Surface Orbit

A surface orbit around a spherical object is the circular orbit with its radius exactly equal to the radius of the central object. Conceptually, this can be thought of as an orbit which skims just barely above the surface.

Its properties can be calculated as follows:

• Period $T=2\pi {\sqrt {\frac {r^{3}}{GM}}}$ (s)
• Speed $v={\sqrt {\frac {GM}{r}}}$ (m/s)

where

• $G$ is Newton's universal gravitational constant, $6.67259\times 10^{-11}{\frac {{\mbox{m}}^{3}}{{\mbox{kg}}\cdot {\mbox{s}}^{2}}}$ in Orbiter (OrbiterAPI.h, line 39)
• $M$ is the mass of the central object in kg (obtainable from the object's config file Mass= parameter)
• $r$ is the radius of the central object in m (obtainable from the object's config file Size= parameter)

In real life, a surface orbit cannot truly be achieved, due to the central body's atmosphere (since Mach 25+sea level=melted vessel, and the drag will slow down the molten fragments of your ship so they crash), terrain (who put that mountain in the way?), and perturbations from other gravity sources. In Orbiter, a surface orbit can be maintained for a long time about a small airless body far from any other objects (like Pluto without a moon), since all objects in Orbiter are perfectly smooth and spherical.

Example: Take a DeltaGlider parked at Brighton Beach on the Moon, and rev up the main engines and start tearing across the surface. For the moon, the surface orbit speed is 1679.556m/s, so when you have an orbital speed (not ground speed) of this much, you will be in orbit, even though you are on the surface. You will be weightless. If you go up even a couple of milimeters, you can raise the landing gear. Unfortunately, due to the gravity of the Earth and Sun, it is unlikely that you will be able to even complete one orbit before skidding back onto the surface at 1680m/s.

The surface orbit is useful because it is a boundary case. All other circular orbits will have longer periods and lower speeds.