Gravity of planets

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adjacent
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Main Question or Discussion Point

force of gravity decreases with distance from the planet.This means the distance from the center of the planet.Is the center only producing the gravity?If i get close to the center the Will the gravity increase towards the center or away?because if the planet is perfectly spherical with uniform density the mass will be around him,∴pulling him away?again pulled back because of more mass now?
 

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  • #2
Bandersnatch
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(Assuming uniform density and perfect spheres)

As long as you are above the sphere of the planet, you can treat the planet as if all of it's mass were concentrated in a single point in its centre. The result will be the same.

Onc you get below the surface of a planet, the shell above the distance from the planet's centre you're currenly at, contributes exactly zero to the gravity experienced by you(the influences from the shell cancel each other out). Thus, you're left with only what's under your feet at any given time.
And since the deeper you go, the less of a planet there is left underneath, the lower the gravity you experience.


Both effects are explained by the Shell Theorem:
http://en.wikipedia.org/wiki/Shell_theorem
 
  • #3
adjacent
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The maths is beyond me.But still thanks for giving an idea
 
  • #4
Bandersnatch
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You can gain a qualitative understanding for the effect without going into the math.

All it is about is the fact that once you're inside the shell, forces coming from opposite directions cancel each other out. In the case of being in the very centre of a shell it is very obvious.
If you're off centre, you effectively have more mass pulling at you from farther away on one side, and less mass closer to you on the other.
The math is there to show that the force increase from being closer to the mass on one side is exactly balanced by the force increase due to having more mass on the other.

The bit of the theorem proving that mass can be treated as concentrated in the centre is very similar. You've got less mass closer to you and more farther away.
 
  • #5
adjacent
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I understood that,again thank you
 
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When it comes to real world bodies (among them the Earth) gravity can sometimes increase with depth due to the difference in density between, for example, the core and mantle.
 
  • #7
DEvens
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Onc you get below the surface of a planet, the shell above the distance from the planet's centre you're currenly at, contributes exactly zero to the gravity experienced by you(the influences from the shell cancel each other out). Thus, you're left with only what's under your feet at any given time.
And since the deeper you go, the less of a planet there is left underneath, the lower the gravity you experience.
http://en.wikipedia.org/wiki/Shell_theorem
It's very cool how that works in Newton's gravity. It's also very cool
that it works in general relativity as well. If you have spherical shells
then the forces of shells you are inside cancel. Only the matter
inside the radius you are at will produce a gravity force. That's
important because it's a measured thing and so GR would be in
big trouble if it didn't work.

But the really cool thing is, while the forces cancel, the overall gravity
effect isn't nothing. You are in effect at a different gravitational
potential. So there is a time dialation effect. Clocks down wells
run at different rates to clocks on the surface.

There's also a special relativity effect because clocks at different
altitudes are moving at different rates due to rotation.

These are pretty hard to measure at the small altitude changes
involved in wells. But GPS sattelites can resolve these effects
with very good accuracy. The clock on a GPS satt has to be
adjusted to account for both of these effects.
Dan
 

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