Optimal Utility of Satellite Constellation Separation with Differential Drag

As small satellite constellations become more frequent, questions as to their deployment and orbit maintenance becomes more critical. Nanosatellites are often deployed together, do not have the luxury of on-board propulsion, and hence must reach their desired orbits by other ‘passive’ means, such as differential drag. The problem is compounded by other factors, such as ground station availability and access, as well as changing atmospheric densities. We present here the optimal control problem solved (with constant atmospheric densities) for varying utility functions such that satellites utilizing differential drag are phased at equal angular distances. During actual operations, a simplified scheme might be preferred. As such, a Taylor series approximation method to analyze a bang-bang control scheme is formulated and compared with the optimal solution. The final solution is not drastically affected by modest varying factors in drag and drag area, but is significantly affected by starting altitude as expected. The solution can be extended to any number of satellites, although the solution does suffer from numerical degradation the longer it takes the constellation to achieve its final configuration.