We know that on the Moon in ~1/6 g the Apollo astronauts couldn't make full steps because they jumped with each step. At what surface gravity could you walk more like on Earth and at what gravity would you rather hop like on the Moon? Would walking on Mercury (0.377 g) and Mars (0.38 g) be more like on Earth, the Moon or something inbetween?

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    $\begingroup$ It was the inflexibility of the pressurized suit that caused the astronauts to jump instead of walk. They could do full steps on the Moon but jumping was easier. $\endgroup$ – Uwe Apr 28 '19 at 13:42
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    $\begingroup$ Are you really sure? On parabolic flights in lunar gravity tourists jump similar to the Apollo astronauts. Although they jump up, I dunno of a video of such a flight where they can walk. $\endgroup$ – Guest55 Apr 28 '19 at 13:49
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    $\begingroup$ I think this is actually a very interesting biomechanics question... Very approximately, a step involves providing a single force with a vertical component that counters weight and a horizontal component to move forward. However the horizontal force must be opposed by a frictional force, which is in turn dependent on the weight. I suspect there may be some lower limit where the weight can no longer allow for a 'recognisable' step. I also suspect there have been some good studies and simulations of this in the past for reference. $\endgroup$ – Jack Apr 28 '19 at 14:13
  • $\begingroup$ What about links to videos of jumping tourists during parabolic flights in lunar gravity? The tourists might jump just to imitate astronauts on the moon. $\endgroup$ – Uwe Apr 28 '19 at 17:21
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    $\begingroup$ Watch the video, the astronauts did steps but also combined stepping with jumping. $\endgroup$ – Uwe Apr 29 '19 at 12:04

Short answer:
You would transition to running at what is a comfortable walking speed on Earth, and movement would take about half of the energy it does on Earth (Source 1). This does not take into account the effect of wearing a giant, restrictive suit.

Imagine walking as if you were switching between support points (legs), and using them as a sort of inverted pendulum. Put one leg out in front of you, it falls down, then meets the ground and pushes you up. Once you are directly over that leg, you start falling down again, but before you face-plant, you put out your other leg, and the cycle repeats. As you walk, your center of mass moves in a sort of bouncing motion. Image from "Human Locomotion in Hypogravity: From Basic Research to Clinical Applications; Lacquaniti et.al; Frontiers in Physiology 2017; PMCID: PMC5682019
Image from Source 1.

From this idea we can derive the Walking Froude Number (Wikipedia link), which is the centripetal force needed to hold the "pendulum" to the ground divided by the force available from the weight of the person: ((m*v^2)/l)/(mg), where m is the mass, v is the forward velocity, and l is the length of the leg. This equation simplifies to: v^2/(gl). A value for this number greater than 1.0 means that the center of mass (the person) will start to float off into space as the foot is pulled off of the ground.

Now, it turns out certain values of the Froude number indicate movement transitions--from walking to running, from running to sprinting, etc.--and the upper bound of walking corresponds to a Froude number of about 0.5 (Source 2). This means that we can calculate the speed at which walking vs. running is preferable, based on the local gravity. Choosing a leg length of 1.0m, the speed of the walking transition on earth should be about 1.9 m/s, while at 0.38g it would be about 1.0m/s. As you had less and less gravity, the speed at which you would transition to running/"hopping" would be slower and slower.

This is not a perfect model, and it turns out that at lower gravity levels, effects such as swinging your arms can lead to more "downforce" available to keep your feet planted than the Froude number would indicate, so the transition at 0.38g would actually take place at around 1.25m/s (Source 2), and at very low gravity levels, the transition will actually take place at a Froude number greater than 1.0. Source 2 goes into a greater depth of analysis if you are interested.

Source 1. Human Locomotion in Hypogravity: From Basic Research to Clinical Applications; Lacquaniti et al.; Frontiers in Physiology 2017; PMCID: PMC5682019"

Source 2. Effect of Reduced Gravity on the Preferred Walk-run Transition Speed; Kram et al.; Journal of Experimental Biology, 1997; JEB0645

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