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Quasi-terminator orbits near primitive bodies

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Abstract

Quasi-terminator orbits are introduced as a class of quasi-periodic trajectories in the solar radiation pressure (SRP) perturbed Hill dynamics. These orbits offer significant displacements along the Sun-direction without the need for station-keeping maneuvers. Thus, quasi-terminator orbits have application to primitive-body mapping missions, where a variety of observation geometries relative to the Sun (or other directions) can be achieved. This paper describes the characteristics of these orbits as a function of normalized SRP strength and invariant torus frequencies and presents a discussion of mission design considerations for a global surface mapping orbit design.

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Notes

  1. References are given when available, otherwise the parameters have been approximated using the authors’ best guess. In the latter cases, the \(\approx \) symbol is used before the numerical data given.

  2. Generally, perturbations in the span of the center manifold evolve on a invariant torus described by three frequencies. This more general motion is not explored in this paper. The two 4-D sub-manifolds of invariant tori studied here are invariant slices in this larger quasi-periodic space. The method used to follow the tori in Eq. 9 ensures that the tori found lie on a sub-manifold where motion is described by only two frequencies.

  3. This is true, but for low \(m/n\) ratios (\(\ne 1\)), this stability seems to be marginal in a non-linear sense. When such a solution to the multiple-shooting corrector algorithm is re-propagated as a single trajectory, the match between starting and ending states is often noticeably less accurate than usual.

  4. Recall from Sect. 5.4 that if \(C\) is larger than the maximum \(C\) for the corresponding terminator family, the quasi-terminator orbits near the RTO are not embedded in the center manifold of the terminator orbit, and thus, do not necessarily have consistent geometries with those shown in Figs. 5 and 6.

  5. This may not be the case for some RTO families at low \(\beta \) values, but RTOs are not usually of interest in these dynamical scenarios because the orbit periods are very long. Further, for small \(\beta \), the dominant perturbation is often the irregular gravity of the primitive body, which is a scenario where the assumptions in this work do not apply.

  6. In a real mission application, this minimum radius should be carefully chosen based on factors including primitive body mass distribution, orbit maintenance frequency, and duration in orbit.

  7. The Sun-relative geometry describes the relative geometry between the orbiting spacecraft, primitive-body center-of-mass, and the Sun. It is independent of the motion of the primitive body surface. As such, actual global surface mapping performance for a particular orbit depends upon the body spin orientation and state.

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Acknowledgments

The work described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. The authors thank Zubin Olikara for the insights he shared with us on torus computation and the dynamical structure of this problem. They also thank Benjamin Villac for some early discussions on the dynamical structure around terminator orbits that led to this work. The authors further thank Benjamin and Roby Wilson for their helpful comments on a draft manuscript.

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  1. Mission Design and Navigation Section, Jet Propulsion Laboratory, California Institute of Technology, M/S: 301-121, 4800 Oak Grove Dr., Pasadena, CA, 91109, USA

    Stephen B. Broschart, Gregory Lantoine & Daniel J. Grebow

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  1. Stephen B. Broschart
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  2. Gregory Lantoine
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Correspondence to Stephen B. Broschart.

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Broschart, S.B., Lantoine, G. & Grebow, D.J. Quasi-terminator orbits near primitive bodies. Celest Mech Dyn Astr 120, 195–215 (2014). https://doi.org/10.1007/s10569-014-9574-3

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