Relative Motion of Satellites Exploiting the Super-Integrability of Kepler’s Problem

P L Palmer,  K. Uldall Kristiansen & M Roberts


This paper builds upon the work of Palmer and Imre [18, 11] exploring the relative
motion of satellites on neighbouring Keplerian orbits. We make use of a general geo-
metrical setting from Hamiltonian systems theory to obtain analytical solutions of the
variational Kepler equations about any Keplerian reference orbit in an Earth centred
inertial coordinate frame in terms of the relevant conserved quantities: relative en-
ergy, relative angular momentum and the relative eccentricity vector. The geometrical
framework assists the design of complex formation flying trajectories. This is demon-
strated by the constructing of a tetrahedral formation, described through the relevant
conserved quantities, for which the satellites are on highly eccentric orbits around the
sun to visit the Kuiper belt.

Paper: Relative Kepler

Ref: Palmer, P.L., Kristiansen, K. Uldall & Roberts, R.M., J Celestial Mechanics & Dynamical Astronomy, 106 , No 4, pp. 371—390, 2010.


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