# Gravity in a lunar base

Imagine a big Moon base situated under a dome. Big means under the dome there is a small city with buildings, streets and ca. 30,000 inhabitants. The best analogue in the movies would be the Ceres colony in "The Expanse".

Now the gravity of the Moon is ca. 1/6 of that of the Earth. How would a human feel in such an environment? I am particularly interested in how would he handle elevation, i.e. would he be able to jump 6 times higher than on Earth, i.e. directly into the window on the first floor? Or the reverse: if he falls out of the window at let's say 12 meters, would this fall be equal to that of 2 meters on Earth (in terms of impact felt by the person falling)?

Or am I understanding the implications of gravity in the wrong way? Will the sealed dome somehow influence the gravity?

• What researches have you done? What have you found? Does jumping inside a sealed dome on Earth makes any difference with respect to jumping outside? – L.Dutch - Reinstate Monica Feb 24 '20 at 15:14
• I'm basically confused by movies and books here. Like when I read about gravity, I imagine a person would be able to jump higher. However when I think about popular movies (e.g. The Expanse) or books (e.g. A Moon is a Hard Mistress), people are always moving "normally" and don't experience gravity effects. – Maxim Zabolotskikh Feb 24 '20 at 15:29
• @Maxim Zabolotskikh At a history website, one person wrote that a viewer should assume that everything historical in a historical movie is false; the viewer shouldn't believe anything in the movie. Similarly, it is reasonable to assume that everything scientific and technological you see in a science fiction movie or show is false. It is very expensive and difficult for movies and tv to show people experiencing low gravity or microgravity. It is much easier for movies and tv to depict the use of fictional generated gravity to create Earth level gravity everywhere. – M. A. Golding Feb 24 '20 at 17:10
• This post appears to have two questions in it, I say that because the answers appear to be directed in two different directions: 1. "How high can you jump on the moon?" and 2. "Does a sealed dome affect gravity?" I would suggest clarifying the post to include only one question and to highlight what information you're actually trying to gather. – Muuski Feb 24 '20 at 17:24
• @MaximZabolotskkikh Movies/TV are filmed on Earth, and it's very expensive to simulate partial/null gravity, so they generally only bother getting it right when absolutely necessary, or they assume artificial gravity. In harder stuff like The Expanse, they assume growing up in low-G means your body naturally develops less muscle mass, so a Martian naturally can't jump any higher on their planet than an Earther can jump on theirs, with obvious problems if they travel somewhere with higher gravity. – StephenS Feb 25 '20 at 17:22

The height of a jump is based on your launch velocity, which is directly related to the energy you can transfer to your center of mass during the short time period you have while pushing off the ground.

For a first order approximation, your lunar launch velocity would be the same as your earth launch velocity. For a simple example, lets pretend gravity is 9 meters per second squared and the moon is 1.5 meters per second squared (to keep math very simple) and we further assume your vertical launch velocity is 4.5 meters per second (considerably more than real world)

On earth, is will take you 0.5 seconds to lose reach the top of your jump. Since your average velocity will be 2.25 meters per sec. you would raise your center of mass by 1.125 meters during that time.

On the moon, you will have the same average velocity, but it takes you 6 times as long to decelerate you to the top of the jump, so you spend 3 seconds at an average velocity of 2.25 meters per second and you jump 7.75 meters high - exactly 6 time as high.

Secondary effects are a bit harder to compute and they will depend upon the person and conditions. 1) Because lunar gravity is smaller, you will actually spend less time during the launch phase (you are accelerating your body against weaker gravity, thus it accelerates more rapidly reducing contact time with the ground, 2) You may be able to start your jump with your knees bend deeper because you can generate positive thrust with less force.

These two effects tend to cancel each other out, though I expect in able bodied people, the first effect will be greater, resulting in jump a little bit less than 6 times as high on the average.

Of course, muscle loss will very quickly become a factor in reduced gravity reducing the jump further.

Unless your dome is made of condensed matter, you can safely ignore its gravity effect.

(Fixed stupid factor of 2 error in initial post)

Had a little spare time, and looked up real-world vertical leap - For men, average leap was 16-20 inches and excellent was over 28 inches. Best of the NBA players was over 40 inches.

• An average leap with a height of 20 inches (0.508m) has a launch velocity of 3.16m/s (using v=a*sqrt(2d/a)). Twice the height is 1.41 times the launch speed, or 4.46m/s. So your 4.5m/s guestimate was pretty good... if your subject is an NBA pro :) – Corey Feb 25 '20 at 2:26
• @Corey - I considered it unrealistic for the average person. I never had any possibility of playing in the NBA - white man can't jump applies to me. YMMV – Gary Walker Feb 25 '20 at 13:51

No, this dome wont change anything in term of gravity.

Gravity is "created" by mass. Dome can have quite mass, but it's minuscule to mass of the Moon.

• To add more info worth referencing in our real life: gravity is not different inside the Bird's Nest Olympic Stadium in Beijing. A high-jump in there feels the same as one anywhere else on the planet. – cyber101 Feb 24 '20 at 18:57
• Gravity is different inside the olympic stadium. Just because it doesn't feel different doesn't make it so. However, the difference is so minuscule, its not worth the hassle to measure it. I do not believe this answer is complete, there were more questions than just "is gravity different inside than out?" – V. Sim Feb 24 '20 at 19:40

A jumper will transform kinetic energy from his vertical jump speed into potential energy, which has the formula E(pot) = mgh (mass times gravity times height). Hence, given the same initial speed, he will jump six times higher if the gravity is one-sixth. Similarly, he would have to fall from six times higher to hit the ground with the same energy.

There are other factors affecting these matters. The major one is air drag. Jumping or falling six times the height means that air drag has six times the effect (roughly, since air drag isn't linear with velocity). Most importantly, air drag will determine your terminal velocity; i.e., the highest velocity you can achieve by falling. Terminal velocity is proportional to the square root of gravity, all else being equal, so for one-sixth gravity, it is ca. 80 km/h compared to ca. 195 km/h on Earth. As a first-order approximation, you would reach this speed after falling ca. 150 m. A faller could likely reduce this speed significantly by holding his jacket or shirt wide, and wearing a wingsuit might even make it safe to fall any distance. This is of course only true inside the sealed dome; outside, an nigh-vacuum, the terminal speed would basically equal the Moon's escape velocity of 2.38 km/s. This is the only effect the dome has on jumping and falling.

Another factor for jumping is that jumpers rarely jump from a stand-still. They run towards the bar and transform some horizontal speed into vertical speed, adding to the height of their jump. I can't tell for sure if this would be more or less difficult on the Moon, or if it is equally easy, but my instinct is that it would be more difficult because the foot's resistance against the floor would be one-sixth due to the lower gravity, making it more likely to skid at high speeds. This may also make it harder to run, and if you bounce, you can't easily transform horizontal energy into vertical energy (but you could bounce on elastic soles).

• You comment re: sliding contact with a running jump is good, I had actually considered adding this in my answer, just got busy and never got to adding it to my answer. Friction would be 1/6th that in Earth (ignoring the possible difference between sliding friction vs. static friction). And sliding contact that is much more likely in lunar gravity would only make the vertical jump worse. – Gary Walker Feb 25 '20 at 17:10
• I would point out that if air drag is a significant factor in a drop even on the moon base, the landing is likely to be unpleasant. – Gary Walker Feb 25 '20 at 17:14