Analysis of the evolution of particles ejected from Lunar Distant Retrograde Orbits
Authors: Pires dos Santos Pryscilla Maria , Winter Othon Cabo , Amarante Luiz Andre 
Published: September 2022

&lt;p align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;The idea of commercially exploring small asteroids in the neighborhood of the Earth-Moon is not new. The interest in such minor objects is due to the fact that many of them have high concentration of metals and volatile (Elvis 2012, 2014), especially water. &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;E&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;xploratory missions could collect water from a near-Earth asteroid (NEA) and transfer it to a lunar orbit, where it could be used to produce fuel for rockets, to maintain human population in space systems, from which round-trip trajectories to other bodies in solar system would be less costly (Sercel 2017, Jedicke 2018, Steklov 2019). However, whether in terms of asteroid resource mining or to improve the scientific techniques for extraction, processing and storage of materials from low-gravity bodies, the cis-lunar space has been considered as a good location (Brophy et al. 2012, Mazanek et al. 2016, Jedicke et al 2018).&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span lang=&quot;en-US&quot;&gt; W&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;e numerically investigate the evolution and fate of ejecta produced by a supposed impact of an artificial projectile with a small asteroid or a boulder from it. In this scenario, we develop an idealized, realistic model to set up the initial state of the ejected particles, considering ejecta released at speeds at or below 1ms&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;en-US&quot;&gt;&amp;#8722;1&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;en-US&quot;&gt; from those stable D&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;istant &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;R&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;etrograde &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;O&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;rbits&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt; previously determined by Pires &amp; Winter (2020). The purpose of this study is to verify how much material might be delivered to the Earth or to the Moon, besides collision time relative to the position it was ejected in orbit. Our approach allows to gain insight into the dynamics of ejecta clouds generated by mining asteroids in the Earth-Moon vicinity.&lt;/span&gt; &lt;span lang=&quot;en-US&quot;&gt;We&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt; verify how long do particles take to fall &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;on&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt; each body. The time it took for particles to collide with massive bodies is an important measure when we deal with the realistic prediction of moving material as a result of impact cratering events or for human deflection. Regardless of the ejection speed, particles that fall &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;on the&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt; Earth or &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;on&lt;/span&gt; &lt;span lang=&quot;en-US&quot;&gt;the Moon, completed they journey in less than 5 years after being launched into space, or take more than 500 years to have about 1% of them colliding with both bodies. &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;B&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;etween 5 and 500 years, the number of collisions is practically null.&lt;/span&gt; &lt;span lang=&quot;en-US&quot;&gt; Most part of the low-speed regolith are lost to space. &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;T&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;hey escape the system as time advances. &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;T&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;he process of loss of ejecta is stronger at the beginning of the numerical simulations and goes to approximately 10 years. &lt;/span&gt; &lt;span lang=&quot;en-US&quot;&gt;T&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;here were a sample of ejected particles that remain bounded to the Earth-Moon system during the whole time of numerical simulations (10 K-years).&lt;/span&gt; &lt;span lang=&quot;en-US&quot;&gt;Our &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;methodology is based on several numerical simulations of ejecta using an N-Body code to calculate their evolution accounting its gravity interaction with the massive bodies: the Earth and the Moon, beyond the Sun. &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;Our &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;numerical simulations inputs covers a small range of low-speed ejecta as a result of impact cratering events. &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;W&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;e have come up with results that have shown impact ejecta moving at speeds of order millimeter to meters-per-second reach the Earth or the Moon very quickly (less than 5 years) for a given range of initial conditions and assumptions. &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;We will present our main results in terms of histograms and orbital evolution.&lt;/span&gt;&lt;/p&gt;