This work examines the problem of planet-centered orbit transfers using solar sail propulsion. Though solar sails offer unlimited $\mathrm{\Delta }V$, they place coupled time-dependent restrictions on thrust magnitude and direction, and the multiple objectives of an orbit transfer can make locally optimal approaches inefficient; it is therefore advantageous to use optimal control to design such trajectories. This paper presents orbit-averaged equinoctial-element equations of motion for a solar sail under a discretized and interpolated control law. These equations are used to study transfer from a geostationary transfer orbit to geostationary orbit; a locally optimal control law is used to generate initial trajectories, and Gaussian pseudospectral optimal control is applied to yield minimum-time transfers. In the default case, with sail area–mass ratio of $30{\mathrm{m}}^2/\mathrm{kg}$, optimization reduces the transfer time from 1222 to 293 days. Finally, sail area per mass, sail reflectivity, and initial sun–Earth orientation are varied to explore their effects, and to provide general design guidelines for planet-centered solar sail transfers. Distinct performance regimes are observed for transfers taking longer or shorter than one year, and for reflectivities greater or less than 0.4. Additionally, initial solar position was found to drastically affect the behavior of transfers in the fast regime.

这项工作研究了利用太阳帆推进以行星为中心的轨道转移的问题。虽然太阳帆可以提供无限的机会$\mathrm{\Delta }\mathrm{伏特}$，它们对推力的大小和方向施加时间相关的限制，并且轨道转移的多个目标可能会使局部最优方法效率低下；因此，使用最佳控制来设计这样的轨迹是有利的。本文提出了在离散和内插控制律下太阳帆运动的轨道平均等量元素方程。这些方程被用来研究从对地静止转移轨道到对地静止轨道的转移。局部最优控制律用于生成初始轨迹，高斯伪谱最优控制用于产生最小时间传递。在默认情况下，帆面积与质量之比为$30{\mathrm{米}}^{\mathrm{2个}}/\mathrm{公斤}$，优化将传输时间从1222减少到293天。最后，改变每质量的帆面积，帆的反射率和初始太阳-地球方向，以探索其影响，并为以行星为中心的太阳帆传递提供一般设计准则。对于转移时间长于或短于一年，反射率大于或小于0.4的情况，观察到不同的绩效制度。此外，发现初始太阳位置会严重影响快速状态下的传递行为。