Jumping and strength in low gravities.

[Solifugae]

Although it's often stated like this, I don't believe that in 0.1g you'd be able to jump ten times as high as on earth. Call it intuition, but I suspect it will have something to do with inability to accelerate enough before take off. Is this true?

Also, what about lifting things, would you really be able to lift ten times as much in 0.1g? Is this even true? Is this functionally equivalent to having ten times the strength?

 

[MeteorWayne]

Intuition is not physics.

You could jump ten times as high.

You could lift ten times as much, but controlling it would be difficult since the object would have the same amount of mass. If you hung on, what you lifted might pull you up off the surface.

 

[origin]

Intuition is not physics.

You could jump ten times as high.

You could lift ten times as much, but controlling it would be difficult since the object would have the same amount of mass. If you hung on, what you lifted might pull you up off the surface.

I hadn't really thought of it in that way. But of course the mass is the same, but the weight is different. It reminds me of something you might see in a cartoon; do a hammer throw but don't let go and you fly off with the hammer... thats kinda cool.

 

[Shpaget]

If you ever find yourself in an environment with 0,1g please do not try to jump as high as you can.
When you hit the ground you'll probably hit it with your nose first, and you'll hit it hard. The same level of hard as face planting on Earth
You wouldn't be able to control your position in air and would probably start to spin around until you finally fall headbutting the poor celestial body.

 

[Planet_Lubber]

This topic seems to generate a lot of speculation. I would like to find an expert in biomechanics and astrophysics willing to sign off on it. Lacking that, I'll put my own 2 cents in.

First, in lower gravity, you would leave the "ground" sooner. There is a limit to how fast your leg muscles can contract, and how much power they can deliver in a short time. If the gravity is low enough, you will leave the ground before your legs are fully extended, so you will not have used all the power in your legs. The same goes for the rest of the body, which helps in jumping.

But suppose you are really quick and this is not a problem.

Here's a simplified analysis (maybe too simplified!):

Suppose you can jump to a height of H meters on Earth. In other words, you can raise your CM (center of mass) from its height S when standing still to height S + H before falling back to Earth.

Your acceleration is -g = -9.8 m/sec^2. Then the speed of your CM (obtained by integration) is v0 - g*t where t is the time after leaving the ground and v0 is the speed when leaving the ground. This speed is 0 when you are at the top of your leap, and that happens at time t = v0/g.

The height of your CM is S + v0*t - (g/2)*t^2 and at time t = v0/g this is S + (v0^2)/(2g). So we have H = (v0^2)/(2g) or equivalently, v0^2 = 2gH = 19.6*H.

v0 = sqrt(19.6*H) B
For a 1 meter jump, that's v0 = srt(19.6) = 4.43 m/sec.

Now consider Deimos, the smaller of Mars's two moons. Wikipedia lists its escape speed as 5.6 m/sec. Of course, Deimos is irregularly shaped, so the escape speed is going to vary from point to point on the surfasce. but 5.6 is a good estimate. A person who could jump to H = 1 meter on Earth would not quite have enough launch speed to escape Deimos (if Deimos was spherical). However, the speed required for a circular orbit (around a spherical body!) is 1/sqrt(2) times the escape speed, and that's only 3.96 m/sec. So it seems that our athlete could jump into orbit around Deimos. Since Deimos is very lumpy, the orbit would not be very circular, and it eventually might crash back into Deimos, or possibly even escape into Mars orbit.

I realize there are some error sources in this simple analysis. You don't leave the ground flat-footed, for example. And when you leave the ground, not all of your body parts are moving with the same speed. But these conditions also hold when jumping in lower gravity.

I don't know if an athlete can really jump to a height of H = 1 meter. People brag about their 40-inch vertical leaping ability. Not humanly possible? Anyone?

PL

 

[Shpaget]

Planet_Lubber, are you new? Welcome

There are couple of wrong assumptions in your post.
The speed your feet are extending away from the rest of your body is in fact the greatest just before the final part of the process of extension. You are accelerating while jumping, right? It is true that the design of human legs is such that the same angular extension will result in greater longitudinal extension at the start of the jump, but it also means that you'll have less strength in your legs at the beginning of acceleration and more towards the end. So your jump would be pretty much the same as in Earth's gravity (that is without the space suit restricting your movements, but we're here exploring low gravity, not the lack of atmosphere).

Second wrong assumption concerns the escape velocity. While you (probably, but not certainly) can't reach Deimos' escape velocity by jumping straight up, there is no reason why you wouldn't be able to achieve it by running. Reaching 20 km/h shouldn't be a problem for anybody with healthy legs.

Third error is that no matter whether you reach escape velocity or not you will not enter the orbit, but rather just circle it once and than fall back at the very same point you jumped away from. To enter the orbit you need to make a direction alteration after reaching certain (any) altitude.

I didn't check your math. I'm too tired for that, but here's an interesting link about vertical jumps.
http://vertcoach.com/highest-vertical-leap.html

 

[Planet_Lubber]

Planet_Lubber, are you new? Welcome

Yes, I'm new around here. Thanks for the welcome! This editor is ... well, I don't want to start off by complaining about the editor. I just hope I am doing this right.

There are couple of wrong assumptions in your post.

There are lots of wrong assumptions in the highly oversimplified model I wrote up. But are they bad enough to invalidate the model? I just want a back-of-the-envelope way to estimate whether a person could jump off a small asteroid or moon. Or throw a baseball off. Etc.

I think this topic has been ignored by serious scientists, and it will start getting a lot of attention only when people actually start walking on small asteroids and moons.

The speed your feet are extending away from the rest of your body is in fact the greatest just before the final part of the process of extension. You are accelerating while jumping, right? It is true that the design of human legs is such that the same angular extension will result in greater longitudinal extension at the start of the jump, but it also means that you'll have less strength in your legs at the beginning of acceleration and more towards the end. So your jump would be pretty much the same as in Earth's gravity (that is without the space suit restricting your movements, but we're here exploring low gravity, not the lack of atmosphere).

Are you claiming that, now matter how low the gravity, you will still be able to get the same amount of work out of your legs as you do on Earth? And that you can push with full strength and your feet will not leave the ground until your legs are fully extended?

Second wrong assumption concerns the escape velocity. While you (probably, but not certainly) can't reach Deimos' escape velocity by jumping straight up, there is no reason why you wouldn't be able to achieve it by running. Reaching 20 km/h shouldn't be a problem for anybody with healthy legs.

Running in low gravity would be very difficult. With the first step, you would go flying, and lose contact with the ground for several seconds. You would have to learn to lean into the run. I suppose you could just take a step every time you come down, and increase your horizontal speed that way. There is also the problem of tumbling. But you're right, with some training, it could be done.

Third error is that no matter whether you reach escape velocity or not you will not enter the orbit, but rather just circle it once and than fall back at the very same point you jumped away from. To enter the orbit you need to make a direction alteration after reaching certain (any) altitude.

If you jump from a spherically homogeneous body, no matter how small or large, you go into an elliptical orbit. If your speed is less than v_esc then your elliptical orbit will intersect the planet at another point, and you have a suborbital flight. You still went into orbit, but not for a full period - only because the planet got in the way.

If you jump straight upwards from a spherically homogeneous body, then your orbit will be a degenerate conic. It is a degenerate ellipse (line segment) if your launch speed is less than v_esc and a degenerate hyperbola (half line) otherwise.

If you jump from a body that is not spherically homogeneous, then it gets much more complicated. There is still an escape speed at every point, because it depends on the potential energy, which depends on the mass distribution of the body. But once you go into orbit, if the body is rotating, then that potential changes. Your orbit is no longer an ellipse or a hyperbola. Just recall the headaches they had with the NEAR mission trying to orbit Eros. So even if you jump straight up, you are not going to come back down in the same place. But certainly, if your launch speed is high enough, you will go into an escape orbit. Not exactly hyperbolic, but you will escape.

I didn't check your math. I'm too tired for that, but here's an interesting link about vertical jumps.
http://vertcoach.com/highest-vertical-leap.html

Thanks for the link. That was just what I was looking for.

PL