AIAA, Reston (1999)īroucke, R.A.: Numerical integration of periodic orbits in the main problem of artificial satellite theory.

Elseiver, Oxford, UK, chapter VI (2010)īattin, R.H.: An Introduction to the Mathematics and Methods of Astrodynamics. Long-term orbital simulation results indicate that the effect of choosing a frozen orbit vis-à-vis a non-frozen orbit can reduce the relative distance drift by hundreds of meters per day.Īlfriend, K., Vadali, S., Gurfil, P., How, J., Breger, L.: Spacecraft Formation Flying: Dynamics, Control and Navigation. On the other hand, if the chief’s orbit is non-frozen, a secular growth in the differential mean argument of latitude leads to a concomitant along-track separation of the deputy from the chief, thereby considerably increasing the relative distance evolution over time.

Using mean orbital element variations, it is proven that if the chief’s orbit is frozen, then the mean differential eccentricity is periodic, leading to a periodic variation of the differential mean argument of latitude. In this paper, it is analytically proven that choosing the chief’s orbit to be a frozen orbit can mitigate the natural relative drift of the satellites. Thus, constraints on the initial conditions must be imposed to mitigate the chief-deputy mutual departure. Generally, any initially-close satellites-chief and deputy-moving on orbits with slightly different orbital elements, will depart each other on locally unbounded relative trajectories.

Frozen orbit