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Our main character Felixa (female, weight about 70kg) is onboard the ISS (altitude 408 km / 254 miles), when something similar to Gravity happens, and the space station is destroyed.

Her assets:

  1. A parachute similar to the one Felix Baumgartner used.
  2. 5 kg CO$_2$ fire extinguisher (brought for experimental reasons)
  3. About 10 space suits with compressed air tanks, with about 12 pounds of liquid air each. The suits have built-in EVA controls for a total of 25 m/s

Is it possible for our main character to propel her body within Earth's gravity with sufficient air to survive all the way to the ground without any harm?

Assume she has sufficient training in parachutes and orbital science.

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  • $\begingroup$ During the re-entry her body will accelerate due to Earth's gravitational pull, she will probably pass out mid free fall when the force exerting on her body becomes unbearable actually the blood inside her head will pool against the back of her skull. In the animated film WALL-E the robot uses the fire extinguisher to propel itself in space and is not falling and I suspect your female subject can't really put out the fire during the atmospheric entry. Nice try though : ) $\endgroup$ – user6760 Sep 17 '15 at 9:56
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    $\begingroup$ Related: XKCD's orbital speed $\endgroup$ – mouviciel Sep 17 '15 at 12:43
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    $\begingroup$ @user6760 first, the acceleration from Earth gravity will be less than she would suffer at surface level (it is far away). Blood won't pull in her head, because blood will be subject to exactly the same forces that the rest of her body (free fall). What could be important is the (de/ac)celeration when she reaches denser strata of the atmosphera and has to decrease her entry velocity to the terminal velocity at such points. $\endgroup$ – SJuan76 Sep 17 '15 at 13:55
  • $\begingroup$ Stating how much does 1 pound of liquid air last for a normal human would be helpful if you want answers. Or are we supposed to know it? $\endgroup$ – SJuan76 Sep 17 '15 at 13:58
  • $\begingroup$ Don't you also have to factor in the weight of her EMU suit too? According to wikipedia the current ones weight 55Kg each. Also looking that the picture of one of these suits, there doesn't seem to be anyway you could easily put on a parachute harness. $\endgroup$ – Steve Bird Sep 17 '15 at 17:31
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Short story: Nope.

The biggest problem here is being able to change your velocity enough to cause you to de-orbit before you suffocate. If we say (for the sake of argument) that below 100km you experience enough drag to slow you down and get you home, they you still have to change your periapsis (point of closest approach) by 300km. To do this you'll have to change your velocity by something in the order of hundreds of meters per second. Your average fire extinguisher might change your velocity by 10m/s in a vacuum (call it 15 for good luck), and if you put all the other suits together and kick off you might get another few if you can jump really high while wearing the restrictive spacesuit.

EDIT: As Molot's comment points out, by paragraph above is probably wrong, however: you still need to make sure you have enough oxygen to survive until you hit the atmosphere, and even after that you still suffer my paragraph below. The time needed is going to be roughly 45 minutes with 110 m/s. I'm not sure how long the oxygen tanks will last, but it's worth assuming they'll last long enough.

Of course: all of the delta-V considerations are sorta thrown out when you consider that even if you manage to get yourself to the edge of the atmosphere you'll be hitting it at somewhere over 7km/s. For reference: Felix was moving at approximately 0km/s, as he wasn't in orbit but jumping from a balloon. Your average spacesuit does not have the right shape to survive that. He also only jumped from 39 km up, much lower than the edge of space, and so didn't have to worry about angle of re-entry or any of that stuff.

So: My recommendation is this: Use the extinguisher to control your attitude, point yourself at the sun, and enjoy as many sunrises as you can before suffocating.

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  • $\begingroup$ See here - basically you need between 61 m/s, and 168 m/s ΔV for LEO Space Shuttle. So "order of hundreds" is a mistake. Fire extinguisher gives you about 1/6 of what you need. Compressed air tanks can give similar amount each. Personal maneuvering units have ΔV between 3 and 80 m/s, so if they are there, total ΔV available may reach almost 1000m/s. Even without them it's 110m/s, well in range required to deorbit from LEO. $\endgroup$ – Mołot Sep 17 '15 at 12:54
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    $\begingroup$ I stand corrected. Still doesn't change the eventual outcome, sadly for the heroine... $\endgroup$ – Joe Bloggs Sep 17 '15 at 14:07
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Maybe enough to deorbit but not nearly enough to avoid reentry heating.

The ISS orbits at 7.66km/s or 4.76 miles per second. A CO2 cannister yields tens of meters per second $\Delta$v. So, Felixa will be able to deorbit herself but not enough to avoid the heat of reentry. Remember, orbit isn't so much high as fast. Hitting the atmosphere at 7km/s is going to hurt.

The ISS is already deorbiting so Felixa will too.

The ISS requires an average 7,000 kg of propellant each year for altitude maintenance, debris avoidance and attitude control. (emphasis mine)

Whether Felixa will run out of oxygen or not in the reentry period is immaterial. She doesn't have the $\Delta$v to "drop out of the sky" like Mr. Baumgartner did and will thus burn up on reentry.

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    $\begingroup$ According to this, 1.4kg of compressed nitrogen gives roughly 3m/s, so assumption that 5kg of extinguisher gases will give around 10m/s is not unreasonable. $\endgroup$ – Mołot Sep 17 '15 at 12:58
  • $\begingroup$ "A canister with only 10m/s isn't going to make a huge difference" - I disagree. Space shuttle manual says it only needs 60m/s to deorbit, and I do consider 1/6 of it a huge difference. Especially given the fact there are 10 more compressed gas canisters with space suits. (12 pound is slightly bigger than 5kg, and also pressure might be higher, too). $\endgroup$ – Mołot Sep 17 '15 at 13:12
  • $\begingroup$ 1/6th of the required thrust doesn't mean that you'll make it. True, that's not insignificant but it may not be sufficient. What we should be doing is the math required to deorbit a 70kg weight from ISS orbit (which I don't have). Comparing a 75000kg space shuttle to a 70kg human without doing any scaling is a bit ludicrous. $\endgroup$ – Green Sep 17 '15 at 13:36
  • $\begingroup$ Related: How could a 90 m/s delta-v be enough to commit the space shuttle to landing? (full disclosure: that is my own question) $\endgroup$ – a CVn Sep 17 '15 at 13:46
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Let's do some (rough!) sums and apply conservative assumptions. Felixa has a gravitation potential energy of

70*9.8*400000 = 274400000 J

But that assumes constant gravitation. Though gravity is not that much weaker at 400 km up. Let's say that GPE is about 200 MJ.

Kinetic energy is more interesting. Assuming a velocity of 7.66 km/s she has

0.5*70*7660^2 = 4107292000 J

So about 2 billion Joules of kinetic energy.

Okay, now how long does she have to get rid of it on the descent? In a parachute the terminal velocity is about 8 m/s. Assuming that she maintains this rate of descent from the top of the stratosphere (which is extremely favorable values, given that the atmosphere is 1/1000th the pressure as at sea level), then Felixa lands in about 6000 seconds.

So to shed all that energy, she needs to be doing about 350 kW. With more realistic assumptions, probably orders of magnitude more. Even more realistically, her chute will be torn to shreds and she'll hit the ground with a boom.

Yeah, she's toast. And no, nothing she can do can save her. None of what she has can match up to the numbers at play here.

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    $\begingroup$ Your KE equation is wrong, its 35*7600^2 (half mass times velocity squared). Unless she manages to slow considerably before reaching the upper atmosphere, she's going to burn up, so you can pretty much ignore the parachute cos she'll never deploy it. $\endgroup$ – KillingTime Sep 17 '15 at 17:12
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    $\begingroup$ Alright, fixed. Well, I'm just trying to throw some maths in there to show what the constraints are, under even very very optimistic assumptions. $\endgroup$ – Fhnuzoag Sep 17 '15 at 18:06

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