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Is there an approximation of what a human would look like walking on Mars? Would it be closer to how the astronauts walked on the moon or the way we walk on the Earth?

With the gravitational acceleration of Earth being 9.8 m/s2, the moon 1.625 m/s2, and Mars 3.71 m/s2, about one-third that of the Earth and a little more than twice that of the moon, it would seem to me a person's gait on Mars would be a lot closer to that of the moon than the Earth.

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    $\begingroup$ What about looking up the surface gravity values for Earth, Mars and Moon and adding them to your question? $\endgroup$ – Uwe Dec 15 '18 at 21:05
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    $\begingroup$ +1 I'm hoping that this walking can include hiking, which would then qualify for the reduced-gravity-sports tag. It's not a perfect fit, but people searching for changes in human movement due to low gravity will now find your question and its answers. $\endgroup$ – uhoh Dec 16 '18 at 1:39
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Indeed Mars's gravity is about twice that of the moon, but getting around on your own two feet will probably be similar, at least when in an environmental suit.

In my answer to the question about walking on Titan I discussed the situation with environmental suits: their stiffness makes a normal gait more effort than we're accustomed to. This led to the Apollo astronauts adopting the "hop" they used on the lunar surface.

Two main aspects can make an environmental suit stiff: pressure containment, and thermal insulation. On Mars the thermal insulation will be much less of a factor than on Titan, being (on average) ~120 K warmer. But Mars's surface atmospheric pressure is only ~6 N/m^2, less than 1/100 of Earth's atmospheric pressure, so for suit pressure containment purposes it is essentially a vacuum. Unless there are significant advances in suit hip and knee joint technologies (discussion of suit technologies here), Mars suits will have pretty much the same stiffness as Apollo suits. So while EVA, the "hop" will probably be popular on Mars as well, until suit technology improves significantly.

Inside a Mars station, or any pressurized and thermally controlled facility, the story is completely different. You'd be in a "shirt-sleeves" environment, similar to being in the ISS except for the gravity, so the clothing you'd be wearing wouldn't impede your leg movements much at all. The usual, Earth-style gait would work very well there, as long as you don't mind going a bit slower.

On Earth, a significant factor in the speed of a comfortable gait is the pendulum frequency (or period) of the human leg, which is a function of the leg's length, its mass distribution, and notably, the acceleration of gravity. If you walk such that this pendulum motion brings your leg from behind you to in front of you, you have to expend little energy to get that leg in front of you. When you speed up—walking faster than your usual speed—you're driving your legs faster than that pendulum rate, so you have to supply more of the energy with your muscles to get them to move that fast. The gravity at Mars is roughly 1/3 that on Earth, and the natural oscillation period of a pendulum is proportional to the inverse square root of the gravitational acceleration, that pendulum period on Mars should be about 1.6 times longer than on Earth, making for a slower gait, unless you "hoof it".

If you're hoofing it indoors you have to be careful, especially when first arriving at Mars, that you don't bump your head on the ceiling! ;-)

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    $\begingroup$ @TomSpiker your answer is better than my question. I did not think about how different it would be inside compared to outside with the environmental suit. Excellent. $\endgroup$ – Bob516 Dec 15 '18 at 22:47

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