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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.

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    $\begingroup$ wow. Now I want the answer as well $\endgroup$ – compi Apr 27 at 6:29
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    $\begingroup$ Not that one is likely to find cans of deodorant in a spacecraft :-); but the estimates for total mass & propellant speed are fun to consider. $\endgroup$ – Carl Witthoft Apr 27 at 12:18
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    $\begingroup$ I suggest to migrate this to what-if.xkcd.com. It have the right spirit for that :-) $\endgroup$ – val is still with Monica Apr 28 at 22:22
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    $\begingroup$ Hoping Axe will depict this in a commercial now $\endgroup$ – Andy Apr 29 at 0:51
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    $\begingroup$ A human in vacuum without an EVA suit will quickly stop being a human. $\endgroup$ – RBarryYoung Apr 29 at 14:39
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Deimos: Radius 6.2 km, Mass 1.47e15kg.

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 17 m/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 popellant 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.

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    $\begingroup$ Awesome! What fragrance? $\endgroup$ – Organic Marble Apr 27 at 13:16
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    $\begingroup$ @OrganicMarble In space no one can smell your spray. $\endgroup$ – SF. Apr 27 at 13:23
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    $\begingroup$ "Lithobreaking" - love this term! $\endgroup$ – IconDaemon Apr 27 at 15:45
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    $\begingroup$ Also after using up a can you can throw it to get some additional delta-v, and lose some mass like in multistage rockets! $\endgroup$ – flawr Apr 27 at 21:39
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    $\begingroup$ @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. $\endgroup$ – SF. Apr 27 at 23:21
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I don't think you would get any significant thrust from them on Diemos.

The max surface temperature is -4 C (https://solarsystem.nasa.gov/moons/mars-moons/phobos/in-depth/).

The boiling point of butane is -2 C (https://www.gasit.co.uk/support/knowledgebase.php?article=59).

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

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    $\begingroup$ Whoa! A major point here ! $\endgroup$ – Fattie Apr 29 at 23:47
  • $\begingroup$ What would be the relevance of the surface-temperature given that the question's about thrust before landing? $\endgroup$ – Nat Apr 30 at 2:22
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    $\begingroup$ @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. $\endgroup$ – Tim Apr 30 at 8:11
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    $\begingroup$ @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. $\endgroup$ – Nat Apr 30 at 8:27
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    $\begingroup$ You take in account temperature, but not pressure. $\endgroup$ – Pierre Cathé Apr 30 at 9:12

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