High Precision Relative Motion Modelling.

There is an increasing interest in missions employing groups of satellites flying in formations and constellations. Such missions require highly autonomous and accurate orbit determination and control systems. The Disaster Monitoring Constellation (DMC) is an international consortium, consisting currently of four remote-sensing satellites equally spaced around a sun-synchronous circular low Earth orbit. We have developed a simple yet flexible and accurate control algorithm for the 3D orbit acquisition of the constellation, inserting the satellite in their designed orbits with respect to each other. While we did not carry out an optimisation in the strictest sense, real world limitations and concerns override the need for a such a scheme. We report our experience in detail, demonstrating the successful in-orbit results of the orbit acquisition, where the flexibility of the algorithm proved invaluable to deal with unforeseen operational issues. Another important aspect of relative dynamics is the relative orbit propagation. Relative navigation systems require high precision relative dynamics models to alleviate the need for relying on highly accurate relative navigation sensors. The existing literature relies on analytic relative orbit propagation schemes that become extremely complicated even for a simple geopotential model employing Earth oblateness effects, not least because of the choice of rotating local coordinate frame they work in. We first present novel and simple analytic solutions which conserve relevant quantities related to the Keplerian motions, and we discuss in detail the choice of initial conditions to improve the order of the approximations involved. Comparing to exact Keplerian models, our results show accuracies much greater than anticipated. Unlike previous work in this area, we describe the relative motion in an inertial frame, enabling the effects of perturbations on the relative motion to be incorporated in a straight-forward manner. Finally we extended this methodology to set up a symplectic relative orbit propagator which can handle an arbitrary number of zonal and tesseral geopotential terms and can be extended to accommodate the effects of atmospheric drag. We exploited the separability of the solution, for much higher computational efficiency. The method is designed to conserve the constants of the motion, resulting in better long term accuracy. The results show that sub-metre accuracy is possible over five days of propagation with a 36 x 36 geopotential model, even for large eccentricities. Furthermore, the relative propagation scheme is significantly faster than differencing two absolute orbit propagations