Optimum trajectories for an Earth–asteroid–Earth mission with a high thrust flight

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Abstract

The trajectories of a mission to an asteroid with the presence of a spacecraft (SC) near the asteroid for some time and including a return to the Earth have been studied. A two-stage method of constructing optimum (with respect to the maximum of the useful SC mass) interplanetary trajectories of an Earth–asteroid–Earth mission with high thrust engines has been developed: in the central Newtonian field of the Sun’s attraction at the first stage and with allowance for disturbances at the second stage. An algorithm of constructing conjugate functions for the case of maximizing the useful mass has been designed. The optimum trajectories for the Earth-Apophis-Earth mission have been constructed and analyzed. The possibility in principle of organizing the Earth-Apophis-Earth space mission based on the "Soyuz" and "Zenit" launch vehicles and "Fregat" upper stage for a flight has been demonstrated.

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About the authors

V. V. Ivashkin

Institute for Applied Mathematics of the Russian Academy of Sciences; Bauman Moscow State Technical University

Author for correspondence.
Email: ivashkin@keldysh.ru
Russian Federation

Anqi Lang

Bauman Moscow State Technical University; Xi’an Jiaotong University

Email: ivashkin@keldysh.ru
Russian Federation, Moscow; China

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Supplementary files

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2. Fig. 1. Isolines of useful mass in the plane of times t1 and ∆t12 for the variant Dt∑ = 690 days, ∆t23 = 7 days. in the vicinity of the optimum.

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3. Fig. 2. Dependences of the velocity Vхар and masses mf, mp on time ∆t23.

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4. Fig. 3. Change of the modulus of the basis vector p (t) on trajectory No. 19: (a) —flight from the Earth to Apophis

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5. Fig. 3. (b) - the flight from Apophis to the Earth.

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