-86, 1944.
