**A Strategy for Maintaining Constant
Distance between Satellites in an Elliptically Orbiting Constellation**

**Abstract:**

A strategy for maintaining separation
distances between several satellites in a coplanar elliptical orbiting constellation is
developed. A possible scientific application of such a system would be in measuring the
curl of the Earth's magnetic field by taking simultaneous measurements along the
elliptical orbit. The strategy involves maneuvers that would cause small shifts in the
direction of the four semi-major axes. With this approach for Keplerian type orbits, the
separation distance between adjacent satellites remains within a few percent of the
nominal separation distance. This paper emphasizes problems of implementation.

1. Initial
deployment. It is assumed that the satellites are launched by a single vehicle. The method
to distribute the satellites into their positions using the least maneuver energy is
studied.

2. Maintenance
of the separation distance. Since the mathematical model is nonlinear and time-variant, a
nonlinear control law based on a Lyapunov function is applied to the osculating orbital
elements of the daughter satellites. The simulation results with this control show that
with perturbations (mainly caused by J2), the response to initial errors converges
smoothly and the control energy spent is at a very low level.