论文标题
地球腰带的四十亿年稳定性
Four Billion Year Stability of the Earth-Mars Belt
论文作者
论文摘要
先前的工作表明，在1.08 au $ <a <$ 1.28 au的区域中，最初是100 Myr的轨道稳定性，最初是100 Myr的近圆形和共面小物体。通过3000个颗粒的数值整合，我们研究了太阳系年龄的1.04-1.30 au的轨道。我们表明，在这个时间尺度上，除了一些与地球均值共振的位置外，只有覆盖$ a \ sim（1.09，1.17）$ au，$ e <0.04 $，$ i <1^\ circ $的较窄的“地球腰带”覆盖了$ a \ sim（1.09，1.17），而$ i <1^\ circ $具有4.5 gyr的最初Orbits的一半。除了平均动作共振之外，我们还可以看到$ν_3$，$ν_4$和$ν_6$世俗共振在GYR时间尺度上有助于外部（1.17-1.30 au）区域的长期不稳定。我们表明，通过与NEO稳态模型进行比较，所有（相当小的）接近地球物体（NEO）似乎与最近到达的瞬态物体一致。鉴于这些NEO的$ <200 $ m的比例，我们估计了半轴轴的Yarkovsky漂移速率，并使用它们来估计直径为100 km或更大的原始小行星在地球腰带中可能会存活。我们得出的结论是，在陆地行星形成末端的皮带区域中，只有几种100公里大小的小行星可以存在。
Previous work has demonstrated orbital stability for 100 Myr of initially near-circular and coplanar small bodies in a region termed the 'Earth-Mars belt' from 1.08 au $< a <$ 1.28 au. Via numerical integration of 3000 particles, we studied orbits from 1.04-1.30 au for the age of the Solar system. We show that on this time scale, except for a few locations where mean-motion resonances with Earth affect stability, only a narrower `Earth-Mars belt' covering $a\sim(1.09, 1.17)$ au, $e<0.04$, and $I<1^\circ$ has over half of the initial orbits survive for 4.5 Gyr. In addition to mean-motion resonances, we are able to see how the $ν_3$, $ν_4$, and $ν_6$ secular resonances contribute to long-term instability in the outer (1.17-1.30 au) region on Gyr time scales. We show that all of the (rather small) near-Earth objects (NEOs) in or close to the Earth-Mars belt appear to be consistent with recently arrived transient objects by comparing to a NEO steady-state model. Given the $<200$ m scale of these NEOs, we estimated the Yarkovsky drift rates in semimajor axis, and use these to estimate that primordial asteroids with a diameter of 100 km or larger in the Earth-Mars belt would likely survive. We conclude that only a few 100-km sized asteroids could have been present in the belt's region at the end of the terrestrial planet formation.
