h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

This is my logic here tell me what you think - people are included as a part of the mass of earth when gravity is calcuated, so if all the people in the world jumped at once and reduced the total mass of the earth, would we fall down slower than if we jumped one at a time?

NO !

I will try to explain. Newtons law of gravity applies to TWO bodys. There it is valid and rather easy to use. Now consider the next step: three bodys. Each mass will interact with two masses not just one, as in the case before. You can easily imagine that the interaction of two masses has some effect on the position of them and therefore the distance two the third mass is altered. You will end up with a problem that you wil have to solve numerically by iteration.

The next thing you have to know is that Newtons law applies to POINT MASSES, that means he is not talking of bodys with masses but of a pointlike mass with no extend !

Now consider the earth and the sun. Obviously, those to bodys are not point like at all ! To calculate the gravitational force between sun and earth you would have to do the following: take ONE small part of the sun say the size of a TV set and one part of the earth about the same size. Now those two bodys (compared to the distance) are somewhat point like and you can calculate the interaction. Now continue with all remaining parts of the sun and calculate the interaction between them and your given part of the earth. Do this with all parts of the eart and then solve the whole problem by iteration !

This would be an unsolveable problem and Newton would not have had any success with his theory !

The solution is easy ! Just try to answer the following question: where would you have to place a point like mass if you wanted to simulated the effect of sun's gravity ?

----> In the center of mass !

Yeah that's true ! Just place a point like mass in the center of mass and you will have the same effect ! It is now amazingly easy to calculate the interaction between earth and sun ! Just calculate the interaction of their center of masses !

Exactly the same is valid if you want to calculate any to bodys, say one human beeing and the earth.

Your center of mass is around your hips or stomache or somewhere (I hope so ) Now the center of mass of the earth is let's say exactly in the middle. If everybody jumps up one meter the center will stay where it is ! So no effect is noticable !

Hope this kind of helps you !

BTW, If you would dig a really deep whole and go down in it, some part of the earth would be above you and some beneath you. Where is the center of mass now ? This problem is much more complicated but it turns out that you are getting closer to the opposite part of the earths crust at the same time, which therefore attracts you a bit more ! And, believe it or not, the amount is exactly the same as the attraction of the mass above you. The center of mass would stay where it is -in the middle of the earth- but the mass you will have to take is the mass of that spherical part of the earth with a radius equal to the distance of your position and the middle of the eart.


But if you just want to fall down a little bit slower after jump I can give you a good tip !

Since the earth is rotating you can take advantage of the centripedal force ! You will fall down a bit slower in the equator region compared to the polare region !

cu

i'm scared

I think gravity should be catched and knocked out.
Then we could have some happy-fly-hours.
I mean, that's my opinion

thanks that was amazingly insightful, that's been something i've been wondering about for a while - might have been a little more that i needed to know, but that's okay. that centre of the earth thing has also been bugging me, i still think it's too confusing/frustrating/annoying to think about but i'll have to deal with that myself.

sounds like a good idea, but it'd be nice if everyone were safely back on the ground when the fun was over. "4 o'clock already? Oh hell..." --plummetts--

Yeah ! Well, my reply was from a *todays* physicist point of view. Perhaps we'll chatch gravity someday

Imagine the possibilities ! Your range of spitting would increase tremendously, your weird haircut wouldn't bother anyone anymore because everyone got his hair like this, no traffic jams anymore...

But their are some minor disadvantages too. Your cat could extend its possibilties in catching birds (does anyone disagree that thiss is a DISadvantage???), but on the other hand your cat is now itself easily caught by dogs. And what about a good glass of beer ?? ("Has anyone seen my beer levitating around, here ????") And afterall, what's with the thing we call atmosphere...... "Don't breath out to heavily, you blow away our whole fresh air. And when I say our *whole* air I mean it !"
....and think of this butterfly effect ! Wow, this goddam butterfly could still increase its power over us all !


Well, I think I am pro gravity !

I had a dog which I named Gravity - she was a 150 lb Newfoundland - and when she ran off whilst out walking, you were pulled by what seemed like Nature's full gravitational force - hence the name.