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- Thread starter Dru
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Gravity is dependent on mass. Force = (G)*M1*M2/(r)^2 (Newton's gravitational law)

where G = is the gravitational constant, M1 and M2 are two masses, and r is the distance between the center of mass of both

Let M1 = PlanetMass. Therefore, M2 = Mass of object on planet. The force on M2 is equal to M2*a, where a is the acceleration ('gravity') due to the planet mass.

Therefore, we have M2*a = G*M1*M2/r^2, so a ('gravity') = G*M1/r^2

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Now, I've demonstrated intuitively that the more mass the object has the more force (i.e.

Hope this helps.

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Danger

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One thing I would like to add is that the acceleration of gravity is only equal for vastly different objects if they're in vacuum (or very thin air). A 50-gram ball bearing will outrace a 100-kilogram guy with a parachute every time in our atmosphere.

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i have another quick question regarding einsteinian space-time geometry. einstein's idea of space-time is analogous to a flat sheet spread out with the objects in the universe creating small or large dips in the sheet, right? and this is what causes a gravity well, to an extent in the general vicinity of a planetoid, right?

ok, this is what i'm wondering - the sheet analogy is only 2-dimensional? are the dips (in space-time) occuring at every angle to the objects? for example, is space warped not just underneath but above as well as at all angles to the object? so the planetoid would create in effect, an almost entire inward limited collapse of space-time? thnx again

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FredGarvin

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Careful there Danger. The acceleration due to gravity is essentially constant on Earth regardless of whether it is in a vacuum or not. The issue you are talking about is the resisting drag force created by the atmosphere. That is a completely different issue.

One thing I would like to add is that the acceleration of gravity is only equal for vastly different objects if they're in vacuum (or very thin air). A 50-gram ball bearing will outrace a 100-kilogram guy with a parachute every time in our atmosphere.

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Danger

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(Maybe I'm using the wrong terminology.)

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Absolutely. The example of a rubber sheet is quite a bad one actually as it indeed does only show a 2D world. The existence of mass causes a spatially 3dimensional warp in spacetime whose force is described by F=G*m1*m2/r (Newtonian) where F is equivalent in any direction with a constant r and constant masses.

i have another quick question regarding einsteinian space-time geometry. einstein's idea of space-time is analogous to a flat sheet spread out with the objects in the universe creating small or large dips in the sheet, right? and this is what causes a gravity well, to an extent in the general vicinity of a planetoid, right?

ok, this is what i'm wondering - the sheet analogy is only 2-dimensional? are the dips (in space-time) occuring at every angle to the objects? for example, is space warped not just underneath but above as well as at all angles to the object? so the planetoid would create in effect, an almost entire inward limited collapse of space-time? thnx again

It is quite hard to picture a 3D example of gravity warped spacetime, and thats why the popular model is the 2D sheet one. For what it is worth if you would like to try, when I attempt to picture what gravity warped space looks like I first picture space as a 3 dimensional grid with x,y, and z. Then I try and picture what it would look like if a point mass was introduced and all the lines in the grid system were bent so that an object traveling trough this grid would experience a circular motion towards the point mass.

Obviously this is only a conceptual model as spacetime cannot be seen directly.

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stewartcs

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No. Gravitational acceleration only varies at different elevations on Earth. It is essentially constant as Fred pointed out.tryingto accelerate everything equally, doesn't the drag in fact decrease theactualacceleration?

(Maybe I'm using the wrong terminology.)

You are thinking about the terminal velocity of an object which is dependent on the drag. Hence, if two different objects are placed in a vacuum, the fall at the same rate.

CS

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hahaha, robertm, that was a really nice example

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there was a screensaver in win98 which sorta did what you just described. i think they called it blackhole.. you could change some parameters like its radius and all, it seemed pretty cool at the time..It is quite hard to picture a 3D example of gravity warped spacetime, and thats why the popular model is the 2D sheet one. For what it is worth if you would like to try, when I attempt to picture what gravity warped space looks like I first picture space as a 3 dimensional grid with x,y, and z. Then I try and picture what it would look like if a point mass was introduced and all the lines in the grid system were bent so that an object traveling trough this grid would experience a circular motion towards the point mass.

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While the gravity istryingto accelerate everything equally, doesn't the drag in fact decrease theactualacceleration?

(Maybe I'm using the wrong terminology.)

I suspect that stewartcs misinterpreted what was said. I interpreted as: "While g is equal for both objects, doesn't the drag decrease the net rate of change in velocity?" Yes, dv/dt ~ g - (b/m)v.No. Gravitational acceleration only varies at different elevations on Earth. It is essentially constant as Fred pointed out.

Alternative example: "One thing I would like to add is that the equal acceleration of gravity is only visually apparent for vastly different objects if there are no other dissimilar forces interfering such as air resistance..."

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Danger

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That is indeed what I meant. Thanks. I like your 'alternative example'.I interpreted as: "While g is equal for both objects, doesn't the drag decrease the net rate of change in velocity?"

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