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ABSTRACT
Interplanetary missions require high velocities to escape the Earth gravitational field and attain far bodies of the solar system. The concept of sphere of influence allows the trajectory to be modelled as a series of two body problems, and thus simplifies the analysis of the missions. The patched conics model highlights the gravity assist phenomenon which provides velocity gains while crossing the planet sphere of influence. The article presents the basis models, the patch conics formulation and implementation and the simplified optimization of the maneuvers at the launch phase and during the interplanetary trip.
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Max CERF: Mission Analysis Engineer ArianeGroup, Les Mureaux, France
INTRODUCTION
During an interplanetary mission, the vehicle is subject to the attraction of all the stars in the solar system. This N-body problem has no analytical solution, and trajectory calculation requires the use of numerical integration methods. These methods offer no physical understanding and are not suitable for studying the mission scenario.
The sphere of influence concept allows us to break down the interplanetary journey into a succession of two-body problems. This model highlights the phenomenon of gravitational assistance, which enables the vehicle's trajectory to be modified "free of charge" in the heliocentric frame of reference. In the most favourable cases, it is even possible to construct an interplanetary trajectory reaching the target destination without any propulsive manoeuvres. As such a scenario is not always possible, the aim is to find a scenario that minimizes the duration of propulsive phases, so as to limit the amount of propellant embarked.
This article explains how to model an interplanetary mission, and how to calculate the maneuvers to be performed at launch and during the journey.
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KEYWORDS
sphere of influence | patched conics | gravity assist | fly-by | two body problem
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