Ejection of solid bodies from comets and its dynamical significance for velocity and rotation of comet
Authors: Czechowski Leszek 
Published: September 2022

&lt;p&gt;&lt;strong&gt;Ejection of solid bodies from comets and its dynamical significance for velocity and rotation of comet&lt;/strong&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;&amp;#160;&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Introduction&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;Observations of comets 9P/Tempe 1 and 67P/Churyumov &amp;#8211; Gerasimenko revealed existence of several ejections of significant masses [1, 2, 3].&lt;/p&gt;
&lt;p&gt;In the present paper we investigate dynamic effects for the comet of similar ejections. Contrary to research presented in [6], we consider here ejections with higher velocity, i.e., 0.71 m s&lt;sup&gt;-1&lt;/sup&gt; or higher from different places mainly on the surface of the comet 67P/Churyumov &amp;#8211; Gerasimenko and some our model body.&amp;#160;&lt;/p&gt;
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&lt;p&gt;&lt;strong&gt;Gravitational field and mechanism of ejection&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;The gravitational field of considered comet is complicated [1, 4]. There are several regions of different slopes of the comet's surface in respect to the local gravity. Note also non-spherical shape of cometary surface of constant potential [6].&lt;/p&gt;
&lt;p&gt;In [6] there are considered slow ejecta (i.e. ejecta with velocity below escape velocity). Here we consider the ejecta with the velocity 0.71 m s&lt;sup&gt;-1&lt;/sup&gt; or higher. Often, the initial velocity is higher than the escape velocity. Note, however, that the for comets of irregular shape, the escape velocity depends strongly on the site of ejection.&lt;/p&gt;
&lt;p&gt;A following model of processes leading to the &amp;#160;ejection is assumed. It is based on [3, 4]. The phase changes supply the heat to a certain underground volume. If the pressure exceeds some critical value then some fragments will be ejected into space. Many places in the comet could be a result of such processes [3]. Note that the initial velocity of ejecta are assumed to be perpendicular to the physical surface. This assumption is used successfully in [4].&lt;/p&gt;
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&lt;p&gt;&lt;strong&gt;Calculations&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;We consider ejecta from different places on comet 67P/G-C. For the comet dynamical effects of slow ejecta is more limited but also more complicated because the comet obtained back some momentum and spin &amp;#160;from the landing ejecta.&lt;/p&gt;
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&lt;p&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160; We performed calculations for 530 ejected particles from different places in the comet 67P/C-G and some for our model body. Total mass of ejecta for the comet 67P is chosen to be: 10&lt;sup&gt;-6&lt;/sup&gt; or 10&lt;sup&gt;-5&lt;/sup&gt; of the mass of the whole comet. These values correspond to ~10&lt;sup&gt;5 &lt;/sup&gt;kg and &lt;sup&gt;&amp;#160;&lt;/sup&gt;~10&lt;sup&gt;6&lt;/sup&gt; kg for each ejected particles (it depends on the number of particles used for given calculation). The following velocities of ejecta are used: 0.7, 1.0, 10 m s&lt;sup&gt;-1&lt;/sup&gt;. Other values are used for the model body. For calculations the program developed by L. Czechowski was used.&lt;/p&gt;
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&lt;p&gt;&lt;strong&gt;Preliminary results and conclusions&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;In general, the effect of ejecta on comet's motion is primarily determined by the total momentum and angular momentum of the ejected particles. However, unlike the gases ejected by comet jets, the movement of solid particles depends heavily on the comet's gravitational field. The solid particles can return to the comet, giving up some of their momentum. Therefore, they have a different effect on comet motion and should be taken into account in more accurate calculations of comet's motion.&lt;/p&gt;
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&lt;p&gt;&lt;strong&gt;Acknowledgements &lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;The research is partly supported by Polish National Science Centre (decision &amp;#160;2018/31/B/ST10/00169)&lt;/p&gt;
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&lt;p&gt;&lt;strong&gt;References &lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;[1] Czechowski L., (2017) Dynamics of landslides on comets of irregular shape. Geophysical Research Abstract. EGU 2017 April, 26, 2017&lt;/p&gt;
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&lt;p&gt;[2] Jorda, L., R. et al. (2016) The global shape, density and rotation of Comet 67P/Churyumov-Gerasimenko from preperihelion Rosetta/OSIRIS observations, Icarus, 277, 257-278, ISSN 0019-1035, https://doi.org/10.1016/ j.icarus.2016.05. 002.&lt;/p&gt;
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&lt;p&gt;[3] Kossacki K., Czechowski L., 2018. Comet 67p/Churyumov&amp;#8211;Gerasimenko, possible &amp;#160;origin of the depression Hatmehit. Icarus vol. 305, pp. 1-14, doi: 10.1016/j.icarus.2017.12.027&lt;/p&gt;
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&lt;p&gt;[4] Czechowski L. and Kossacki K. J. 2021. Dynamics of material ejected from depression Hatmehit and landslides on comet 67P/Churyumov&amp;#8211;Gerasimenko. Planetary and Space Science 209, 105358, https://doi.org/10.1016/j.pss.2021. 105358 &amp;#160;&lt;/p&gt;