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首页> 外文期刊>Acta Astronautica >OPTIMAL TRANSFERS FROM AN EARTH ORBIT TO A MARS ORBITT
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OPTIMAL TRANSFERS FROM AN EARTH ORBIT TO A MARS ORBITT

机译：从地球轨道到火星轨道的最佳转移

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This paper deals with the optimal transfer of a spacecraft from a low Earth orbit (LEO) to a low Mars orbit (LMO). The transfer problem is formulated via a restricted four-body mode1 in that the spacecraft is considered subject to the gravitational fields of Earth, Mars, and Sun along the entire trajectory. This is done to achieve increased accuracy with respect to the method of patched conics. The optimal transfer problem is solved via the sequential gradient-restoration algorithm employed in conjunction with a variable-stepsize integration technique to overcome numerical difficulties due to large changes in the gravitational field near Earth or near Mars. First, for given LEO and LMO radii, a basic optimization problem is considered: the minimization of the total characteristic velocity, the sum of the velocity impulses at LEO and LMO, assuming that the departure date is free, hence assuming that the planetary Mars/Earth phase angle difference at departure is free. At both departure and arrival, the optimal trajectory exhibits an asymptotic parallelism condition at the end of near-Earth space, the spacecraft inertial velocity is parallel to the Earth inertial velocity; analogously, at the beginning of near-Mars space, the spacecraft inertial velocity is parallel to the Mars inertial velocity. The total characteristic velocity is AV△V = 5.652 km/s, corresponding to a ratio of payload mass to initial mass of 0.224 for typical specific impulse and structural factor. Then, for given LEO and LMO radii, a departure window is generated by changing the departure date, hence changing the planetary Mars/Earth phase angle difference at departure, and then reoptimizing the transfer. This results into an one-parameter family of suboptimal transfers retaining the asymptotic parallelism condition at arrival, but not at departure. For the suboptimal transfers, the phase ang1e travel and transfer time decrease with late departure and increase with early departure. Also, a change in departure date of + 32 days [-32 days] causes a characteristic velocity increase of 8/100 [5/100], implying a payload mass decrease of l3/100 [8/100].
机译：本文探讨了航天器从低地球轨道（LEO）到低火星轨道（LMO）的最佳转移。传递问题是通过受限的四体模式1提出的，其中认为航天器在整个轨迹上都受到地球，火星和太阳的重力场的影响。这样做是为了获得有关修补圆锥形方法的更高的准确性。最佳传递问题是通过与可变步长积分技术结合使用的顺序梯度恢复算法解决的，以克服由于地球或火星附近的引力场发生较大变化而造成的数值困难。首先，对于给定的LEO和LMO半径，要考虑一个基本的优化问题：总特征速度的最小化，LEO和LMO处的速度脉冲总和（假设出发日期是自由的），因此假设行星火星/出发时地球相角差是免费的。在出发和到达时，最佳轨迹在近地空间的末端表现出渐近的平行度条件，航天器的惯性速度与地球的惯性速度平行；类似地，在接近火星的空间开始时，航天器的惯性速度与火星的惯性速度平行。总特征速度为AV△V = 5.652 km / s，对应于典型比冲和结构因子，有效载荷质量与初始质量之比为0.224。然后，对于给定的LEO和LMO半径，通过更改出发日期来生成出发窗口，从而更改出发时的行星火星/地球相角差，然后重新优化传输。这导致一参数系列次优传递在到达时保留渐近并行性条件，但不在出发时保持渐近并行性条件。对于次优的传输，相角行程和传输时间随着延迟的离开而减少，而随着早期的离开而增加。同样，出发日期更改为+ 32天[-32天]会导致速度特征值增加8/100 [5/100]，这意味着有效载荷质量减少了13/100 [8/100]。

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