An escape orbit (also known as C3 = 0 orbit) is a high-energy parabolic orbit around the central body. A body in this orbit has at each position the escape velocity with respect to this central body, for this position. If this energy were further increased the orbit would turn to a hyperbolic trajectory.
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:
, is the standard gravitational parameter
corresponds to the extrapolated time of the fictitious starting at the center of the central body.
At any time the average speed from , is 1.5 times the current speed, i.e. 1.5 times the local escape velocity.
To have 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 later the height above the surface is three times the radius, etc.
* List of orbits
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