Editing Orbital mechanics (section)

===Circular orbits===
{{Main|Circular orbit}}
All bounded orbits where the gravity of a central body dominates are elliptical in nature. A special case of this is the circular orbit, which is an ellipse of zero eccentricity. The formula for the velocity of a body in a circular orbit at distance ''r'' from the center of gravity of mass ''M'' can be derived as follows:

Centrifugal acceleration matches the acceleration due to gravity.

So, <math display="block">\frac{v^2}{r} = \frac{GM}{r^2}</math>

Therefore,
:<math>\ v = \sqrt{\frac{GM} {r}\ }</math>

where <math>G</math> is the [[gravitational constant]], equal to
:6.6743 &times; 10<sup>&minus;11</sup> m<sup>3</sup>/(kg·s<sup>2</sup>)

To properly use this formula, the units must be consistent; for example, <math>M</math> must be in kilograms, and <math>r</math> must be in meters. The answer will be in meters per second.

The quantity <math>GM</math> is often termed the [[standard gravitational parameter]], which has a different value for every planet or moon in the [[Solar System]].

Once the circular orbital velocity is known, the [[escape velocity]] is easily found by multiplying by <math>\sqrt{2}</math>:
:<math>\ v = \sqrt 2\sqrt{\frac {GM} {r}\ } = \sqrt{\frac {2GM} {r}\ }.</math>

To escape from gravity, the kinetic energy must at least match the negative potential energy. Therefore, <math display="block">\frac{1}{2}mv^2 = \frac{GMm}{r}</math>
:<math>v = \sqrt{\frac {2GM} {r}\ }.</math>