Editing Synchronous orbit (section)

== Formula ==

For a stationary synchronous orbit:

: <math>R_{syn} = \sqrt[3]{{G(m_2)T^2\over 4 \pi^2}}</math><ref>{{Cite news|url=https://www.askwillonline.com/2012/12/calculating-radius-of-geostationary.html|title=Calculating the Radius of a Geostationary Orbit - Ask Will Online|date=2012-12-27|work=Ask Will Online|access-date=2017-11-21|language=en-GB}}</ref>
: G = [[Gravitational constant]]
: m<sub>2</sub> = Mass of the celestial body
: T = [[Sidereal time|Sidereal]] rotational period of the body
:<math>R_{syn}</math> = Radius of orbit

By this formula, one can find the synchronous orbital radius of a body, given its mass and sidereal rotational period. 

Orbital speed (how fast a satellite is moving through space) is calculated by multiplying the angular speed of the satellite by the orbital radius.<ref>see [[Circular motion#Formulas]]</ref>

Due to obscure quirks of [[orbital mechanics]], no [[Tidal locking|tidally locked]] body in a 1:1 spin-orbit resonance (i.e. a moon locked to a planet or a planet locked to a star) can have a stable satellite in a synchronous orbit, as the synchronous orbital radius lies outside the body's [[Hill sphere]].<ref>{{Cite web |title=Is it possible to achieve a stable "selenostationary" orbit around the Moon? |url=https://astronomy.stackexchange.com/questions/20499/is-it-possible-to-achieve-a-stable-selenostationary-orbit-around-the-moon/55436#55436 |access-date=2025-05-29 |website=Astronomy Stack Exchange |language=en}}</ref> This is universal and irrespective of the masses and distances involved.