Radius of geostationary orbit

A geostationary orbit is a circular orbit located above the Earth’s equator (0° latitude), where an artificial satellite orbits the planet with an angular velocity equal to the angular speed of the Earth’s rotation around its axis.

Notation:

1. \(G\) (G) is gravitational_constant.

Links:

1. Wikipedia, possible formula derivable from here.

orbital_radius

radius of the satellite’s geostationary orbit.

Symbol:

r

Latex:

\(r\)

Dimension:

length

planet_mass

mass

Symbol:

m

Latex:

\(m\)

Dimension:

mass

satellite_angular_speed

angular_speed of the satellite’s rotation.

Symbol:

w

Latex:

\(\omega\)

Dimension:

angle/time

law

r = (G * m / w^2)^(1/3)

Latex:

\[r = \sqrt[3]{\frac{G m}{\omega^{2}}}\]