Orbit phasing

In astrodynamics, orbit phasing is the adjustment of the time-position of spacecraft along its orbit, usually described as adjusting the orbiting spacecraft's true anomaly. Orbital phasing is primarily used in scenarios where a spacecraft in a given orbit must be moved to a different location within the same orbit. The change in position within the orbit is usually defined as the phase angle, ϕ,and is the change in true anomaly required between the spacecraft’s current position to the final position.

The phase angle can be converted in terms of time using Kepler’s Equation:

where

This time derived from the phase angle is the required time the spacecraft must gain or loss to be located at the final position within the orbit. To gain or loss this time, the spacecraft must be subjected to a simple two-impulse Hohmann transfer which takes the spacecraft away from, and then back to, its original orbit. The first impulse to change the spacecraft’s orbit is performed at a specific point in the original orbit (point of impulse, POI), usually performed in the original orbit’s periapsis or apoapsis. The impulse creates a new orbit called the “phasing orbit” and is larger or smaller than the original orbit resulting in a different period time than the original orbit. The difference in period time between the original and phasing orbits will be equal to the time converted from the phase angle. Once one period of the phasing orbit is complete, the spacecraft will return to the POI and the spacecraft will once again be subjected to a second impulse, equal and opposite to the first impulse, to return it to the original orbit. When complete, the spacecraft will be in the targeted final position within the original obit.