The problem of optimization of a spacecraft transfer to the Apophis asteroid is investigated. The scheme of transfer under analysis includes a geocentric stage of boosting the spacecraft with high thrust, a heliocentric stage of control by a low thrust engine, and a stage of deceleration with injection to an orbit of the asteroid’s satellite. In doing this, the problem of optimal control is solved for cases of ideal and piecewise-constant low thrust, and the optimal magnitude and direction of spacecraft’s hyperbolic velocity “at infinity” during departure from the Earth are determined. The spacecraft trajectories are found based on a specially developed comprehensive method of optimization. This method combines the method of dynamic programming at the first stage of analysis and the Pontryagin maximum principle at the concluding stage, together with the parameter continuation method. The estimates are obtained for the spacecraft’s final mass and for the payload mass that can be delivered to the asteroid using the Soyuz-Fregat carrier launcher.
[1]
V. V. Ivashkin,et al.
Optimal trajectories for spacecraft with low electric-jet thrust in mission to asteroid Apophis
,
2012
.
[2]
V. G. Petukhov,et al.
Method of continuation for optimization of interplanetary low-thrust trajectories
,
2012
.
[3]
R. Bellman.
The theory of dynamic programming
,
1954
.
[4]
V. V. Ivashkin,et al.
On the prevention of a possible collision of asteroid Apophis with the Earth
,
2009
.
[5]
T. Y. Na,et al.
Computational methods in engineering boundary value problems
,
1979
.
[6]
G. L. Grodzovskii,et al.
PROBLEMS OF OPTIMIZATION IN THE MECHANICS OF SPACEFLIGHT WITH SMALL THRUSTS (PROBLEMY OPTIMIZATSII V MEKHANIKE KOSMICHESKOGO POLETA S MALOI TYAGOI)
,
1967
.