How weak would gravity need to be in order for a human to reliably survive the terminal velocity of falling through air?
(Context: watching scifi on a space station with a variety of artificial gravities, it occurred to me that medium-strength gravity would have some advantages; also I note that insects already seem to have this luxury on earth, with their small masses and high air resistances…)
Best Answer
References for the terminal falling velocity of a skydiver give numbers in the range of $54 m/s$ to $76 m/s$. I expect that the real range is even larger, since it's strongly affected by the orientation and body position of the skydiver.
For normal atmospheric drag on this scale, we have the fairly good approximation that force is proportional to velocity squared, $F_{air} \propto v^2$. For normal terminal falling conditions, the upward air force is exactly equal to gravity, and the air force is a function of velocity exclusively because we're assuming the same air composition for now.
You ask about a fall that is "reliably survivable", I should note that this would still NOT be a comfortable fall. In low gravity environments, you could expect some gnarly bounces to top it all off. I don't have a good reference for this, but I would anecdotally put it in the neighborhood of a $40 ft$ fall, which would equate to about $15 m/s$.
I will refer to the air force during a normal terminal velocity fall on Earth as $F_{air}$ and introduce $F_{air}'$ for the force on the new planet. I'll do some simple equivalencies to get an answer for the new gravity needed.
$$ m g = F_{air} = (\text{const}) v^2$$
$$\frac{F_{air}}{F_{air}'} = \frac{v^2}{v'^2} = \frac{g}{g'}$$
$$\frac{v}{v'} = \frac{60 m/s}{15 m/s} $$
$$ \frac{g}{g'} = \left(\frac{60}{15}\right)^2 = 16$$
So my answer is quite simply that gravity would have to be 1/16th as strong as it is on Earth, or $0.6 m/s$. Are there any bodies in the solar system quite like this? Wikipedia is helpful here. Several bodies come close, like Pluto, Eris, or Triton, but none of them have much of an atmosphere. It is fun to think about, but I doubt that an atmosphere of such a high density with such a low gravity will be found in our local celestial neighborhood.
Walking would be difficult if such a planet existed, but not impossible. The moon is 1/3rd the gravity of Earth, so this hypothetical planet would be roughly 5 times less gravity than the moon. It would be very bouncy, but still very different from zero-gravity.