| Abstract: | This paper deals with the coverage analysis problem of elliptical
orbits. An algorithm based on ergodic theory, for long-term coverage
of elliptical orbits, is proposed. The differential form of the
invariant measure is constructed via the perturbation on mean
orbital elements resulted from the $J_{2}$ term of non-spherical
shape of the earth. A rigorous proof for this is then given.
Different from the case of circular orbits, here the flow and its
space of the dynamical system are defined on a physical space, and
the real-value function is defined as the characteristic function on
station mask. Therefore, the long-term coverage is reduced to a
double integral via Birkhoff--Khinchin theorem. The numerical
implementation indicates that the ergodic algorithm developed is
available for a wide range of eccentricities. |
