汽车的随机行走及其与行星的碰撞概率
The random walk of cars and their collision probabilities with planets
摘要：
2018年2月6日，SpaceX在火星轨道上发射了一辆特斯拉跑车。我们进行N体模拟，以确定未来1500万年该物体的命运。轨道演变最初主要是与地球近距离接触。虽然由于这些重复的混沌散射，在未来几个世纪之后无法预测精确的轨道，但通过统计分析大量可能的轨道，可以可靠地预测长期结果，这些轨道具有轻微的扰动初始条件。与地球的重复引力散射导致随机行走。与地球、金星和太阳的碰撞是跑车轨道演变的主要原因。与水星和火星的碰撞，或者木星从太阳系的抛射，都是极不可能的。我们计算出特斯拉的动态半衰期约为1500万年，其中约22%，12%和12%的Roadster轨道实现在一个半衰期内分别影响地球，金星和太阳。由于平均运动和长期共振，我们的系综中的偏心率和倾角随着时间的推移而增加，与类地行星的撞击率在几百万年后会下降，而对太阳的撞击率大致保持不变。
英文摘要：
On February 6th, 2018 SpaceX launched a Tesla Roadster on a Mars-crossing orbit. We perform N-body simulations to determine the fate of the object over the next 15 Myr. The orbital evolution is initially dominated by close encounters with the Earth. While a precise orbit can not be predicted beyond the next several centuries due to these repeated chaotic scatterings, one can reliably predict the long-term outcomes by statistically analyzing a large suite of possible trajectories with slightly perturbed initial conditions. Repeated gravitational scatterings with Earth lead to a random walk. Collisions with the Earth, Venus and the Sun represent primary sinks for the Roadster's orbital evolution. Collisions with Mercury and Mars, or ejections from the Solar System by Jupiter, are highly unlikely. We calculate a dynamical half-life of the Tesla of approximately 15 Myr, with some 22%, 12% and 12% of Roadster orbit realizations impacting the Earth, Venus, and the Sun within one half-life, respectively. Because the eccentricities and inclinations in our ensemble increase over time due to mean-motion and secular resonances, the impact rates with the terrestrial planets decrease beyond a few million years, whereas the impact rate on the Sun remains roughly constant.
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