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Let’s say we have a micro-gravity environment where people are staying afloat in the air because they have wings or some other means of resisting the low gravity, but then for some reason they find themselves bereft of that ability and start being pulled by the gravity… would they break their legs or be killed outright when they fell to the body generating the gravity, even though the gravity is low? How would that be calculated?

I am thinking of a dwarf planet with the same mass and gravity as Ceres. This planetoid has an earth-like atmosphere (hand wave that part for now). Characters there can float/fly, but an accident creates the scenario where one is lost and is being pulled by the gravity. What happens when he/she finally “crash lands”?

Edit-

Here's the scenario in more detail: human astronauts find this microgravity environment. Small planetoid/dwarf planet, approximately the size of Ceres, that has an atmosphere that is just like Earth's (again never mind how). The creatures there can keep afloat in the sky with their wings.

One of the astronauts goes exploring using a "jet pack" to fly around. A creature attacks him, damages the jet pack, and the astronaut is left with no means of getting around. He's just floating there. No one comes to his rescue. Sooner or later the gravity, though low, does pull on him and he starts "falling".

Barring a rescue or any ability of his own to "float/fly" what happens next? When he hits the ground does he go splat or does the lower gravity give him any chance of survival?

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    $\begingroup$ The answer to this depends on many factors. Specifically it depends on all of them. Altitude, air density, how broken the wings are, whether the individual is unconscious, whether the space is rotating quickly or not. However, one rule may help you: if you jump up, you will land with exactly the same speed as you left the surface, no matter what gravity you have. $\endgroup$ – Cort Ammon Jan 22 '18 at 21:12
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    $\begingroup$ It depends on the altitude and terminal velocity. Birds don't break their legs in normal scenarios, but should their wings fail them when flying, they can break more than just legs. $\endgroup$ – Alexander Jan 22 '18 at 21:17
  • $\begingroup$ @ Cort Ammon, So you would need me to give you more particulars? Would it help if I gave you that the planetoid is the size of Ceres and has an earth type atmosphere Again, handwave)? I don't need exactness, just a ball park understanding will do. $\endgroup$ – Len Jan 22 '18 at 21:31
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    $\begingroup$ It would also depend on their physiology. Are their bones sufficiently dense enough to withstand the force of terminal velocity, or are they light due to the decreased gravity? Do they spend all their time in the atmosphere, or do they walk on the surface? $\endgroup$ – Jonathan Jan 22 '18 at 21:49
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    $\begingroup$ You need far less gravity than that of Earth's moon (which is about 1/6 of Earth's gravity) to float. Do you mean soaring? But soaring is unrelated to low gravity, and certainly to microgravity, except insofar as a low gravity would make it easier (require less wing area), as long as you've still got the same air pressure, which you might not if you reduce the gravity sufficiently... Honestly, this feels like a XY question to me. What's the real problem you're actually trying to solve by asking this? $\endgroup$ – a CVn Jan 22 '18 at 21:56
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This question is ultimately about terminal velocity.

The equation to compute this is...

$$\sqrt{\frac{2mg}{ρAC_d}}$$

where m is the mass, g is acceleration due to gravity, ρ is the density of the fluid through which the object is falling, A is the projected area of the falling object, and $C_d$ is Drag Coefficient.

Given your Assumptions

  1. The size of Ceres
  2. Earth-like Atmosphere (handwavehandwavehandwave)

We can determine that your environment has an acceleration due to gravity of $0.28m/s^2$. The earthlike atmosphere gives us a density of $1.23kg/m^3$.

Assuming our falling person has the good sense to go belly-down for descent, an 'average human' would have a mass of $90kg$, and a projected area of $0.7m^2$. A splayed human has a Drag Coefficient of about $1$

So...

$$\sqrt{\frac{2*90*0.28}{1.23*0.7*1}}$$

Solving gives us...

$$V_{terminal} = 7.65m/s$$

Or, about 17 miles per hour at the low-end.

To check on the high-end, if the falling human assumes the narrowest possible profile, their projected Area is reduced to $0.18m^2$ and their Drag Coefficient is reduced to $0.7$. Re-calculating based on this gives us...

$$V_{terminal}=18.03m/s$$

Or, about 40 miles per hour.

So, depending on how they orient their body while falling, our plummeting human can reach a peak speed of between 17 and 40mph.

For comparison's sake:

17mph is about the speed at which a parachuter generally hits the ground. You need to know what you're doing to not get hurt, but even a bad landing is survivable with relatively minor injuries.

40mph is about how fast you'd hit the ground on Earth if you jumped off a 6 storey building. You might live, but you're going to break bones.

Disclaimer: this is a worse-case scenario that assumes the falling individual falls from a great enough height to achieve Terminal Velocity, and does nothing to arrest or slow their fall...like flapping. In a microgravity environment with earth-like atmosphere, that will make a difference.

Main Source, Secondary Source

Note: This question includes an assumption from the comments that has not yet been included into the main question

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  • $\begingroup$ So at the 17mph end he could survive the fall! Sweet. Basically if he knows something about aerodynamics and has the means to at least create drag and slow his descent somewhat (He knows what position to get into, he's wearing a coat that he opens to create a very makeshift parachute/glider), he might make it with maybe a sprained ankle or broken leg at most. Is that about right? $\endgroup$ – Len Jan 23 '18 at 18:41
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    $\begingroup$ @Len Yeah, pretty much. And anything he can do to further increase his projected area would slow him down even more. In such a low-gravity environment with normal atmospheric density, the largest determining factor in his terminal velocity is going to be his Projected Area. Put on a squirrel suit, and you really don't have to worry about falling anymore. $\endgroup$ – guildsbounty Jan 23 '18 at 19:32
  • $\begingroup$ One problem is that the orientation to fall as slow as possible and the orientation to land the most comfortably are pretty much polar opposites. You keep your terminal velocity lowest by spreading your arms and legs out and facing straight up or down. But you want to land on your feet, preferably with your legs fairly straight. $\endgroup$ – Ryan_L Jan 19 at 20:38

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