Optimal low-thrust trajectories for the impulsive deflection of Near Earth Objects
- Paper number
IAC-05-C1.5.06
- Author
Dr. Dario Izzo, European Space Agency (ESA)/ESTEC, The Netherlands
- Year
2005
- Abstract
The possibility of deflecting a potentially hazardous asteroid in collision route with our planet is being studied in connection with different deflection strategies and scenarios. Recent results seem to suggest that a spacecraft equipped with low-thrust propulsion may be effectively used to accelerate towards the asteroid in order to maximise the impact effect on the resulting Earth miss-distance. The optimisation of the interplanetary part of such a trajectory is quite complex as the objective function evaluation, even in the simple case of a perfectly inelastic impact, requires to propagate the asteroid position to the impact point and then to locate the minimum distance between the asteroid and the Earth along this modified trajectory. Even though simple keplerian models may be patched together to facilitate the orbit propagation, the problem remains complex and the explicit dependence between the impact geometry and the resulting miss-distance is not revealed.
In this paper we propose a generic analytical expression, named the Asteroid Deflection Formula, relating the deflection strategy, e.g. the action transferred to the asteroid, to the miss-distance and we use it as an objective function in our optimal low-thrust problem. It turns out that the quantity one wants to maximise is m t s vec v cdot vec U where m is the spacecraft mass at rendezvous, t s is the time before impact the rendezvous takes place, vec v is the asteroid velocity at rendezvous and vec U is the relative velocity between the spacecraft and the asteroid at rendezvous. As the final mass is involved in the objective function the optimal control is likely to have a complex switching structure. We then solve the optimal control problem using a direct transcription method based on Finite Element in Time by first considering a simplified expression for the objective function and then using the solution found as a starting point for the complete optimisation. Optimal trajectories for the impulsive deflection strategy are presented for different asteroid classes (Amors, Apollos, Athens, etc.) and spacecraft thrusting capabilities. A first estimate on the minimum spacecraft initial mass that allows a given deflection is also given for the various cases.
- Abstract document
- Manuscript document
IAC-05-C1.5.06.pdf (🔒 authorized access only).
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