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Of course, research on Mars is first needed to explore if there is life or has been in the past.
But after that, boulders could be thrown from Phobos at specific areas on Mars, like Utopia Planitia, to evaporate or liquify enormous amounts of water ice and CO2 ice.
By dosing the number of impacts, destroying the surface could be minimized.

Could Phobos deliver enough boulders to significantly improve the atmosphere?

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$$\text{Some initial thoughts:}$$

Is Phobos even big enough to make a difference? Slowing Phobos down to hit the Martian atmosphere costs about 540m/s. Reaching escape velocity and then hitting the atmosphere costs more, but the impact energy is greater, corresponding to about [75 days](https://www.wolframalpha.com/input/?i=4(((mars+escape+velocity)%5E2++phobos+mass+%2F2)%2Fmars+area)%2Fmars+solar+flux) of sunlight on Mars ($1.36\cdot10^{23}J$). That is a significant amount of energy.

However, there are rocks much easier to throw than Phobos. The dwarf planet Vesta (too large to move, of course) is only 920m/s away from hitting Mars, and there are thousands of Phobos-size asteroids only about 50-100m/s away from hitting Mars at slightly more than escape velocity. Many asteroid are closer to Mars than Phobos itself in terms of $\Delta v$. Asteroids are also favourable as you can use them to hit the poles without any extra cost for an inclination change.

$$\text{What can we melt?}$$

The Martian polar icecaps contain about 3.2 million km³ of mixed ice, or about $3.5\cdot10^{18}kg$ of volatiles. That is equivalent to the mass 0.68 Earth atmospheres. Very promising. It only takes about $1\cdot10^{21}J$ to melt that, a lot less than crashing Phobos or an asteroid into Mars.

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  • $\begingroup$ Thank you for this very interesting alternative ! Is not the key question here: is it possible in orbital mechanics to trigger an event which releases much more energy than the energy that is needed to trigger that event ? In this case: one has to find an asteroid that is already heading to the environment of Mars so the orbit of it needs only to be corrected a little bit ? $\endgroup$ – Cornelisinspace Apr 23 '17 at 15:03
  • $\begingroup$ @Conelisinspace Yes you can! Here is an article showing exactly that kind of approach to catch an asteroid and set it into orbit around the Moon. $\endgroup$ – SE - stop firing the good guys Apr 23 '17 at 15:15
  • $\begingroup$ Possibly relevant: en.wikipedia.org/wiki/List_of_Mars-crossing_minor_planets ; "The smallest known MCAs have an absolute magnitude (H) of around 24 and are typically less than 100 meters in diameter." $\endgroup$ – Russell Borogove Apr 23 '17 at 19:51
  • $\begingroup$ @Hohmannfan Thank you again, looks promissing ! So, regarding Mars, we will just have to wait till the suitable asteroid appears ! $\endgroup$ – Cornelisinspace Apr 23 '17 at 20:44
  • $\begingroup$ @Conelisinspace Don't forget that you can mark an answer as 'accepted' if it anwered your question sufficiently. $\endgroup$ – SE - stop firing the good guys Apr 23 '17 at 21:07

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