Capture orbit

A capture orbit is the high-energy parabolic orbit that allows the capture other than crashing directly to the central body's surface (or atmospheric re-entry).

Capture orbit is identical to escape orbit – just the direction is reverse. Both are also known as "C3 = 0 orbit".

For capture velocities see the table in escape velocity.

Position as function of time

Finding the position as function of time corresponds to solving a differential equation. In the theoretical case of falling on a central body in a straight trajectory there is a rather simple expression for the solution:

<math>r=(4.5\mu t^2)^{1/3}\!\,<math>

where

• <math>\mu\!\,<math> is the standard gravitational parameter
• <math>t=0\!\,<math> corresponds to the extrapolated time of the fictitious arrival at the center of the central body; either t is negative, or t is the time until this arrival, counting down.

To count down to impact at the surface, apply a time shift; for the Earth (and any other spherically symmetric body with the same average density) as central body this time shift is 6 minutes and 20 seconds; seven of these periods earlier the height above the surface is three times the radius, etc.

See also

• Escape orbit