# Synchronous Orbit

A satellite in a synchronous orbit has an orbital period equal to the rotational period of the object it is orbiting. If the orbit has zero eccentricity and inclination, the satellite will remain stationary over a point on the object's equator at all times.

The semi-major axis of a synchronous orbit around a primary object is:
$r_s \ = \ (G m_p (\frac{\tau}{2\pi})^2)^{1/3}$
where G is the gravitational constant, mp is the primary's mass, and τ is the rotational period of the primary. The semi-major axes of synchronous orbits around several Solar System bodies are given in the table below.

Planetary
Object
Mass
Rotational
Period
Planetary
Synchronous
Synchronous
Orbit Altitude

[kg]
[hours]
[km]
[km]
[km]
Earth
5.974×1024
23.94
6,378
42,170
35,790
Mars
6.419×1023
24.62
3,396
20,430
17,030
Ceres
9.43×1020
9.074
487*
1,190
700
Vesta
2.67×1020
5.342
258†
551
293
* Equatorial
† Average