# Spec Tech: Jumping on the Moon

**Spec Tech** is the new Thursday series at the Clarion Foundation blog. This “college of science fiction and fantasy” will explore the uses of physics, astronomy, biology, sociology and more, as they apply to the writing of speculative fiction. Whether you’re in the midst of intricate world-building or just want a juicy fact to bolster a short story, we hope Spec Tech will be useful to you. If you’re interested in writing for Spec Tech, please email blog@theclarionfoundation.org with information about your area of expertise. Currently seeking historians!

*Also, between now and June 30, we’re holding a design contest. Submit the winning design for a “Spec Tech” college crest, and you’ll receive your pick of a current signed first-edition speculative fiction title from Mysterious Galaxy Books. You may send your designs (or questions) to the email address above.*

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Writing a story that uses outer space as a location has its own set of research challenges. So many things we take for granted on the Earth—like gravity—are different on other planets. Part of the fun, of course, is imagining what things might be like. But in some cases we (read: science) already know what things would be like. For instance: if you were standing on the Moon right now, how high could you jump? When the astronauts walked on the Moon in the 1960’s and 70’s they were wearing bulky, restrictive, 200 pound suits. Any jumping they did was limited at best. Instead, lets imagine being on a moon-base with a large pressurized gymnasium wearing normal clothing. How does the lower gravity change things? This is to some degree an answerable question.

This question of jumping is less straightforward to answer than it would seem at first. The Moon has about one sixth the gravity of Earth, so the naïve guess would be you could jump six times higher than on Earth. Things are somewhat more complicated than that. When you jump on Earth you have to expend a certain amount of energy to overcome gravity as you are jumping. Once your feet leave the ground you are in free-fall until you land again. The height of the jump depends on gravity and the speed at which you can propel yourself upwards (because of the slow speeds involved you can safely ignore air resistance). However, calculating the speed at which you leave the ground depends on many things: how strong your legs are, how much mass you have and how strong gravity is. When you move from the Earth to the Moon only the gravity changes. Your legs are the same and your mass is the same. What you have to do is calculate *how much faster you leave the ground* to find out how high you will go.

## How High You Can Jump on the Moon

Figuring out your jump speed is a little complex^{1} and beyond the scope of this post, so I have simplified it by taking some average weights and jump forces and working out the answer for a typical human. Here I have graphed how high an average person should be able to jump as a function of surface gravity, with annotations for some common places around the Solar System.

You can see on the Moon you can jump about 22 feet! That’s about 11 times higher than on Earth. I for one can’t wait for the Moon Olympics.

## Falling on the Moon

Another interesting thing to consider is what the highest thing you could jump off of without getting hurt would be. On Earth I can easily jump off an eight foot obstacle and not be seriously injured. The falling relationship is similar to jumping. Falling from eight feet on Earth means I will be moving about fifteen miles per hour when I hit the ground. Because of the lessened gravity I could probably survive a faster impact on the moon. If I can jump eleven times higher, I can probably jump off something 11 times higher as well. But I am trying not to get hurt, so let’s be conservative and say that I can survive a fall ten times higher. So my eight foot dive becomes eighty feet! I could essentially jump off an eight story building and not break anything.

## Walking

It’s hard to walk in low gravity. I don’t see this discussed too often, but it’s really hard to walk on the moon. One of the effects of low gravity is the friction between your feet and the ground is greatly reduced. The characteristic skipping motion the astronauts used to hop around the surface of the moon was a necessity, not just for show. I can attest personally to this effect, as I once had the pleasure of being strapped into a spring loaded machine designed to simulate Moon gravity. Sure enough, as I try to walk forward my feet just slip out from under me. And once I finally do get going it’s just as hard to stop. I makes you wonder if humans do end up colonizing the Moon what sort of architectural choices we will make. Why bother with stairs? Just jump. Do we adopt extra sticky floors? High ceilings will be a necessity.

If your writing takes place anywhere that has gravity different than Earth, keep in mind a lot of things will be different. If you’re going for realism, start by looking at old Moon-walk footage. Notice how the astronauts move, or how the moon-buggy they drive bounces. It looks very different than it would on Earth. Do some quick calculations; ask yourself what would change if everything was suddenly drastically lighter.

### Resources

[2] http://www.exploratorium.edu/ronh/weight/

[3] YouTube: Bunny Hop on the Moon – http://www.youtube.com/watch?v=HKdwcLytloU

One example of a science fiction novel that uses lessened gravity to great effect is Red Mars, by Kim Stanley Robinson. Being more of a fantasy fan than a science fiction fan, I never would have read this book if KSR hadn’t been one of my Clarion instructors. I’m so glad I broke out of my comfort zone and gave it a try. There are no plot points that hinge directly on the lower gravitational forces, but the constant presence of this alien factor of the environment (among others) makes the setting seem so much more real. It just goes to prove how important it is to ground a story in these kind of scientific details.

There are other factors to consider as well, because one isn’t likely to use 1 Earth atmosphere (101 kPa) air pressure on a Lunar base. So air resistance is going to be lower, though that will be by far a smaller change than gravity. Also, if you’re going to fall 80 feet, you’re still going to have to orient yourself and land properly.

In my Writers of the Future XXIV story “A Man in the Moon”, I have a senior astronaut chide a group of newbies fresh up from Earth with letting their Earth “reflexes” influence their thinking too much. (grin) But then I am a Physics professor. (double-grin)

“You guys are all incompetents.”The newbies turned to see Gene on their side of the first hatch. He took several large, loping steps and then with an effortless grace, launched himself up to the top of the dome. In the reduced gravity of the Moon it was surprisingly balletic and he timed it to reach his apex exactly at the last handhold. By then the others noticed the hissing sound above their heads and watched as Gene closed the louvers on the vacuum line. The alarms silenced as well.Dr. Phil

“Falling from eight feet on Earth means I will be moving about fifteen miles per hour when I hit the ground. Because of the lessened gravity I could probably survive a faster impact on the moon. If I can jump eleven times higher, I can probably jump off something 11 times higher as well.”

I do not know where damage comes from in impacts but I would guess that kinetic energy (proportional to velocity-squared) is more salient than momentum (proportional to velocity). Furthermore, I do not see why you’d survive a “faster impact”. I think you should consider the relevant equations. Good luck.

Ignoring air resistance, for Free Fall from rest (or jump from ground to stopping at the Turning Point):

Kinetic Energy (KE) = Potential Energy (PE)

½mv² = mgh

since mass cancels on both sides:

½v² = gh

If the local gravity changes the free-fall acceleration g by a value of 1/6th, then for the same speed v, and hence the same KE to absorb on impact, h increases by factor of 6.

Thus an 8-foot Earth fall is equivalent to a 48-foot Lunar fall.

Dr. Phil

I should point out that falling to the ground is a totally inelastic collision with an immovable object, so as the poster noted, absorbing the KE is the critical issue. Going from 6 times the height to 11 times the height will increase the final speed on impact by 35%. (And the energy absorbed increases by 83%.)

11 ÷ 6 = 1.83

So the PE increases by a factor of 1.83, as does the KE. That means that v is increased by the square root of the factor.

sqrt(1.83) = 1.35

That’d be equivalent to jumping from a 10.8 foot height on Earth.

Yeah, it’d hurt.

Aren’t you glad you asked? (grin)

Dr. Phil

Ooops — used the wrong number in the calculator.

Equivalent to a 14.6 foot fall on Earth.

Dr. Phil

Normally, when faced with a couple of options I would do an experiment to figure out what’s happening. But in this case, most unfortunately, that’s not possible.

My thinking goes like this. Your legs have to provide a certain amount of force when you hit the ground at some speed. On Earth that force will slow you down as you hit the ground. My guess is that force is what does the hurting, or rather if you can provide some force X on Earth to counter a fall, then you can provide at least that same force on the Moon safely.

If you consider hitting the ground and bending you legs until you stop (squatting) you are doing two things, you are taking out the energy of the fall (your fall KE) and at the same time you’re fighting gravity. Thus you have a force down on you, mg and some acceleration (taken to be negative in this case because it’s counteracting the fall, and I made mg positive) -ma. Taking an average acceleration through your knee bend we would have constant leg forces of F = mg+ ma.

If there were no gravity and you only had do dissipate the energy of the “fall” this would become F = ma. Without the gravity term, with the same force you would be able to withstand a higher acceleration (and thus, presumably, a higher fall speed). On the Moon it’s somewhere in between.

A potentially useful thought experiment: Is falling from some height (and impacting at some speed) the same as sliding horizontally at that same speed into a wall?

The intuitive explanation for this you weight less on the Moon. On Earth when you hit the ground you have to do work against gravity and on top of that you have to dissipate the fall energy. On the Moon you weigh less so you can fall higher than just 6 times more.

Yeah but — Since you are coming to a stop within a very short distance, given the compression length of your leg bending, the value of the acceleration a > g, whether you use g(Earth) or g(Moon). As I’m always telling my students, you have to do a free body diagram on a force problem and work out all the forces, so you’re correct there.

You can skip to the

Bottom Lineat the bottom if you don’t care about the Physics Lesson. (big grin) Apologies in advance.According to my quick calculations, freefalling on Earth from 8 feet leads to a final speed of 6.92 m/s. If one comes to a rest in a compression distance of 1.00 meters, that is a net acceleration of 23.9 m/s² or 2.44 g. Note that the speed or net acceleration in stopping over 1.00 m does not change whether on the Earth or the Moon, if you are jumping from the Moon height which gives the same final speed.

The force/mass (which gives an acceleration, but this is not your acceleration — I just don’t want to put a hypothetical mass in the problem) you have to apply against the falling while stopping comes out to be 33.7 m/s² on Earth or 25.5 m/s² on the Moon.

Your reasonable argument is that if you apply the same force/mass of 33.7 m/s² on the Moon, then your net acceleration is 32.1 m/s², which would be for a final speed of 8.01 m/s, which would result from an effective Earth jump of 3.27 m or 10.7 feet and a Moon jump of 19.6 m or 64.3 feet. (Remember, you are really comparing the Moon jump to an 8.0 feet Earth jump.)

BUT… as they teach at Jump School at Fort Benning, you really don’t want to land with a straightened leg. If your legs are bent and your stopping distance isn’t 1.0 meters but say 0.5 meters, then the force/mass increases and the effect of g is lessened. I get a final speed of 7.49 m/s, which would be an effective Earth jump of 2.86 m (9.37 feet) or 17.2 m or 56.4 feet on the Moon.

Most impressive, young Jedi.Bottom Line:You can jump at least 6 times as high on the Moon as you can on Earth, but given the lower gravity, you can actually eke that out to between 7 and 8 times as high — all for the same collision with the ground, assuming that you are oriented and prepared properly for landing.I have my newbies on Moon bases wear ankle weights for the first few days so they think twice about launching themselves upward. (grin)

Dr. Phil

(Note: all calcs assumed the simple ratio of the Moon’s gravity being 1/6th that of Earth.)

I always start with a free body diagram

That is an excellent point about the full vs. partial knee bending. There are a lot of things going on during a landing so most of my assumptions are probably at least partially wrong. Assume a spherical cow, and all that. I purposely chose 8 feet on Earth because I know I can actually do 10 (I jumped off _a lot_ of things as a kid). So I left some room for over-estimating the fall height. It’s hard to say really because there is a lot going on when you land, for instance I usually tuck and roll, and I’m not sure how to quantify how much extra energy that takes away (if any, but it always felt easier). Also, getting close to 8 m/s and, over the longer distance, air resistance will start to have some noticeable effect.

At any rate it would be really nice to actually have a Moon base to practice on and see what people are capable of. But then again I have always been more of an experimentalist than a theorist!

So… I suppose people are now wondering why Dr. Phil is saying 6 to 8 times as high versus 11 times as high. It’s because of the law of diminishing returns. The 11 times factor was for a two foot vertical jump UP on Earth — NOT the absorbing of an eight foot vertical drop DOWN on Earth. Just because you can absorb an eight foot drop does not mean you can do a vertical leap of eight feet on Earth.

Different problems, different calculations.

Then there’s the Hollywood Effect where they get it completely wrong in filming most of the time and it’s easy to see why such technical accuracy doesn’t get stuck in a lot of SF stories.

What is frustrating for SF writers is that you tend to look at this as

Why yes this is rocket science, which is kind of bad if you are interested in telling a story and not trained to do calculations. BUT… this is why you cultivate friends and experts. Indeed, at the 2004 Clarion they handed out index cards and asked us to sign up to be workshop experts in various fields — and some of us were. (grin)Whew — I brought this back ’round to Clarion. Yay — for the win! (happy grin)

Dr. Phil

Hello,

So, from what I gather on your site, if a person were to jump from an 80 foot ledge in an environment with earth sea level air pressure that happened to be on the moon and they fell on their head instead of their feet, they would end up just as dead as crashing on the earth. If they fell on their feet, in the same situation, it would depend upon their strength and how they fell as to whether or not they would survive.

Thank you,

Jim west

How would jump height in reduced gravity scale with jump height at 1g? For instance, if a person had a 3 ft vertical leap at 1g, would the vertical leap be 3/2 of the value shown in the chart based on 2 ft leap at 1g? My thinking is that it would not be linear.

Due to smaller value of g a man can jump higher on the surface of moon.can he run faster on this account.? please answer this question. please ………………………….