Energy Consumption Assessment of the Inter-Orbital Transfer from the Elliptical Orbit to the Geometrically-Stable Orbit around Mars

Аuthors

Elnikov R. V.^*, Zhukov G. E.^**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: elnikov_rv@mail.ru
**e-mail: zhykov99@gmail.com

Abstract

The article considers the spacecraft transfer to a polar, near-circular, frozen sun-synchronous orbit (SSO) around Mars. Such an orbit may be utilized for the effective planet probing. It is assumed that the spacecraft overflight in the Martian gravitational sphere from a highly elliptical orbit is performed by a low-thrust propulsion system. The authors solve the problem of the optimal parameters determining of an intermediate orbit, which ensure delivery of the spacecraft of maximum weight.
The authors analyzed characteristics of the target frozen orbit, and Mars gravitational field non-centrality impact on its evolution. Dependencies of the energy and temporal expenditures required for the transfer are obtained.
Geometrically stable orbits differ in that they have virtually no change in the profile of the spacecraft areodetic flight altitude from revolution to revolution. Such orbits are employed in practice for the planet remote probing. 
An algorithm for the frozen solar-synchronous orbits parameters computing in the geopotential model with acount for the seventh zonal harmonic was described in [8]. As a result, D.Y. Vinogradov and E.A. Davydov derived analytical relationships for parameters computing of such orbits, ensuring stable patterns of sub-satellite point altitude variations over the first few hundred revolutions of the spacecraft passive motion.
Transfer to such orbits was as well considered by several authors [9-12]. Application of low-thrust engines at that is the most feasible approach since payload delivering to Martian orbits requires significant energy consumption. Low-thrust engines allow significant fuel consumption reduction for the transfer maneuvers [12]. However, the control program determining for such spacecraft is a highly complex and nontrivial task. There are studies in the domestic sources on the transfers to highly elliptical orbits, such as those of the Moon [13], but unfortunately, similar works for Mars are almost nonexistent. One of the goals of this study is to address this gap. The approach being proposed is, on the one hand, relatively simple to implement, and on the other hand, highly effective and in demand, without compromising performance.
This article examines parameters selection for a frozen multiple-repeat sun-synchronous Martian orbit to achieve full coverage of the planet equator [14-16], as well as assesses the impact of Mars gravitational field non-centrality on the frozen condition. The authors consider the flat optimal interorbital transfer by the low-thrust engine from the intermediate eliptical orbit to the target frozen sun-synchronous orbit around Mars. It is assumed that the spacecraft is impulsively transferred from the interplanetary flyby orbit to an intermediate elliptical orbit. Its further motion (“twisting” to the working near-circular orbit) is being performed by the low-thrust propulsion system. To estimate the energy costs of a low-thrust interorbital transfer between an intermediate elliptical orbit and a near-circular operational trajectory, an approximation of a grid of dimensionless characteristic velocities for planar transfer (without inclination change) is used. The grid parameters are the radii of the apocenter and pericenter of the intermediate elliptical orbit. This grid was obtained by solving the interorbital transfer problem within the Pontryagin's maximum principle [17]. A similar approach has been considered before, for example, in [18]. The authors of that study derived a table of dimensionless characteristic velocities on a three-dimensional grid of pericenter radius, apocenter radius, and inclination of the intermediate orbit when solving the time-optimal averaged interorbital transfer problem. The dependencies obtained in [18] are widely used in mission design and ballistic analysis for the rapid estimation of the final spacecraft mass when using an electric propulsion system (EPS).
This article analyzes characteristics of the multiple-repeat sun-synchronous orbits and the Martian gravitational potential effect on the orbit evolution. Estimation of both energy and temporal costs of a low-thrust transfer revealed that the considered class of operational orbits enables stable remote probing of the planet due to minimal variations in the areodetic altitude profile.
Universal dependencies for the energy costs estimation of transferring from an intermediate elliptical orbit to the target near-circular orbit were derived.

Keywords:

low-thrust transfer, optimal interorbital transfer, Pontryagin's maximum principle inter-orbital transfer, Martial frozen orbit, sun-synchronous orbit, remote sensing of Mars

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