Abstract
Temporarily-captured Natural Earth Satellites (NES) are very appealing targets for space missions for many reasons. Indeed, NES get captured by the Earth's gravity for some period of time, making for a more cost-effective and time-effective mission compared to a deep-space mission, such as the 7-year Hayabusa mission. Moreover, their small size introduces the possibility of returning with the entire temporarily-captured orbiter (TCO) to Earth. Additionally, NES can be seen as interesting targets when examining figures of their orbits. It requires to expand the current state-of-art of the techniques in geometric optimal control applied to low-thrust orbital transfers. Based on a catalogue of over sixteen-thousand NES, and assuming ionic propulsion for the spacecraft, we compute time minimal rendezvous missions for more than $96%$ of the NES. The time optimal control transfers are calculated using classical indirect methods of optimal control based on the Pontryagin Maximum Principle. Additionally we verify the local optimality of the transfers using second order conditions.
Highlights
Our era is witnessing an expansion in the complexity of endeavors beyond the Earth’s orbit
Near Earth asteroid rendezvous (NEAR) and Hayabusa are completed missions that involved a rendezvous with an asteroid including a safe landing
This includes, in particular, brilliant methods based on chaotic motion in celestial mechanics, presented in details in [6] and successfully put into practice to rescue the Japanese spacecraft Hiten [7]
Summary
Our era is witnessing an expansion in the complexity of endeavors beyond the Earth’s orbit. It can be observed that temporarily-captured natural Earth satellites presents a large variety of orbits from very regular to extremely scattered. This diversity of orbits is appealing because we can test the capabilities of our transfer computation methods, and develop experience designing transfer maneuvers that may not have been completed before. Over the last two decades, the application of theory of dynamical systems to astrodynamics has enabled the construction of new types of low-energy transfers This includes, in particular, brilliant methods based on chaotic motion in celestial mechanics, presented in details in [6] and successfully put into practice to rescue the Japanese spacecraft Hiten [7]. The design of the Genesis discovery mission [22] relies, for instance, on this idea
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