General Coplanar Transfer between Circular Orbits

Transfer between circular coplanar orbits only requires that the transfer orbit intersect or at least be tangent to both of the circular orbits. It is obvious that the periapsis radius of the transfer orbit must be equal to or less than the radius of the inner orbit and the apoapsis radius must be equal to or exceed the radius of the outer orbit if the transfer orbit is to touch both circular orbits. This condition can be expressed mathematically in Figure 9-10.

Figure 9-10.General coplanar transfer between circular orbits.

Phasing Maneuver

Most coplanar maneuver involves change of orbit size and shape. However, in some situation, the spacecraft required to change its position at a given time. Especially for the spacecraft rendezous case where the interceptor spacecraft required to intercept (or meet) the target spacecraft when it is behind or ahead of the target spacecraft in the orbit.

Figure 9-11. Phasing Maneuver.

Figure 9-11 shows an illustration of phasing maneuver. If the interceptor is behind the target spacecraft, then the phasing orbit required to be smaller than the original orbit, and vice versa.

Given that the phase angle (or difference of two true anomaly) between two spacecraft is ∆θ. Then, the one orbit period required by the phasing orbit is:

(9-11)

where n_tgt is the mean motion of target spacecraft (or the original orbit). Then, we can determine the semimajor axis for the phasing orbit, that is,

	(9‑12)
Example 9-7
Determine the semimajor axis of the phasing orbit, given that the position of target and interceptor spacecraft are:
Solution
First, the phase angle between spacecraft is, The mean motion of the original orbit is, Then, the one orbit period required for the phasing orbit is, The semimajor axis for the phasing orbit is,

Date: 2016-04-22; view: 901