Dynamics of orbits close to asteroid 4179 Toutatis
Dynamics of orbits close to asteroid 4179 Toutatis
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DOI：
10.1006/icar.1997.5870
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发表时间：
1998-03-01
期刊：
影响因子：
3.2
通讯作者：
Suzuki, S
中科院分区：
文献类型：
--
作者：
Scheeres, DJ;Ostro, SJ;Suzuki, S
我们使用雷达导出的物理模型4179 Toutatis（哈德逊and Ostro 1995，Science 270，84-86），以研究不规则形状，非主轴旋转器周围的近轨道动力学。这个天体的轨道动力学与匀速旋转的小行星的动力学明显不同。本文的结果一般适用于非主轴转动状态下物体的轨道动力学。雷达结果支持Toutatis具有均匀密度分布的假设，我们假设密度为2.5 g/cc。小行星的重力场是在其外接球体外使用截断谐波展开计算的，而在该球体内使用任意多面体的势场的封闭形式表达式计算的。由于小行星的复杂旋转，完整的运动方程在Toutatis固定坐标系中具有时间周期性。该系统是哈密尔顿的，具有这种系统的所有特征，包括相体积守恒，但没有运动的雅可比常数，零速度表面不能用于分析系统的行为。我们也用拉格朗日行星形式的运动方程研究了一些近轨道动力学。人们发现，轨道要素变化极小的准周期性“冻结轨道”族存在于非常靠近小行星的地方;其中一些是稳定的，因此可以容纳天然或人造卫星。一个逆行的冻结轨道家族特别强大，持续到大约2.5公里的半长轴，相当于Toutatis最长维度的一半。我们确定家庭的周期性轨道，重复Toutatis固定的框架。由于运动方程的时间周期性质，所有围绕图塔蒂斯的周期轨道在其身体固定的框架必须与这些方程相关的5.42天周期相当。对稳定和不稳定的周期轨道进行了精确计算。作用在Toutatis上的粒子上的表面力的总和是随时间变化的，因此小行星上和小行星中的粒子以5.42天的周期不断震动，这可能增强了风化层分布的均匀性。全球重力斜坡地图显示，对于这样一个细长的，形状不规则的物体来说，它是令人惊讶的浅，全球平均16度，96%的表面小于35度。切向加速度的全局图显示，在70%的表面上，没有大于0.5 mm/s（2）的值，平均值为0.2 mm/s（2），并且小于0.25 mm/s（2）。垂直于表面发射的逃逸速度的全球地图显示，在大多数表面上，逃逸速度在1.2和1.8米/秒之间。这些映射的量中的每一个都具有小的周期性变化。我们发现了离开表面的轨迹，持续存在于冻结轨道周围的相空间区域，然后在飞行时间超过100天后撞击表面。返回轨道持续数年似乎是可能的。虽然一个均匀旋转的小行星优先积累非逃逸的喷出物在其领先的一面，Toutatis积累喷出物均匀在其表面。我们在惯性系和物体固定系中绘制了各种近距离轨道。(C)北京：科学出版社.
We use a radar-derived physical model of 4179 Toutatis (Hudson and Ostro 1995, Science 270, 84-86) to investigate close-orbit dynamics around that irregularly shaped, non-principal-axis rotator. The orbital dynamics about this body are markedly different than the dynamics about uniformly rotating asteroids. The results of this paper are generally applicable to orbit dynamics about bodies in a non-principal-axis rotation state. The radar results support the hypothesis that Toutatis has a homogeneous density distribution, and we assume a density of 2.5 g/cc. The asteroid's gravity field is computed using a truncated harmonic expansion when outside of its circumscribing sphere and a closed-form expression for the potential field of an arbitrary polyhedron when inside that sphere. The complete equations of motion are time-periodic in the Toutatis-fixed frame due to the complex rotation of the asteroid. The system is Hamiltonian and has all the characteristics of such a system, including conservation of phase volume, but there is no Jacobi constant of the motion and zero velocity surfaces cannot be used to analyze the system's behavior. We also examine some of the close-orbit dynamics with the Lagrange planetary form of the equations of motion. Families of quasi-periodic "frozen orbits" that shaw minimal variations in orbital elements are found to exist very close to the asteroid; some of them are stable and hence can hold natural or artificial satellites. A retrograde family of frozen orbits is especially robust and persists down to semi-major axes of about 2.5 km, comparable to half of Toutatis' longest dimension. We identify families of periodic orbits, which repeat in the Toutatis-fixed frame. Due to the time-periodic nature of the equations of motion, all periodic orbits about Toutatis in its body-fixed frame must be commensurate with the 5.42-day period associated with those equations. Exact calculations of both stable and unstable periodic orbits are made. The sum of surface forces acting on a particle on Toutatis is time-varying, so particles on and in the asteroid are being continually shaken with a period of 5.42 days, perhaps enhancing the uniformity of the regolith distribution. A global map of the gravitational slope reveals that it is surprisingly shallow for such an elongated, irregularly shaped object, averaging 16 degrees globally and less than 35 degrees over 96% of the surface. A global map of tangential accelerations shows no values larger than 0.5 mm/s(2), an average value of 0.2 mm/s(2), and less than 0.25 mm/s(2) over 70% of the surface. A global map of the escape speed for launch normal to the surface shows that quantity to be between 1.2 and 1.8 m/s over most of the surface. Each of these mapped quantities has small periodic variations. We have found trajectories that leave the surface, persist in the region of phase space around a frozen orbit, and then impact the surface after a flight time of more than 100 days. Return orbit durations of years seem possible. Whereas a uniformly rotating asteroid preferentially accumulates non-escaping ejecta on its leading sides, Toutatis accumulates ejecta uniformly over its surface. We render a variety of close orbits in inertial and body-fixed frames. (C) 1998 Academic Press.