22 Orbit Stability Determination of Satellites Using Harmonic Force Excitation Analysis 215 Fig. 22.3 Perihelion and aphelion points for a body orbiting the sun Fig. 22.4 NEO types as categorized by NASA [2] Fig. 22.5 Asteroid 25143 Itokawa as seen from Hayabusa [6] The control problem in an NEO environment is being studied by researchers all around the world. NASA and the Japanese Aerospace Exploration Agency (JAXA) have sent unmanned spacecraft to operate in close-proximity to these objects [4, 5]. What makes the NEO environment so unique is the gravity field surrounding an NEO is tenuous and it is quite complex. Gravitational force is a function of the spacecraft and NEO mass elements that decays proportionally to the inverse square of the distance between these element. Therefore, when dealing with small NEOs, the gravitational force exerted on an orbiting spacecraft is much weaker than it is for much larger bodies, like Earth or Mars. Furthermore, the gravitational field is correlated the shape of the body but can have variations based on varying mass distributions throughout. This study focuses on asteroid 25143 Itokawa, which the Hayabusa satellite visited in 2005 (Fig. 22.5). The shape of Itokawa resembles that of a potato, so a satellite in a circular orbit experiences higher gravitational force as it passes by either of the two protruding ends. This increased force can be enough to upset the orbital trajectory such that the satellite escapes the weak gravity field, or that the satellite crashes into the body.
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