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A possible way of heating up Mars is to use mirrors to direct more sunlight towards the planet. I am not asking about the feasibility or cost of such a gigantic project, but I have a question regarding the placement of the mirror in order to make it stay in place. If the mirror is placed trailing behind Mars, the light pressure required to compensate for the gravity of Mars is also adding a component force vector accelerating the mirror outward.

mirror trailing Mars

There are two different locations were this is not a problem, between Mars and the Sun, and directly behind Mars, both relatively useless for directing more light towards Mars.

I wonder, can the mirror orbit in circles outside the shadow cone, thereby adding the missing compensating force by inertia? mirror orbiting shadow cone

Is this possible? And if not, are there other ways of placing it?

edit: I am not looking for a solution were the mirrors orbit the planet.

To clarify, I want a location similar to L-points, but that also consider radiation pressure as well as inertia, gravity of Mars and gravity of the Sun, while still pointing the reflected light beam at Mars. In the terminology of Forward, this is a special kind of near Mars statite.

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  • $\begingroup$ Have you considered Fresnel lens in a statite-like areosynchronous low solar orbit? Alternatively, mirrors ahead of SML4 and trailing SML5 might work, but they'd have to be ginormous. Orbiting rainbows-like dispersed reflective clouds perhaps? $\endgroup$ – TildalWave Dec 21 '15 at 16:15
  • $\begingroup$ @TildalWave Interesting proposals, the low altitude solar statite especially, but do you have a solution for near-Mars space? $\endgroup$ – SE - stop firing the good guys Dec 21 '15 at 16:30
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    $\begingroup$ Your image of the shadow cone is wrong. The region of full shadow gets narrower as you go further from the planet. A mirror at Mars's L2 would see Mars blocking only a tiny part of the Suns disk, and so could reflect light onto the night side of Mars. Light pressure would push it out, so it would need to be a bit closer to Mars than L2, but not much. A hollow cylindrical mirror just sunward of L1 would also work, diverting light that would have narrowly missed Mars. $\endgroup$ – Steve Linton Jan 17 at 23:51
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    $\begingroup$ @uhoh, I am working on an answer, but do not expect to submit it before the bounty times out. I don't care that much about the rep points, but have found this a very interesting topic. I've looked at three options, with an optical system at L1, L2, or a Sun synchronous polar orbit. I've analyzed each option and found feasible answers for two. I'm in the process of documenting now, including drawings and references. $\endgroup$ – Vince 49 Jan 24 at 22:28
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    $\begingroup$ @uhoh, I'd almost finished my answer when something game up at work. It should be resolved by next Wednesday, the 12th I should then be able to get back to my answer, clean up a couple of sketches and, hopefully post soon after. $\endgroup$ – Vince 49 Feb 6 at 20:28
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You have missed another option for mirror placement, orbit them around the Mars. In much the same way as Larry Niven's, Ringworld is built. Your circle of mirrors are in a polar orbit of Mars. The mirrors always face the sun and direct the light to the surface of Mars. You might need to do something with the moons of Mars to prevent issues between the moons and your mirrors, but the upside is that they might be good material sources.

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  • $\begingroup$ I am specifically not interested in orbiting mirrors, as they a large amount of the time have a bad solar angle. The Ringworld arrangement is more useful for sunshades than mirrors. I am however interested if you can tell me how the light-pressure alter orbital mirrors. $\endgroup$ – SE - stop firing the good guys Dec 21 '15 at 15:23
  • $\begingroup$ @Hohmannfan have you looked at the Lagrangian points of Mars? $\endgroup$ – James Jenkins Dec 21 '15 at 15:31
  • $\begingroup$ I am totally aware of them, the reason I am asking is that the radiation pressure will totally change the conditions. $\endgroup$ – SE - stop firing the good guys Dec 21 '15 at 15:42
  • $\begingroup$ Also, a mirror in SML1 reflects light that is already going to hit Mars, in SML2 some of the light is blocked by Mars, and SML3,4,5 are too far away. $\endgroup$ – SE - stop firing the good guys Dec 21 '15 at 15:48
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    $\begingroup$ @Hohmannfan Yeah, that sentence came out all wrong! A perfect mirror in such a "terminator orbit" should not spin up by some YORP effect and won't overheat. But it would of course drift outwards (as long as its beam hits Mars it won't matter globally for terraforming). You'll never get away from paying for some station keeping. The sunlight itself should help power it, though. The high exhaust speed of solar electric propulsion, with massive nobel gasses, makes me think you'd only need to pay way less than half the Solar power reflected to Mars, to counteract the Solar pressure. $\endgroup$ – LocalFluff Dec 21 '15 at 17:12
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There are a couple of potential solutions to this problem. One would be to place the mirrors at a distance just a little closer to Mars than the L2 point and let the radiation pressure counter the weak Mars net gravity field. One doesn't have to be right in line either, but a "halo" orbit circling the Mars/Sun line would allow you to balance forces while avoiding Mars' shadow.

Another option is to use the radiation to "hover" over the poles at the very edge of the Mars gravity field. Again, a halo orbit of this point is a bit easier to maintain than trying to nail a single spot with zero relative velocity, but I'm fairly certain these types of halos aren't stable so they would need constant maintenance.

Finally, instead of a single flat mirror, one could employ a compound mirror like a Cassegrain telescope and use a halo orbit about the L1 point to redirect light that would otherwise miss the planet. The compound mirror preserves most of the light momentum so you only have to space the halo orbit a bit higher than the L1 point. To counteract the tendency to spiral out as a result of redirecting the beam on to the Mars, one could include a little additional mirror surface to spill some light away from Mars.

And, as mentioned, the use of a Fresnel lens at L1 is also workable and has been described in several books including Kim Stanley Robinson's Red Mars.

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  • $\begingroup$ The first proposed solution is interesting in that the Sun's radiation pressure would result in a repulsive $1/r^2$ force opposing the Sun's gravity's attractive $1/r^2$ force, as if the Sun were a little lower in mass, making the mass ratio slightly closer to unity and putting the new, effective $L2$ slightly farther from Mars rather than closer, wouldn't it? See plots in this answer. $\endgroup$ – uhoh Jan 22 at 3:55
  • $\begingroup$ @uhoh the reason the closer mass ratio puts $L2$ farther out is that it reduces the orbital velocity of the planet, lowering the angular velocity. But in the case of radiation pressure, the angular velocity is unchanged. $\endgroup$ – SE - stop firing the good guys Jan 22 at 6:10
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Strategically placed reflective material on Phobos on the tidally locked half facing mars. The mars moon appears one third compared to earths in the martian sky. If reflective, it would shine roughly ten times as bright as earths moon. Mars atmosphere is one hundredth thinner than earths. At that earths atmosphere cuts down on the affects of our moons reflective light benefits. On mars since the atmosphere is thinner the reflected light from phobos would be more substancial. There it would be next to permanent as can be and protected from space debris from the other half of Phobos.

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    $\begingroup$ This doesn't quite answer what I'm asking about. I'm specifically looking for the orbital dynamics of a solar sail, not alternative schemes for heating. $\endgroup$ – SE - stop firing the good guys Jan 18 at 12:17

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