Techniques for deploying elliptically orbiting constellations in along-track formation

Abstract

Two techniques to deploy four spacecraft in an along-track formation with 500 km separation distance in an elliptical orbit are developed and evaluated: (1) The deployment from the original (parking) circular orbit into the final elliptical orbit is based on the solution of the associated non-linear two-point boundary value problem (TPBVP) following Pontryagin's principle for each spacecraft in the constellation. The control energy is minimized subject to a terminal time which is sequentially shortened until at least one component of the control thrust vector exhibits bang-bang characteristics. (2) Deployment is also based on the sequential deployment of all the spacecraft from the original circular orbit to the final elliptical orbit based on the concept of the Hohmann transfer and incorporating the logic for two impulsive line of apsides shifting maneuvers. The mother satellite would be placed into a regular Hohmann transfer orbit, while the remaining (three) daughter satellites would be placed into modified Hohmann transfer orbits to account for the desired final spacing and small differences in transient orbital periods. The TPBVP approach can result in much shorter total deployment times, but at a greater propulsive cost than for the Hohmann transfer approach.