Editing General relativity (section)

=== Total force in general relativity ===
{{See also|Two-body problem in general relativity}}
In general relativity, the effective [[gravitational potential energy]] of an object of mass ''m'' revolving around a massive central body ''M'' is given by<ref>{{cite book |title=Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity|last=Weinberg, Steven|publisher=John Wiley|year=1972|isbn=978-0-471-92567-5}}</ref><ref>{{cite book |title=Relativity, Gravitation and Cosmology: a Basic Introduction|last=Cheng, Ta-Pei|publisher=Oxford and New York: Oxford University Press|year=2005|isbn=978-0-19-852957-6}}</ref>

:<math>U_f(r) =-\frac{GMm}{r}+\frac{L^{2}}{2mr^{2}}-\frac{GML^{2}}{mc^{2}r^{3}}</math>

A conservative total [[force]] can then be obtained as its [[Force#Potential_energy|negative gradient]]

:<math>F_f(r)=-\frac{GMm}{r^{2}}+\frac{L^{2}}{mr^{3}}-\frac{3GML^{2}}{mc^{2}r^{4}}</math>

where ''L'' is the [[angular momentum]]. The first term represents the [[Newton's law of universal gravitation|force of Newtonian gravity]], which is described by the inverse-square law. The second term represents the [[centrifugal force]] in the circular motion. The third term represents the relativistic effect.