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If you didn't have to deal with a cumbersome spacesuit, I imagine you could run, but you'd lean over much more towards the horizontal - like maybe 45° or lower, so each 'step' would be a push backwards in line with your longitudinal axis. Don't waste energy by bounding up.
Source: wild speculation.
In all fairness I'm speculating on this too, so feel free to poke holes in my argument.
We probably need to refine our goal question a little bit. Is it:
or
What you're suggesting is matching the amount of effort to move to the body with the position of the center of gravity on the body to be closer to equal to on Earth. I don't know the math here.
This might work toward the sprint scenario. However I think we'd run into in efficiencies in our physiology toward the other scenario. Walking or running for bipeds like us means we lean forward to move our center of gravity in a space in front of us. We're essentially falling forward, and moving our feet under that center of gravity so we don't fall down. On Earth a sprint might move our body's center of gravity up to the upper part of our chest, like this runner here where I've put the red line:
With only 1/6th the gravity you'd need to move the center of gravity WAY farther forward to the top of your head (and beyond?). At the lean you would have to have, would you even be able to draw your knees up to your chest, or would they drag on the ground as you move your leg forward to take the next step. Then the body mechanics wouldn't match our evolutionary advantages for running, but closer to climbing a ladder or running up very steep stairs. While we can do those things, our physiology isn't really optimized for it.
Further, we don't have the ability to perfectly translate all of our motion forward. Some of it is going to go up. Not much "up" would mean we lose friction with the ground and have to wait to fall back to re-engage to impart more forward motion.
Do these two things together mean that because our center of gravity is so far forward, and errant "up" motion would cause us to fall flat on our faces? Certainly we could dial back the forward motion to prevent the fall, but at that point perhaps we aren't leaning very far over, and therefor aren't moving forward very fast with each step.
Here's some work from the Univerity of Alaska explaining the physics of running here on Earth I used for reference in forming my opinion source
Full disclaimer, I am NOT a Kinesiologist, doctor, or physicist. I have no credentials of expertise in this area. I'm just some dude on the internet. Take everything I'm saying as suspect.
One thing the lean does is use gravity to cancel out the torque caused by our feet doing the moving. If you don't lean, you fall backwards because your feet move faster than the rest of your body. It's not so much that we're falling forward and catching ourselves as the lean position is where we need to be for equilibrium.
The angle plays into it, but it's more about the distance ahead of the feet that the centre of mass is to cancel out that torque. Gravity is weaker on the moon, but that also means your foot can't apply as much pressure, so there would be less torque to cancel. Leaning more would further reduce that pressure.
Ultimately, I think the way we'd end up doing it (assuming a more mobile suit or let's say within a pressurized dome) is we'd have to learn to apply less force when trying to sprint/run on the moon. Then we can find an equilibrium that has a similar lean to what we do on earth (and I agree that we didn't evolve for running on the moon and would not be very good at running with a much deeper lean).
This thread is the reason I posted this. So my question is can we calculate the angle you would need to point your shoulders at, and the amount of bounce for optimal speed. (disregarding danger from obstacles and whatnot)
Not a cheetah, maybe more a gazel or kangaroo.
Moon run like Sheik, makes sense to me!