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If we placed a comet at Mars L1 point would we get a coma and tail that would add volatiles to the Martian atmosphere? I've also read comets create a bow shock with the solar wind, slowing it down, so would the comet's coma and tail at L1 provide Mars's atmosphere some protection from the solar wind?

The coma can grow to the size of Jupiter or even bigger than the sun. The hydrogen gas halo can be as large as 1 AU in radius! But by the time a comet gets to within 1.5 AU of the sun, ie the orbit of Mars, the size decreases and the tail increases as the solar wind gets strong enough to blow the gas and dust away from the coma. https://en.wikipedia.org/wiki/Coma_(cometary)

The particles given off by the comet slow down and deflect the solar wind. So would this be enough to protect Mars from the solar wind? spacephysics.ucr.edu/index.php?content=solar_wind/sw/swq5.html

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TL;DR: It wouldn't work, because you wouldn't be able to keep the comet at L1.

The collinear Lagrangian points (L1, L2, and L3) are unstable; if a body were to be placed at one of these points, any perturbation - no matter how small - will move the body away from the point, at which point gravitational and/or centrifugal forces will move the body further and further away from the point. Think of a ball balanced on the tip of a hill. Anything placed at one of the collinear Lagrangian points, or in an orbit around one of said points, will require constant stationkeeping to keep it in place.

Unless you have a large enough rocket to counteract the inevitable perturbations from things such as the solar wind the comet is meant to protect against as one of its functions, plus enough propellant to keep said rocket fuelled for a long time, it wouldn't matter if a comet at Sun-Mars L1 would block the solar wind, since it wouldn't stay at L1 long enough to make any sort of meaningful difference.

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    $\begingroup$ Good answer! Since Mars' orbit is so elliptical, moving closer and farther from the Sun, the positions of the collinear Lagrangian points in the classical CR3BP (circular, restricted 3-body problem), as such, aren't even well defined to begin with. $\endgroup$ – uhoh Mar 22 '18 at 0:30
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    $\begingroup$ I'd put the TL;DR at the top ;-) $\endgroup$ – uhoh Mar 22 '18 at 0:30
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    $\begingroup$ @uhoh: Good idea - moved. $\endgroup$ – Sean Mar 22 '18 at 0:34
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    $\begingroup$ A comet is basically a pile of reaction mass and the Sun is power source, so if you could get the comet there, it wouldn't be hard to keep it on station. It would probably be enough just to use sun-shields to control which bit of the coment boiled off fastest. $\endgroup$ – Steve Linton Mar 22 '18 at 11:25
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    $\begingroup$ @uhoh I am considering, however I can't show it quantitatively now. :-( $\endgroup$ – peterh - Reinstate Monica Mar 22 '18 at 17:59

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