Approximate calculation of initial conditions of a spacecraft with solar electric-rocket propulsion plant starting while transferring from highly elliptic orbit to geostationary one

Aeronautical and Space-Rocket Engineering

Dynamics, ballistics, movement control of flying vehicles


DOI: 10.34759/vst-2021-1-147-160

Аuthors

Salmin V. V.*, Petrukhina K. V.**, Kvetkin A. A.***

Samara National Research University named after Academician S.P. Korolev, 34, Moskovskoye shosse, Samara, 443086, Russia

*e-mail: sputnik@ssau.ru
**e-mail: ksusha_10_05@mail.ru
***e-mail: emancipee163@yandex.ru

Abstract

The subject of this research is ballistic schemes optimization for the spacecraft with solar electric propulsion system. The article considers the problem of the initial conditions search for a spacecraft launch, at which the total time of its staying in the shadow at the insertion phase would be minimal.

The total duration of shadow sections during interorbital flight will depend on the relative position of the Sun and the spacecraft’s orbital plane. To solve the problem of the initial launch conditions selection, the dependence of the shadow section duration on the set of ballistic parameters, such as the ascending node longitude, the perigee argument, and the launch date of the flight, is being considered.

A ballistic scheme for leading out, at which elliptica transfer orbit forming is being performed by the upper stage of the rocket-carrier is selected, and a spacecraft finishing up to the working orbit is being performed by its own electric propulsion unit.

The article proposes a model for duration computing of the orbit shadow sections. Equations of motion in osculating elements are assumed as a mathematical model of the spacecraft controlled motion under the impact of the electric propulsion. An algorithm for solving the problem of optimal initial flight conditions search has been developed. The total duration of a spacecraft with the solar propulsion unit staying in the Earth shadow along the whole trajectory of the multi-turn flight was accepted as an optimality criterion. The following parameters, namely the launch date — perigee argument — the ascending node longitude, were selected as the optimized parameters of the elliptical orbit.

Computations of the spacecraft flight trajectories from high-elliptical orbit to the geostationary one for three initial orbit inclinations, performed with variation of the parameters being optimized, were carried out. The spacecraft launch windows and corresponding initial conditions of the orbit, rational in terms of the flight duration reduction, were found based on the simulation results. Analysis of the simulation results array revealed that launching date selection did not affect significantly the flight time at optimal combinations of the perigee argument and the ascending node longitude, and the time difference for the flights in 2020 lies within the limits of 1%.

The combination of the initial ascending node longitude and the perigee argument has a much greater impact than the launch date selection. The worst combinations of these parameters may increase the maneuver time by 12% of the minimum value, which gives their optimization the highest priority. Thus, the flight initial conditions selecting is an important problem of the low-thrust interorbital flights optimizing.

It may be noted as well that while flights with three initial values of the orbital inclinations simulating, a tendency for the increase in the relative difference in flight time between the optimal and non-optimal initial flight conditions with a decrease in the initial orbit inclination was found. As the result, the orbits with lower initial inclinations are more demanding in the initial parameters selection.

The article demonstrates the possibility of the approximate optimal control method and the «NEOS» software application for the flight tasks with account for shadow sections, including those with multiple simulation.

The obtained results can be applied for evaluating the design ballistic parameters of a spacecraft with electric propulsion unit flight, as well as determining the optimal initial launch conditions.

Keywords:

orbital eclipse period, highly elliptical orbit, geostationary orbit, shadow area model, close-optimal control law, electric propulsion engine, spacecraft launch

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