Innermost stable circular orbit

The innermost stable circular orbit ( Innermost stable circular orbit , ISCO ) is the smallest circular orbit in which a test particle can turn around a massive body when considering a problem in the framework of the general theory of relativity . ^{[1] The} location of such an orbit and its radius ( $r_{isco}$ ${\ displaystyle r_ {isco}}$ ${\ displaystyle r_ {isco}}$ ) depend on the angular momentum (back) of the central object.

Content

Massive body

In the case of a non-rotating massive object, when the gravitational field can be expressed in the Schwarzschild metric , the orbit has a radius

r_{isco}={\frac {6\,GM}{c^{2}}}.

{\ displaystyle r_ {isco} = {\ frac {6 \, GM} {c ^ {2}}}.}

As the angular momentum of the central object increases, the radius $r_{isco}$ ${\ displaystyle r_ {isco}}$ decreases. Even for a non-rotating object, the radius of the orbit is only three Schwarzschild radii , therefore only black holes have an orbit of this type lying above the surface.

Photons

For a photon, the radius of the innermost circular orbit is ^[2]

r={\frac {3\,GM}{c^{2}}}.

{\ displaystyle r = {\ frac {3 \, GM} {c ^ {2}}}.}

Notes

↑ Misner, Thorne & Wheeler, 1973
Roll Carroll, Sean M. Lecture Notes on General Relativity: The Schwarzschild Solution and Black Holes (Neopr.) (December 1997). The appeal date is April 11, 2017.

Literature

Misner, Charles ; Thorne, Kip S. & Wheeler, John (1973), Gravitation , WH Freeman and Company, ISBN 0-7167-0344-0

[1] Misner, Thorne & Wheeler, 1973

[2] Roll Carroll, Sean M. Lecture Notes on General Relativity: The Schwarzschild Solution and Black Holes (Neopr.) (December 1997). The appeal date is April 11, 2017.