Long-Lifetime Lunar Repeat Ground Track Orbits

A high degree and order lunar gravitational field is superimposed on the Earth-moon restricted three-body model to capture the dominating forces on a spacecraft in the vicinity of the moon. For the synchronously rotating moon, periodic orbits in this unaveraged model map repeat ground tracks and represent higher-order solutions to the frozen orbit problem. The stable or near-stable solutions are found over a wide range of defining characteristics, making them suitable for long-lifetime parking applications such as science orbits, crew exploration vehicle parking orbits, and global coverage constellation orbits. A full ephemeris is considered for selected orbits to evaluate the validity of the time-invariant, simplified model. Of the most promising results are the low-altitude families of near-circular, inclined orbits that maintain long-term stability despite the highly nonspherical lunar gravity. The method is systematic and enables rapid design and analysis of long-life orbits around any tidally locked celestial body with an arbitrarily high degree and order spherical harmonic gravity field.

[1]  Martin Lara,et al.  Repeat Ground Track Orbits of the Earth Tesseral Problem as Bifurcations of the Equatorial Family of Periodic Orbits , 2003 .

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

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

[4]  B. Tapley,et al.  Statistical Orbit Determination , 2004 .

[5]  D. Scheeres,et al.  Stability Analysis of Planetary Satellite Orbiters: Application to the Europa Orbiter , 2001 .

[6]  W. Wiesel.  Relative Satellite Motion About an Oblate Planet , 2002 .

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

[8]  Byron D. Tapley,et al.  Chapter 4 – Fundamentals of Orbit Determination , 2004 .

[9]  Ryan P. Russell,et al.  Global search for planar and three-dimensional periodic orbits near Europa , 2006 .

[10]  R. Broucke.  Long-Term Third-Body Effects via Double Averaging , 2003 .

[11]  Prasun N. Desai,et al.  Lifetimes of Lunar Satellite Orbits , 1998 .

[12]  R. A. Cook,et al.  A high resolution lunar gravity field and predicted orbit behavior , 1993 .

[13]  R. Battin.  An introduction to the mathematics and methods of astrodynamics , 1987 .

[14]  J. San-Juan,et al.  Phase Space Structure Around Oblate Planetary Satellites , 2006 .

[15]  R. L. Duncombe,et al.  Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites , 1980 .

[16]  R. Russell,et al.  A Dynamical Systems Approach to the Design of the Science Orbit Around Europa , 2006 .

[17]  David Quinn,et al.  Lunar Frozen Orbits , 2006 .

[18]  T. Ely,et al.  Constellations of elliptical inclined lunar orbits providing polar and global coverage , 2006 .

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

[20]  C. Ulivieri,et al.  Long-term effects on lunar orbiter , 1997 .

[21]  R. Russell,et al.  Computation of a Science Orbit About Europa , 2007 .

[22]  Victor Szebehely,et al.  Theory of Orbits. , 1967 .

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

[24]  Gerard Gómez,et al.  Dynamics and Mission Design Near Libration Points , 2001 .

[25]  J. Junkins,et al.  Orbital mission analysis for a lunar mapping satellite , 1994 .

[26]  Kathleen C. Howell,et al.  Three-Dimensional Periodic Halo Orbits , 1981 .

[27]  A. Nayfeh,et al.  Applied nonlinear dynamics : analytical, computational, and experimental methods , 1995 .

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

[29]  Todd A. Ely,et al.  Stable Constellations of Frozen Elliptical Inclined Lunar Orbits , 2005 .

[30]  A. Milani,et al.  Integration error over very long time spans , 1987 .