Computing the perturbed impulse trajectory of transferring between the near-earth and near-lunar orbits by the continuation method

Aeronautical and Space-Rocket Engineering

Dynamics, ballistics, movement control of flying vehicles


Аuthors

Petukhov V. G.1*, Zhou R. 2**

1. Research Institute of Applied Mechanics and Electrodynamics of Moscow Aviation Institute (RIAME MAI), Moscow, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: vgpetukhov@gmail.com
**e-mail: 420790076@qq.com

Abstract

The problem of computing a two-impulse flight between circular near-Earth and near-lunar orbits with specified altitudes and inclinations over a specified time is considered. A mathematical model of motion, accounting for the Earth, Moon and Sun attractive forces as point masses and the second zonal harmonic of the Earth gravity potential at all spacecraft movement sections is used. The first velocity impulse is formed at the initial near-Earth orbit, and puts the spacecraft on the lunar flight trajectory. At the Moon passage instant at the minimum distance the second impulse is formed putting the spacecraft on the near-lunar orbit.

A numerical method for calculating two-impulse transfer between the circular orbits of the Earth and the Moon for a fixed time with account for the main perturbing accelerations has been developed. The method consists of the procedure for calculating the guess values, using the method of point-like spheres of impact, and the procedure for solving the boundary value problem for calculating the perturbed flight trajectory using the continuation method for reducing the boundary value problem to the Cauchy problem.

The advantage of the developed method is the procedure automation for selecting the initial guess values for solving the boundary value problem, and the computational stability of the solving process of the boundary value problem itself. The method revealed its efficiency and computational stability when calculating a series of transfers to a polar circular low lunar orbit of an artificial lunar satellite for various start dates and flight durations. The developed method may be applied for the design-ballistic analysis and operational planning of prospective lunar missions.

The article presents the numerical examples of trajectories computing for the flights between the low near-Earth and near-lunar orbits. Computing of the series of such trajectories allowed calculate the optimal start date and optimal flight duration, as well as dependencies of the required velocity impulses and longitude of the ascending node of the near-lunar orbit on start date and flight duration.

Keywords:

translunar trajectory, two-impulse trajectory, near-lunar orbit, continuation method, lunar mission analysis and design

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