Repeat Ground Track Orbits of the Earth Tesseral Problem as Bifurcations of the Equatorial Family of Periodic Orbits

Orbits repeating their ground track on the surface of the earth are found to be members of periodic-orbit families (in a synodic frame) of the tesseral problem of the Earth artificial satellite. Families of repeat ground track orbits appear as vertical bifurcations of the equatorial family of periodic orbits, and they evolve from retrograde to direct motion throughout the 180 degrees of inclination. These bifurcations are always close to the resonances of the Earth's rotation rate and the mean motion of the orbiter.

[1]  V. V. Markellos,et al.  Numerical determination of three-dimensional periodic orbits generated from vertical self-resonant satellite orbits , 1980 .

[2]  Jaume Llibre,et al.  On the families of periodic orbits which bifurcate from the circular Sitnikov motions , 1994 .

[3]  A. Deprit.  Intrinsic variational equations in three dimensions , 1981 .

[4]  R. Broucke,et al.  Stability of periodic orbits in the elliptic restricted three-body problem. , 1969 .

[5]  V. Szebehely,et al.  Theory of Orbits: The Restricted Problem of Three Bodies , 1967 .

[6]  M. Hénon,et al.  Vertical stability of periodic orbits in the restricted problem , 1973 .

[7]  Bruce R. Miller,et al.  The critical inclination in artificial satellite theory , 1986 .

[8]  P. Farinella,et al.  Non-gravitational perturbations and satellite geodesy , 1987 .

[9]  Martin Lara,et al.  On the numerical continuation of periodic orbits: An intrinsic, 3-dimensional, differential, predictor-corrector algorithm , 2002 .

[10]  B L Decker,et al.  World Geodetic System 1984 , 1986 .

[11]  J. Henrard,et al.  NATURAL FAMILIES OF PERIODIC ORBITS , 1967 .

[12]  Emmanuel Davoust,et al.  A manifold of periodic orbits in the planar general three-body problem with equal masses , 1982 .

[13]  Joan R. Pacha.  The 3D elliptic restricted three-body problem: periodic orbits which bifurcate from limiting restricted problems , 1999 .

[14]  Shannon L. Coffey,et al.  Frozen orbits for satellites close to an Earth-like planet , 1994 .

[15]  Antonio Elipe,et al.  Numerical continuation of families of frozen orbits in the zonal problem of artificial satellite theory , 1995 .

[16]  G. H. Born,et al.  Orbit analysis for Seasat-A , 1978 .

[17]  Jürgen Moser,et al.  Lectures on Celestial Mechanics , 1971 .