Some problems of gravity assist and terraforming of Mars

Some problems of gravity assist and terraforming of Mars IntroductionHere we consider versions of terraforming that would allow colonists to live without pressure suits. The current mass of the Martian atmosphere is 2.5x1016 kg [1]. We consider 4 variants of terraforming. C indicates how many times we need to increase the mass of the atmosphere. For version v1 we assume a pressure of 10 kPa at the bottom of Hellas Planitia, C= 8.6, for v2 we use 10 kPa at the reference level for Mars and C=16.4, for v3 we use 101.3 kPa at the bottom of Hellas Planitia, C= 87.3, and for v4 we use 101.3 kPa at the reference level for Mars, C= 166.1.For variant v4, 1 body with a radius of ~100 km (and density of 1000 kg m-3) would be sufficient.  Possible sources Celestial bodies orbiting far from the Sun contain large amounts of water, CO2, nitrogen, etc. There are two places where there are enough bodies useful to our problem: the Kuiper Belt (KB) and the Oort Cloud (OC) [2]. The Kuiper Belt (KB) contains over 70,000 objects with diameters larger than 100 km. The mass of the KB is large enough [2, 3]. The total mass of the OC is ~3×1025 kg [4]. The problem is the large distance from the Sun, so we consider only the KB as the source. Transporting bodies Initially ion engines change orbit of the chosen body, in order to later use the effect of gravity assist. This requires precise maneuvering. Since there are many bodies in the KB whose size is sufficient for gravity assist, we assume that a change in velocity of ~50 m/s  (using the engine) is sufficient. However, in our case, gravity assist is fraught with significant danger. KB bodies are unstable when volatiles escape. To calculate possible tidal effects, we use the methods developed in [5].The gravity assist may be used to reduce the relative velocity of Mars and the impactor. This is important because strong heating of the atmosphere will lead to the escape of gases [6]. [1] Mars Fact Sheet. NASA. [2] Hargitai, H. and Kereszturi, A., 2015, ISBN 978-1-4614-3133-6. [3] Lorenzo I. 2007. Monthly Notices RAS. 4 (375), 1311–1314.[4] Weissman, P. R. 1983. Astronomy and Astrophysics. 118 (1): 90–94. [5] Czechowski, L., 1991. Earth, Moon and Planets, 52, 2, 113-130 DOI: 10.1007/BF00054178[6] Czechowski, L., et al., 2023. Icarus, doi.org/10.1016/j.icarus. 2023.115473.