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Trying to ask a series of questions but I'm breaking up the overall point into easier "chunks" to not make the overall question too broad.

Question 1: Designing a craft for transfer from Earth to Lunar Orbit.

Situation: Move three people, and/or supplies to lunar orbit.

Assume:

  • For ease of calculations, say the mass of the vehicle is 31,000 kg (similar mass of the SM and CM for Apollo 11) including the mass of the solar sail.

  • Starting Earth orbit is LEO, say 600 km (to greatly reduce drag rather than being at ISS levels), and the ending orbit around the Moon will be at 300 km (also similar to Apollo 11's orbit).

  • According to wikipedia: 800 x 800 m sail would generate 5 newtons (1.1 lbf) of force.

  • OR hoping someone can use the thrust calculations that apply: $$F=\frac{2RSA}{c}\sin^2\theta=9.113\times10^{-6}\frac{RA}{D^2}\sin^2\theta$$ Where, $F$ is the thrust; $R$ is the fraction of incident light; $D$ is the distance from the Sun in astronomical units; $S$ the solar flux in $W/m^2$; $c$ the speed of light; $A$ the sail area in $m^2$ and $\theta$ the sail tilt angle.(via Chris R.'s post: Solar sail thrust calculation)

Questions:

  • How large would the sails need to be to propel the ship from Earth to Lunar Orbit with a turnaround of 5 days (Apollo 11 took 4 days 6 hours 45 mins)? (relevant sub-question: what would be the mass of the sail itself, subtract that from the total assumed mass of 31,000 kg)

  • Would this method be feasible to perform the transfer orbit?

  • Could this trip be repeatable? As in, could they return from Lunar orbit to that of the Earth? - POSSIBLY ANSWERED by TidalWave (see comments)

I know there are issues like this trip like radiation protection, can only be made at certain times, etc. What I'm hoping is to basically prove or disprove a personal hypothesis about the feasibility and sustainability of a solar sail "powered" craft for purposes of shipping. More on what is shipped in another question :)

I tried to make this as concise and fill as many variables as I could so that those who are more in the know with this stuff and the math (that's giving me a headache LOL) could have an easier go. If I didn't explain something clearly enough or you need me to fill in more variables I can try my best to do that. Thanks in advance to those who answer :)

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    $\begingroup$ How about cycler orbits that could be sustained, instead of established by solar sails? I think that 5 day Earth-Moon "visit" orbits with gravity assist are possible (IIRC I've seen some 6-leg per synodic period lunar cyclers somewhere, with a rosetta shaped orbit... here's a 5-leg one as an example), and the sails could be used to reboost the orbit of the "castle" for the losses during "taxiing". $\endgroup$
    – TildalWave
    May 30, 2014 at 23:18
  • $\begingroup$ Thanks again for the formatting, first day here, still learning. The vessel was intended to link a space station in Earth orbit to another in Lunar orbit, so they would need to dock and transfer personnel and cargo. I removed that aspect from the question because it added too many variables. So I simplified it to just include the feasibility of the craft's propulsion from the Earth to the Moon. Perhaps I oversimplified. Gravity assisted return orbits would be substantially easier on the return flight. I seem to have forgotten good old Newton once again. Thanks. $\endgroup$
    – Alexinawe
    May 31, 2014 at 0:10

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How large would the sail need to be for a five day transfer? Too large. Solar sails are typically not very useful to increase your semimajor axis when orbiting a body other than the Sun (eg Earth). This is because when you're travelling away from the sun, the solar pressure will accelerate you, and when you're travelling towards the sun, it will slow you down, so the net result is 0. That's not strictly true, but you can make a sail much more useful if you have active control over its attitude. For example, have the sail perpendicular to the solar pressure when moving away, but parallel when moving towards. Still, solar radiation pressure is small.

Trans-Lunar Injection requires about 3 km/s delta V. Solar radiation pressure is about 10 micro newtons/meter squared. Assuming you have a turn around of 5 days, you'll need to get all the required force in that time. Your craft weighs 31,000 kg, so we have the mass. From F=ma we can see that since a=dV/dt, F=31,000 x 3000/(5 x 24 x 3600) which is 215N of constant force. Not too high, considering. The sail area however is Force/Pressure = 215/10E-6 = 215E5 or 21,500,000 meters squared. That's big, 49 times the size of Vatican city. That also has a bunch of assumptions that make this estimate lower than the true value (such as 100% pressure in right direction, zero shade, minimum delta V).

Now for the mass. If we make it out of pretty thin kapton, lets say 0.1 micrometer thickness, then we're looking at a reasonable material for the job. The sail weight would be 0.0000001 x 21500000 x 1420 (Density of kapton) then we're only talking a mass of about 3,000kg. Reasonable. Except when you consider the real mass driver in sail systems is the structure. Up to 99% of the mass is structure. If that's the case here, then you're talking about 300,000kg. And that's bigger than your system mass. Woops!

Is it feasible? No. Could you return using this method, yes. If you have attitude control.

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  • $\begingroup$ Well you could throw out some more specific dimensional analysis for the weight of the support structure too. If it is of a "parachute" type construction, then tethers might do the job. Divide 215 N by Kevlar's specific strength, and then assume you'll need at least 3 tethers, which are each as long as the sail is wide, then that only puts you at about 1 kg of kevlar. But, that's a deliberate underestimate which uses impossibly thin tethers and ignores the majority of the structural needs within the sail itself. Also increases sail mass due to lower angles. $\endgroup$
    – AlanSE
    Jun 2, 2014 at 14:38
  • $\begingroup$ @AlanSE I really couldn't. Not without a vastly more accuracy problem statement. I've made the assumption that the sail is planar at the rear of the craft. I've worked on a drag sail in this configuration, and generally speaking the mass of the 4 support booms used outweighed the kapton by such a large factor. I can however say a parachute probably wouldn't work. Parachutes only hold their shape due to constant atmospheric drag, a solar sail would have no way of being deployed if it was like a parachute. As you release the Kevlar it wouldn't spread out. $\endgroup$
    – ThePlanMan
    Jun 2, 2014 at 15:25
  • $\begingroup$ The angles of the sunlight would at least, in theory, hold its shape. That level of force-balance analysis isn't the issue. It certainly can unfurl itself with strictly those considerations. Tidal forces are probably larger than the photon pressure, so I have a hard time thinking of any practical version for the OP's concept. $\endgroup$
    – AlanSE
    Jun 2, 2014 at 17:58
  • $\begingroup$ @AlanSE The second point I made was that a parachute sail would never take up the shape. Typically with a parachute, you pull the cord and it opens up, it is then dragged out by the the force of the air. In space if you release an object from your spacecraft but keep it attached with string, it will stay right outside your craft. It wont move away and stretch the string. If it does eventually move away it would start to oscillate, causing move complex issues. $\endgroup$
    – ThePlanMan
    Jun 2, 2014 at 19:23
  • $\begingroup$ Re-reading your answer gave me a thought: contrary to what is written, Solar Sails must be able to propel themselves and a craft attached to it. The Japanese probes Akatsuki and IKAROS were successfully propelled via solar sail (though I believe they had a more conventionally tested engine as well and were closer to the Sun than the Earth). I don't deny my question here is not possible (or practical), but I have thought of a new question because of this answer. Thanks for the replies FraserOfSmeg and AlanSE. $\endgroup$
    – Alexinawe
    Jun 2, 2014 at 20:34

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