TY - GEN

T1 - Preliminary assessment of the next generation equations of relative motion

AU - Benavides, Julio C.

AU - Spencer, David B.

PY - 2008/12/1

Y1 - 2008/12/1

N2 - The restricted four-body problem is used to derive linearized equations of relative motion that take into account the perturbing effects of a larger, secondary gravitational source. The result is a system of coupled, first-order, linear differential equations that has a complete analytical solution. In this paper, we numerically integrate these linearized equations and compare the results to the outcomes of the restricted four-body problem and the well known Hill-Clohessy-Wiltshire equations. Various cases pertaining to two scenarios are analyzed: the relative motion of a chase spacecraft with respect to a target satellite orbiting an asteroid while both are perturbed by the Sun, and the relative motion of a chase spacecraft with respect to a target satellite orbiting the Moon while both are perturbed by the Earth. The results demonstrate that the Benavides-Spencer formulation is far more accurate than the results given by the Hill-Clohessy-Wiltshire equations when compared to the real-life outcomes returned by the numerical integration of the restricted four-body problem. Future work will unveil the complete analytical solution of the Benavides-Spencer formulation both as an initial value problem and a boundary value problem.

AB - The restricted four-body problem is used to derive linearized equations of relative motion that take into account the perturbing effects of a larger, secondary gravitational source. The result is a system of coupled, first-order, linear differential equations that has a complete analytical solution. In this paper, we numerically integrate these linearized equations and compare the results to the outcomes of the restricted four-body problem and the well known Hill-Clohessy-Wiltshire equations. Various cases pertaining to two scenarios are analyzed: the relative motion of a chase spacecraft with respect to a target satellite orbiting an asteroid while both are perturbed by the Sun, and the relative motion of a chase spacecraft with respect to a target satellite orbiting the Moon while both are perturbed by the Earth. The results demonstrate that the Benavides-Spencer formulation is far more accurate than the results given by the Hill-Clohessy-Wiltshire equations when compared to the real-life outcomes returned by the numerical integration of the restricted four-body problem. Future work will unveil the complete analytical solution of the Benavides-Spencer formulation both as an initial value problem and a boundary value problem.

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M3 - Conference contribution

AN - SCOPUS:77950510345

SN - 9781615671601

T3 - International Astronautical Federation - 59th International Astronautical Congress 2008, IAC 2008

SP - 4690

EP - 4699

BT - International Astronautical Federation - 59th International Astronautical Congress 2008, IAC 2008

T2 - 59th International Astronautical Congress 2008, IAC 2008

Y2 - 29 September 2008 through 3 October 2008

ER -