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The other day, we posted the following fact:
• Since the moon's gravity is only one-sixth that of Earth's, it is possible to jump 36 (six squared) times higher there.
Since that time, a number of people have written in to say that that was untrue. Here are some samples:
¤ "The relation between gravity and potential energy (energy at a certain height AKA energy needed to jump to that height) is proportional. You can only jump 6 times as high."
¤ "The ratio of kinetic energy to potential gravity is exponentially increased as the planetary spherical mass is decreased. Newton's Law of gravity is F =GmM/R^2 , where G is the gravitational constant, m and M are the masses of the bodies being considered, and R is the distance separating the masses m and M."
¤ "Your bewilderment results simply from the words "six squared" implying that there is a law of physics behind that which involves a quadratic dependency. This is not so."
¤ "The existence of the moon as a hoax. See concrete proof at http://www.revisionism.nl/Moon/The-Mad-Revisionist.htm ."
Clearly the last person is a nut. Of course the moon exists! In fact, my neighbor "Buzz" Collins told me that he used to be an astronaut and that he was the second person on the moon, right after that "Stretch" Armstrong guy. So, if you can't trust your neighbors, who can you trust?
As to the other people, while I'm not some super-smart rocket scientists like the rest of you, I'm pretty sure that I'm right. But I'm willing to keep an open mind. After all, as Carl Sagan used to say, "A preponderance of evidence is not evidence of preponderance."
First, I've seen videos of astronauts on the moon, and they typically jump about 18 feet high. I make that estimate based mainly on the pictures that my buddy Buzz Collins showed me of him jumping over the LEM, which looks to be at least 15 feet high. Given that they're wearing suits with an average weight of 350 pounds, that makes a person with suit weighing about 525 pounds jumping 18 feet. But you guys seem to be saying that's the equivalent of a 525 pound person jumping 3 feet high on Earth? I don't think so. I don't know any morbidly obese people that could jump that high. I think that 6 inches is much more plausible.
Next, I did some experiments.
First, I jumped up as high as I could, which came to about 2 feet. However, I could feel the woosh of the air going past me. I'm pretty sure that's called air resistance. I estimate that if I didn't have all that air slowing me down, I'd quicky suffocate due to lack of oxygen. But more to the point, I think that I'd be able to jump much higher. At least 3 or 4 feet high. So, since there's no air on the moon, ignoring the effects of gravity, I'd be able to jump maybe twice as high.
My next experiment was to chart how high I could jump at different heights. I live near the ocean, which is what is called C-level. As you know, E=MC^2, so at C-Level, there should be maximum energy or something like that, which makes it a good base case.
Anyway, at home, I could jump about 2 feet high. I then drove up to one of the hills nearby, and I could jump about 2 feet and 1 inch. And thinking back to when I was in Denver when I was a kid, I'm pretty sure that I would have been able to jump about 3 feet high. So, we can plot that in a graph:
0 feet: 24 inches
200 feet: 25 inches
6000 feet: 36 inches
So, by extrapolating the pattern, it is logical to believe that if I was as high as the moon, which is at least 100 miles above us, that I should be able to jump around 850 inches, which is pretty close to 36 times higher.
And that's ignoring the lack of air resistance.
But of course, that's all empirical evidence. Now consider the equations.
From my extensive scientific background at Fremont Unified High School (G.E.D.), I can tell you that the perimiter of a circle is equal to pi times radius squared. Yes, squared. And since the moon is a circle, that formula (or one like it) should apply. Or are you now going to debate that the moon is actually flat and the formula shouldn't apply? Clearly, you can just look up in the sky and see that it's a circle.
Furthermore, I used Wikipedia, and I see that the gravitational acceleration on Earth is 9.8 meters per second squared. There's that "debatable" squared again. On the moon, it's 1.6 meters per second squared. Or are you trying to claim that it's only 1.6 meters per second (not squared) on the moon? That the square falls away due to your "flat moon" hypothesis?
Like I said, I'm willing to keep an open mind, but frankly, I don't see how you believe that you can debate science. And this is clearly science. My buddy Buzz told me so.
This is a very simple problem, if you ignore air resistance. Two equations are all you need. One is the kinetic energy which is .5*mass*velocity^2, the second is gravitational potential energy, which is mass*height*g, where g is the acceleration due to gravity. Now, when you jump, you start with a certain amount of kinetic energy which is dependent on your velocity when your feet leave the ground. You continue to move upwards until all you kinetic energy is transformed into potential energy, and then you stop. Then you fall until all the potential energy is turned back into kinetic energy, and then you hit the ground. So setting the two equations equal will give you your height. Now, if your initial velocity is the same on the moon as it is on earth, your height will only be linear function dependent on gravity, not quadratic, meaning 6 times the height.
Unfortunately, you initial velocity is not the same, but nor is it 6 times what it would be on earth. Your force in the jump will be the same, however. The math gets a little long handed at this point, so I won’t write it all here, but basically the initial kinetic energy will be ((6^2) – A) times as much on the moon, where A is some constant that is dependent on mass and your jumping force. So, you will be able to jump more than 6 times as high, but less than 36 times as high.
By the way, the moon is around 250,000 miles away, a lot more than 100 miles. Most satellites orbit farther than 100 miles out.
I have a related story here...
I happen to be related to someone who has walked on the moon (Harrison Schmitt), and the person he was up there with actually tried to see how high he could jump. What both of them forgot was that on Earth, their space suits weighed a couple hundred pounds, with most of the weight in the backpack area, thus throwing the center of gravity way off. So when the guy jumped, he got quite a bit of air, but made a nice bacwards arc and landed right on his back! Harrison said it scared the bejeebers out of both of them, but everything was OK, and no harm was done to the suit.
Jim
http://www.humanbeingcurious.com
yep, the velocity as you leave the ground is more on the moon. This is because your muscles still exert the same force, but on a 6 times lighter weight.
Taed, there are a lot of things wrong with your reasoning. The height you jump on the moon is always 11 times greater than the height you jump on the earth, everything else (such as the clothes you wear) held constant. I'm going to email you right now with an explanation. Please edit this article or delete it altogether because it shows up in google searches, and people will get the wrong ideas from it.
Taed's reasoning is totally consistent with the exaitudidness expected here at Gullible. Taed, please don't change a word! These pointy-deaded pencilpushers probably don't even know that the cow jumped *over* the moon!
11 times? That's just crazy talk. I suspect they learned their physics on the streets, not at some respectable school like Rice University.
Posted By: T-Shirtbut basically the initial kinetic energy will be ((6^2) – A) times as much on the moon, where A is some constant that is dependent on mass and your jumping force. So, you will be able to jump more than 6 times as high, but less than 36 times as high.
By the way, the moon is around 250,000 miles away, a lot more than 100 miles. Most satellites orbit farther than 100 miles out.
It just so happens that "A" is the gravity exerted on you by the earth, so these terms cancel out and 6^2 is the height one jumps.
Posted By: UdoboyPosted By: T-Shirtbut basically the initial kinetic energy will be ((6^2) – A) times as much on the moon, where A is some constant that is dependent on mass and your jumping force. So, you will be able to jump more than 6 times as high, but less than 36 times as high.
By the way, the moon is around 250,000 miles away, a lot more than 100 miles. Most satellites orbit farther than 100 miles out.
It just so happens that "A" is the gravity exerted on you by the earth, so these terms cancel out and 6^2 is the height one jumps.
If A when you're on earth is the gravity exerted on you by the earth, shouldn't A when you're on the moon be the gravity exerted on you by the moon?
No -- it would be O -- we're using the 2nd letter of the body's name.
It is very exiting to reach on moon and jump on it on moon low gravity so it is very different to run between moon and earth.
http://www.bemingled.com
Posted By: John_mickleIt is very exiting to reach on moon and jump on it on moon low gravity so it is very different to run between moon and earth.
http://www.bemingled.com
You have such a way with words.
Anyone any idea what distance could be achieved in the Lunar Triple Jump? Maybe some day we will have Lunar Olympics. Certain events like sailing would be a touch boring, and the stadium would have to be a little larger for the javelin.
Posted By: Fact totumNo -- it would be O -- we're using the 2nd letter of the body's name.
How many times do I have to tell you that the moon's name is Luna? Come on, people!
I call it Dave.
Posted By: UdoboyPosted By: Fact totumNo -- it would be O -- we're using the 2nd letter of the body's name.
How many times do I have to tell you that the moon's name is Luna? Come on, people!
If you call a dog's tail a leg, how many legs does the dog have?
Weird. His one leg looks more like two. I count....6 sticking-out-of-main-body parts. Not counting his head. 7 counting his head, but not his ears. Ok, 9 counting the ears...but not counting the really long hairs...and that's enough for me.
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