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arXiv 1408.5553astro-ph.EP
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绕小行星飞行器的四阶重力梯度力矩

Fourth-order gravity gradient torque of spacecraft orbiting asteroids

Yue Wang, Hong Guan, Shijie Xu

摘要:

小行星周围航天器的动力学行为是设计这类飞行任务的一个关键要素。小行星的不规则形状、非球形质量分布和自转状态使得航天器的动力学十分复杂。研究了航天器绕非球形小行星飞行时的重力梯度力矩。小行星的重力场近似为二阶和二阶重力场,调和系数为C20和C22。通过引入航天器的高阶惯性积分,由重力位导数建立了航天器的完整的四阶重力梯度力矩模型。由于考虑了航天器的高阶惯性积分,我们的全四阶模型比以前的四阶模型更精确。得出了一些关于重力梯度力矩模型的有趣结论。最后通过数值模拟对模型进行了验证。在数值模拟中,考虑了一个特殊的航天器由36个点质量连接的刚性无质量杆。假设小行星绕其最大力矩主轴作匀速自转,航天器位于赤道平面内的静止轨道上。仿真结果表明,以前的四阶模型的运动与精确运动有很大的差异,而我们的全四阶模型很好地拟合了精确运动。我们的模型是足够精确的实际应用。

英文摘要:

The dynamical behavior of spacecraft around asteroids is a key element in design of such missions. An asteroid's irregular shape, non-spherical mass distribution and its rotational sate make the dynamics of spacecraft quite complex. This paper focuses on the gravity gradient torque of spacecraft around non-spherical asteroids. The gravity field of the asteroid is approximated as a 2nd degree and order-gravity field with harmonic coefficients C20 and C22. By introducing the spacecraft's higher-order inertia integrals, a full fourth-order gravity gradient torque model of the spacecraft is established through the gravitational potential derivatives. Our full fourth-order model is more precise than previous fourth-order model due to the consideration of higher-order inertia integrals of the spacecraft. Some interesting conclusions about the gravity gradient torque model are reached. Then a numerical simulation is carried out to verify our model. In the numerical simulation, a special spacecraft consisted of 36 point masses connected by rigid massless rods is considered. We assume that the asteroid is in a uniform rotation around its maximum-moment principal axis, and the spacecraft is on the stationary orbit in the equatorial plane. Simulation results show that the motion of previous fourth-order model is quite different from the exact motion, while our full fourth-order model fits the exact motion very well. And our model is precise enough for practical applications.

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