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Based on the Newton's law of gravity

$$g= \frac{GM}{r^2}$$

we calculate the gravity acceleration, gravity exerted, etc.

And now, provided there exist the correct gasses to create a humanly survivable atmosphere, the only thing remaining is to have just enough gravity so that the gasses don't escape. And boom: we have our atmosphere.

Now on to my question:

I want to have enough gravity so as to handicap the humans a bit, but not cause them problems, whether that means more or less gravity.

I'm leaning towards less gravity, but, what's the limit I can reach, without destroying my atmosphere, and being able to have them live in it for an extended period of time without many long term health problems?

The loosening of the skeleton and weakening of our muscles is somewhat acceptable within a limit.

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Since one of the things you want to know what atmosphere a planet can hold onto which is calculated by escape velocity, there is this fun little gas retention plot for planets with different density, radius, and temperature.

If you know the escape velocity of your planet, you can find Jeans escape pretty easily. And if you don't know escape velocity you can mess around with even more variables here to be able to get it with math done for you. If you use that place be sure to remember they give you Escape Velocity in Kilometers/Second.

Velocity of Escape Jeans (In Meters/Second) = Escape Velocity / 6 (In Meters/Second)

Now that you know this, you are further along into seeing the specific number of how easy or hard it is for a molecule of something to get out of your atmosphere. And if you know the average temperature of the planet, you can even calculate how fast those molecules are going and compare it to the escape velocity.

$$ \text{Velocity of Molecule (in m/s)} \\ = \sqrt{\frac{3 \times \text{Molar Gas Constant} \times \text{Planet's Temperature in Kelvin}}{\text{Molecular Weight}}} $$

Molar Gas Constant = 8314.41

Some Molecular Weights include,

  • H2O = 18
  • O2 = 32
  • CO2 = 44

Any gas that you calculate that has a higher Molecular Velocity than Jeans Escape, then your planet can not hold onto it for long, if at all.

I get my info here from Atomic Rockets section on Escape Velocity and Jeans Escape. In case I messed up putting it here you can go look around for yourself.

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  • $\begingroup$ Neat gadget, but it really should show the surface gravity of the world also. A bigger, lower density world can hold atmosphere despite having a lower surface gravity. $\endgroup$ – Loren Pechtel Apr 27 '17 at 0:10
  • $\begingroup$ True, you can go between a large radius and low density or small radius and high density. Changing it though would change the gravity and mass from the formulas I have read. Could be wrong myself though, I have been really interested in this type of question too. Artifexian is also a pretty fun learning tool. youtube.com/watch?v=RxbIoIM_Uck $\endgroup$ – Ferret Civilization Apr 27 '17 at 0:53
  • $\begingroup$ Well, your answer is pretty much the best one, and it truly helps a lot. Accepted! $\endgroup$ – Marios Zaglas Apr 27 '17 at 19:42
  • $\begingroup$ Well thanks, sorry I could not try to go and answer everything. Probably would have just continued trying to pull up some vaguely close to what you wanted answers. Though a good side note for pushing your humans to the limit with gravity is also the atmospheric pressure which has plenty of reading. Mount Everest can give some good examples of having that be too low. hypertextbook.com/facts/2001/JaredGoldberger.shtml pbs.org/wgbh/nova/everest/exposure/pressure.html $\endgroup$ – Ferret Civilization Apr 28 '17 at 2:36
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Yeah, you can balance the two out.

I don't have any numbers to give you, but keep in mind that a strong magnetic field can also help keep in gases.

Gases basically can't reach escape velocity under even the most extreme weather on Earth. Solar winds and meteors are what strip atmospheres away. So as long as you don't have tiny gravity, just make your planet's core hot enough to balance out the lower gravity and you'll have a good enough excuse for an atmosphere.

Read: How Mars Lost its Atmosphere

Mars probably has gravity enough to disorient people. I'm sure it has some health side effects, but I'd say it's on the safe side of that border.

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  • $\begingroup$ “the two”? Are you talking about supplying new gas? $\endgroup$ – JDługosz Apr 27 '17 at 5:21
  • $\begingroup$ «I'd say it's on the safe side of that border.» speaking as an expert in astro-health? You should say why your feeling is better than the OP's guessing. $\endgroup$ – JDługosz Apr 27 '17 at 5:23

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