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Can an astronaut use deodorant sprays which contain pressurized butane as cold gas thrusters to land on Deimos from Deimos' orbit?

If yes, how many cans would be required to get 5 m/s of delta-v for a human with and without a EVA suit?

What is the Isp and thrust of such a contraption?

Ignore problems like deodorant cans exploding or getting humans to Deimos and other life support systems needed.

IconDaemon
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Ashvin
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2 Answers2

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Deimos: radius 6.2km, mass 1.47 $\cdot$ 1015kg.

Let's pick an initial circular orbit radius at a safe 8km.

Orbital velocity calculator gives 3.502m/s orbital velocity.

To deorbit, we'd need to drop periapsis to ~6km so the same calculator gives us 3.242m/s for apoapsis of 8km and periapsis of 6. (Lithobraking by digging boots into the surface at 3m/s should be enough to shed the rest of the velocity.) We need to extract 26cm/s of delta-v out of our cans.

After a good bit of searching, I managed to find "For single-hole nozzle without surfactant, the droplets velocity was around 17m/s just near the nozzle exit (area 1)" source for an insecticide spray. That's 1.73s of specific impulse - good enough.

The rocket equation calculator for 100kg of astronaut (final mass), 17m/s propellant speed, and 0.26m/s delta-v gives 101.54kg of initial mass. So, 1.54kg. Big bathroom air fresheners are 550 grams, so 3 cans will do, 4 if you want to be safe. Just fire retrograde (can nozzle directed prograde) near apoapsis.

If you wanted to land vertically, shedding 100% of orbital velocity using the aerosol sprays, 22.86kg would be enough.

No Nonsense
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SF.
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    Awesome! What fragrance? – Organic Marble Apr 27 '21 at 13:16
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    @OrganicMarble In space no one can smell your spray. – SF. Apr 27 '21 at 13:23
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    "Lithobreaking" - love this term! – IconDaemon Apr 27 '21 at 15:45
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    Also after using up a can you can throw it to get some additional delta-v, and lose some mass like in multistage rockets! – flawr Apr 27 '21 at 21:39
  • Extension - does it make any difference it you somehow ignite the spray? I suspect not, the ejected mass is about the same. – Criggie Apr 27 '21 at 23:06
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    @Criggie No oxygen/oxidizer. If yo were able to ignite it and provide a de Laval nozzle (eh, even a cone out of tinfoil) you'd gain considerable amount of specific impulse. But without oxidizer that won't happen and without nozzle you won't gain anything. – SF. Apr 27 '21 at 23:21
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    If you're a good baseball pitcher, you'll probably gain more delta-V just by yeeting the can instead of spraying it. Bonus is you get all the delta-V from the empty can too! – March Ho Apr 28 '21 at 04:36
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    @MarchHo It would be hard not to send yourself into a spin though. The low thrust of spraying allows for adjustments/corrections on-the-fly. – SF. Apr 28 '21 at 08:39
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    @MarchHo Throwing the can introduces the danger of being hit on the back of the head by a can at orbital velocity. Admittedly the orbital velocity is far lower there, but it still could lead to unpleasant consequences. – zovits Apr 28 '21 at 09:38
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    @zovits Very slim chance though. The orbits will touch at this point but the orbital periods won't, and the chance the can will be in an orbit resonant to yours at any reasonably low factor is near zero - by the time the can is at the same altitude and location where you can be, you'll be completely elsewhere. – SF. Apr 28 '21 at 10:04
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    So you use the gas as required by the question, then throw the empty can. Use next can to first stabilise your spin, then slow down further... – user2702772 Apr 28 '21 at 13:27
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    @zovits the relative velocity of the empty can would only be as big as you threw it plus whatever speed you gained from emptying the next can in sequence. Since you're in a spacesuit, I suspect you might not even notice. – John Dvorak Apr 28 '21 at 15:13
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    No danger of being hit by the can--it's going to be in an escape orbit. (That is, assuming your suit is flexible enough that you can yeet decently.) You definitely need at least 4 cans, though--not all of the spray is going to be exactly aligned with the desired thrust axis. – Loren Pechtel Apr 29 '21 at 03:46
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    This all assumes that you cannot throw the full can at 61km/h or faster(most 10-year olds are up to this. equivalent of throwing the can total distance of 30m on earth). If you can, you are better off just throwing the whole dang thing. So I guess it depends on the quality of your spacesuit. – CuteKItty_pleaseStopBArking Apr 29 '21 at 14:16
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    I don’t think that the 550 grams of air freshener are all propellant and exhaust, are they? I’m pretty sure that they are mostly container. Unless we plan on throwing the container once empty. – RBarryYoung Apr 29 '21 at 14:42
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    Digging in your boots won't be so easy in microgravity. – Matt Apr 29 '21 at 20:48
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    @Matt true - a rope-and-anchor would be quite helpful, something you can drag through regolith and it digs itself in as you pull it. – SF. Apr 29 '21 at 20:51
  • Be careful how you're holding them when you discharge them; otherwise you'll start rotating around your center of mass. – RonJohn Apr 30 '21 at 03:31
  • Puncturing the can will provide a lot more thrust than using the valve. – Matt Apr 30 '21 at 08:46
  • @Matt Thrust, sure. Specific impulse - dubious. – SF. Apr 30 '21 at 09:51
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I don't think you would get any significant thrust from them on Deimos.

The maximum surface temperature is -4 °C (source).

The boiling point of butane is -2 °C (source).

I don't think the can would really spray at that temperature, and -4 °C is a light side's maximum (down to -112 °C on the dark side).

No Nonsense
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Jesse Bugden
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    Whoa! A major point here ! – Fattie Apr 29 '21 at 23:47
  • What would be the relevance of the surface-temperature given that the question's about thrust before landing? – Nat Apr 30 '21 at 02:22
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    @Nat the relevance is that the solar radiation at this distance is so low that the deodorant cans will condense to liquid, and thus offer no thrust at all. – Tim Apr 30 '21 at 08:11
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    @Tim: I think I'm just unclear about how this might come up. For example, if an astronaut were planning to descend with a spray-can, presumably they'd just keep it warm, e.g. in thermal-contact with their own body before use. – Nat Apr 30 '21 at 08:27
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    You take in account temperature, but not pressure. – Pierre Cathé Apr 30 '21 at 09:12
  • The points raised here need to be explored more ! – Fattie May 05 '21 at 20:32
  • @Nat Yes, the issue I'm highlighting could be mitigated. – Jesse Bugden Jul 04 '21 at 22:58
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    @PierreCathé I don't know if that's relevant, can you elaborate? Looking at https://astronomy.stackexchange.com/questions/28531/what-liquids-can-be-found-in-the-void-space I guess the question then is what is the vapour pressure of butane in the range of -112 to -4 C? (and does that produce thrust?) I found an equation but couldn't replicate the existing results here: https://www.eng-tips.com/viewthread.cfm?qid=136983 – Jesse Bugden Jul 04 '21 at 22:58
  • Deodorants and other such products besides the two isomers of butane, also contain propane. Propane's boiling point is much lower than that of both butane and isobutane, around -40 °C. – No Nonsense May 20 '22 at 21:27