An efficient method for searching periodic orbits in Earth observation missions

Frozen orbits are required for Earth observational missions, where the trace is repeated on the surface after a certain number of revolutions. The design of those missions is facilitated with the method we present here, which permits us to calculate families of periodic orbits in a reference system that rotates with the Earth. An application to the TOPEX/POSEIDON orbit is presented.

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

[2]  M. Lara,et al.  Periodic Orbits Around a Massive Straight Segment , 1999 .

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

[4]  Carl Wunsch,et al.  The global frequency-wave number spectrum of oceanic variability estimated from TOPEX/POSEIDON altimetric measurements. Volume 100, No. C12; The Journal of Geophysical Research , 1995 .

[5]  G. M. Clemence,et al.  Methods of Celestial Mechanics , 1962 .

[6]  Chris Sabol Application of sun-synchronous, critically inclined orbits to global personal communications systems , 1995 .

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

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

[9]  W. M. Kaula Theory of satellite geodesy , 1966 .

[10]  F. Scheck Mechanics: From Newton's Laws to Deterministic Chaos , 2018 .

[11]  R. Broucke,et al.  Numerical integration of periodic orbits in the main problem of artificial satellite theory , 1994 .

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

[13]  Antonio Elipe,et al.  Periodic Orbits Around a Massive Straight Segment , 1999 .

[14]  Antonio Elipe,et al.  Frozen Orbits About the Moon , 2003 .

[15]  Stephen Wolfram,et al.  Mathematica: a system for doing mathematics by computer (2nd ed.) , 1991 .

[16]  T. Teichmann,et al.  Fundamentals of celestial mechanics , 1963 .

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

[18]  Bulusu Subrahmanyam,et al.  Indian Ocean Rossby waves observed in TOPEX/POSEIDON altimeter data and in model simulations , 2001 .