Parabolic Trajectory - Radial Parabolic Trajectory

Radial Parabolic Trajectory

A radial parabolic trajectory is a non-periodic trajectory on a straight line where the relative velocity of the two objects is always the escape velocity. There are two cases: the bodies move away from each other or towards each other.

There is a rather simple expression for the position as function of time:

where

• μ is the standard gravitational parameter
• corresponds to the extrapolated time of the fictitious starting or ending 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.