The Fysics of World Jump Day
Wow! Mark you calendar. July 20th, 2006 is world Jump Day. Better than Jello or solving world hunger, or solving world hunger with Jello because World Jump day solves everything: Global warming, the heath care crisis and the need to fully understand Newtonian physics. It is on the net and they used flash animation, it must be true. They even got real scientists and a bunch of other reliable Internet sources.
Check it out then come back for some post game analysis...
http://www.worldjumpday.org/
Many of you might have been disappointed that is wasn't the start of some massive Van Halen or Criss-Cross global tour and some of you might have failed out of high school physics have already set an alarm, bought a T-shirt and signed up to jump. I'm sure the fear mongering block watch vigilante type who stumble across this site will undoubtedly tell people to stop jumping as to avoid the hazard of jumping at the wrong time to push us into the sun.
To fully appreciate what is going on I turned to dust off my old friends Fishbane, Gariorowicz and Thornton and their knowledge that they so tightly packed into the extended edition of Physics for Scientists and Engineers (2nd edition).
The simple argument of using a force to shift the orbit of earth is quite legitimate, however, the scale and source of the force which our astrophysicists have conjured-up eclipse the dim glow of this idea. Lets analyze this together... Assuming the average weighs 50kg and they are able to jump 0.5 m. Each person could create ~250 Newton-Meters of force (E=mgh assume g~10m/s^2). With 600 million people that is 150million KJ of energy. We all know the Earth weights approximately 5.976 e 24 Kg and the sun in turn weights 1.989 e 30 Kg and is a mean distance of 1.496 e 11 m (to be generous we will add an extra 1% to this distance as the earth is not always a constant distance from the sun). Plugging this puppy into Newton's Law of universal gravitation we get the centripetal force which holds the earth, ~3.33 e 22 Newtons.
Pouring all of our jumping energy into counter-acting this force (W=F*d) gives us a total displacement of 0.0000000000000045 meters. That ought to help curve our global warming trend. Granted I did a lot of rounding and made a few major assumptions along the way but I fail to see how tighter number crunching will dramatically improve the result.
So you ask, what if we jumped a lot, trained elephants to jump or have serious doubts about my math skills? Let me assure you that such optimism is in vain thanks to the reality of Newton's third law. "When a force acts upon an object the object exerts an equal and opposite force in return."
You see this whole operation Jump Day ignores where the force is coming from. When you jump pushing the earth away from you and out of is current orbit, the earth's and your gravitational field (yes, you have a gravitational field) interact and pull the earth back to your feet. This essentially brings you and the earth back to their original positions. In other words if 600 million people jump on the 20th of July we won't even get our negligible 4.5 e -15 meter increase in orbital radius. Kind of puts a damper on the day doesn't it.
In order for orbital change to occur, the source of the force cannot be generated by the earth's gravitational field. I started thinking and decided that our only hope for a quick fix to global warming was to lasso passing comets and hitch a ride. I'll save the physics of that one for another blog but rest assured it would work if we could find a way to do it. Until such technology exists we will have to stick with public transit, leaving your fridge door open and other more traditional means of slowing global warming.
Check it out then come back for some post game analysis...
http://www.worldjumpday.org/
Many of you might have been disappointed that is wasn't the start of some massive Van Halen or Criss-Cross global tour and some of you might have failed out of high school physics have already set an alarm, bought a T-shirt and signed up to jump. I'm sure the fear mongering block watch vigilante type who stumble across this site will undoubtedly tell people to stop jumping as to avoid the hazard of jumping at the wrong time to push us into the sun.
To fully appreciate what is going on I turned to dust off my old friends Fishbane, Gariorowicz and Thornton and their knowledge that they so tightly packed into the extended edition of Physics for Scientists and Engineers (2nd edition).
The simple argument of using a force to shift the orbit of earth is quite legitimate, however, the scale and source of the force which our astrophysicists have conjured-up eclipse the dim glow of this idea. Lets analyze this together... Assuming the average weighs 50kg and they are able to jump 0.5 m. Each person could create ~250 Newton-Meters of force (E=mgh assume g~10m/s^2). With 600 million people that is 150million KJ of energy. We all know the Earth weights approximately 5.976 e 24 Kg and the sun in turn weights 1.989 e 30 Kg and is a mean distance of 1.496 e 11 m (to be generous we will add an extra 1% to this distance as the earth is not always a constant distance from the sun). Plugging this puppy into Newton's Law of universal gravitation we get the centripetal force which holds the earth, ~3.33 e 22 Newtons.
Pouring all of our jumping energy into counter-acting this force (W=F*d) gives us a total displacement of 0.0000000000000045 meters. That ought to help curve our global warming trend. Granted I did a lot of rounding and made a few major assumptions along the way but I fail to see how tighter number crunching will dramatically improve the result.
So you ask, what if we jumped a lot, trained elephants to jump or have serious doubts about my math skills? Let me assure you that such optimism is in vain thanks to the reality of Newton's third law. "When a force acts upon an object the object exerts an equal and opposite force in return."
You see this whole operation Jump Day ignores where the force is coming from. When you jump pushing the earth away from you and out of is current orbit, the earth's and your gravitational field (yes, you have a gravitational field) interact and pull the earth back to your feet. This essentially brings you and the earth back to their original positions. In other words if 600 million people jump on the 20th of July we won't even get our negligible 4.5 e -15 meter increase in orbital radius. Kind of puts a damper on the day doesn't it.
In order for orbital change to occur, the source of the force cannot be generated by the earth's gravitational field. I started thinking and decided that our only hope for a quick fix to global warming was to lasso passing comets and hitch a ride. I'll save the physics of that one for another blog but rest assured it would work if we could find a way to do it. Until such technology exists we will have to stick with public transit, leaving your fridge door open and other more traditional means of slowing global warming.
posted by neseirf ekim at 10:42 PM
5 Comments:
If they manage to get 600M people to jump all at the same time Physics would be the wrong way to determine the affect of the change. Socialology would perhaps be the best disipline to measure or atleast observe the overall effect this would have on our society as a whole. That many people all thinking at the same time about making our world a better place would have far longer and positive affects then us moving the Earth’s orbit abit then if it did work (physics excluded of course…) then we’d all need to be jumping all the time to sort out or worldly problems… Imagine the logistics! Everyone GPS sync’d and commanded to jump… Hmmmm, this sounds like a great opportunity for a product development! (patent pending)
--Scott
You're right Scott. I just check my work, I made a mistake with my calculations. World Jump Day could work with sycn'd GPS watches... so long as everyone bought one.
Hi Mike. That's hilarious. So you're not signing up for it eh? I was one of those who hated high school physics (though I didn't fail). But the concepts are interesting. Minus the numbers ofcourse, because that's where you lose me. Still, I would like to know the physics behind lassoing passing comets ;) Can I link to you from my blog?
Nice work Mike. I'm glad to see Fishbane still comes in handy these days. It makes me think I might open mine up again in the future.
Hey Mike...this is hilarious! Well, I am signin' up that's for sure. I love the whole 'it has to be true cause it's on the internet and they use flash...' Sweet. Tom 's going to love this blog.
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