Analytical Theory for Spacecraft Motion About Mercury

Paper number

IAC-08.C1.3.11

Author

Dr. Patricia Yanguas, Universidad Publica de Navarra, Spain

Coauthor

Dr. Martin Lara, Real Observatorio de la Armada, Spain

Coauthor

Mr. Carlos Corral van Damme, GMV S.A., Spain

Coauthor

Dr. Jesus Palacian, Universidad Publica de Navarra, Spain

Year

2008

Abstract

Analytical theories for mission designing of artificial satellites
normally rest on simplified models that capture the majority of the
dynamics. Thus, it is common to consider either the inhomogeneities of
the potential of the central body, for instance for earth artificial
satellites, or the third body perturbation, e.g. for interplanetary
missions, or a combination of both effects, as in the case of science
missions about planetary satellites. The long-term dynamics reveals
after averaging, and a full knowledge of the long-term dynamics is
quite useful for mission designing purposes.

In most cases it is enough to take the third body perturbation in the
Hill problem or the Circular Restricted Three-body approximation
---both models assuming the circularity of the primaries' orbit in its
relative motion. However, the circular approximation does not fit to
Mercury, whose orbit around the sun clearly exhibits a non-negligible
eccentricity. Hence, the dynamics around Mercury must be studied in
the context of the Elliptic Restricted Three-body Problem (ERTBP), in
spite of this model introduces one more variable to average.

The importance of including the ellipticity of the orbit of Mercury
manifests through first order effects related to the time averaging,
as it has been recently shown. However, an analytical theory including
the combined effects of the ERTBP and the non-spherical mass
distribution of Mercury has not been considered yet. Since Mercury has
a known oblateness with an important effect on orbit stability and,
probably, a latitudinal asymmetry without significant effects on
stability but important effects on the shape of the science orbit, we
feel compelled to develop a theory including both J2 and J3
coefficients, and the sun gravitational perturbation in the ERTBP
approximation.

In our work we depart from the classical approach of using the
Lagrange Planetary Equations of an averaged perturbing function for
describing the long-term dynamics, and use modern perturbation theory
that besides the averaged equations provides also the transformation
equations between the averaged and non-averaged problems ---equations
that are essential to recover the short and long period effects lost
in the averaging.

With our analytical theory, we find a very good agreement between
averaged and non-averaged models. But to further test the reliance of
our theory we propagate a selected set of initial conditions chosen
from the analytical theory in full ephemeris using JPL files. The
long-term propagations show that the analytical theory provides a very
good approximation of the real dynamics about Mercury.

Abstract document

IAC-08.C1.3.11.pdf

Manuscript document

IAC-08.C1.3.11.pdf (🔒 authorized access only).

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