Gravity questions.

[Ceritus]

Ok, I have a few questions and I am going to try to write it out in the correct fashion.


There are 2 planets in 2 identical solar systems but not connected and both are in seperate vaccums.

If one planet was earth and the other planet was identical to earth but rotated on its axis slower would the gravitational force the planet exudes increase?

If one planet was earth and the other planet was identical to earth but 10 times larger in every aspect to include mass and rotated on its axis 10 times the speed earth rotates would the planets gravitational force be equal?

If one planet was earth and the other planet was identical to earth but 30 times its size but had 1/2 the mass of earth and rotated as fast as earth would the gravitational force be less?

Does rotation or movement of any kind have an effect on gravity?

 

[geni]

Ok, I have a few questions and I am going to try to write it out in the correct fashion.


There are 2 planets in 2 identical solar systems but not connected and both are in seperate vaccums.

If one planet was earth and the other planet was identical to earth but rotated on its axis slower would the gravitational force the planet exudes increase?

no

Does rotation or movement of any kind have an effect on gravity?

The gravitational effects of a rotating body on space time can have some interesting effects if it is massive enough.

 

[Walter Wayne]

Ok, I have a few questions and I am going to try to write it out in the correct fashion.


There are 2 planets in 2 identical solar systems but not connected and both are in seperate vaccums.

If one planet was earth and the other planet was identical to earth but rotated on its axis slower would the gravitational force the planet exudes increase?

Any change would be incredibly small if any. I've never done the calculation so don't know. There would however be a different tangential component to the gravity. However, on something as small as earth, and rotating as slowly that tangential component if very small.

If one planet was earth and the other planet was identical to earth but 10 times larger in every aspect to include mass and rotated on its axis 10 times the speed earth rotates would the planets gravitational force be equal?

No, the gravitational force would be 10 times larger for the larger planet.

If one planet was earth and the other planet was identical to earth but 30 times its size but had 1/2 the mass of earth and rotated as fast as earth would the gravitational force be less?

Half the mass, half the gravitational pull.

Does rotation or movement of any kind have an effect on gravity?

Yes it does, but an incredibly small one. To get an idea of how small, Gravity Probe B has to use incredibly sensitive gyroscopes suspended in superfluids to measure the affect of earths rotation on it gravity field.

If you read up on black hole theory, you'll find that a stationary black hole has a spherical event horizon, where as a rotating one doesn't. Of course the numbers one is dealing with in a black hole are so much larger that the affect would be noticeable.

Walt

ETA: Woot, the result of the Gravity Probe B experiment are due out in April 2007.

 

[Almo]

To my knowledge, the only thing that matters for gravity is mass. That's assuming no weird relativistic speeds or anything.

So, directly answering your questions:

The slower rotating planet in the first example would have identical gravity to the faster one.

In the second example, if the larger planet has 10x the mass, then it has 10x the gravitational pull, regardless of rotation (again, I'm unsure about what happens at relativistic speeds).

In the third example, if the larger planet has half the mass, then it has half the gravitiational pull.

This all assumes you measure the gravitational pull at the same distance from the center.

If you're standing on a planet that has the same mass as the earth, but it's smaller, you'll be closer to the center, and therefore feel a greater gravitiational pull. But at the same distance from the center (provided you remain outside the surface of the planet), you'll measure the same gravity for both.

ETA: HUGE masses (black holes) mess with this as well. I add this because what Walt said reminded me of it.

 

[fuelair]

Well said Almo - beat me to it!!

 

[Ceritus]

Thank you everyone

 

[TjW]

Well, he may be asking about the apparent gravity on the surface of the planet.
That could change with the rotation rate. As the speed of the planet's surface approached orbital velocity, the apparent gravity would approach zero.
See Hal Clement's "Mission of Gravity".

 

[Ceritus]

I was speaking on the surface of the planet.

 

[kalen]

Does rotation or movement of any kind have an effect on gravity?

There will be the tiniest of GR effects.

And there's the centrifugal force as well. At the poles (spin axes) that will be zero. At other places on the earth, it is

where v is the tangential component to a persons velocity around the spin axis and R is the distance to the spin axis. For a 75 kg person at the equator where this effect is the largest, he will weigh less by about 2.5 N. The earth is flattened at the poles and is bulging slightly at the equator because of this, as well.

ETA: [latex]v^2/R[/latex] is an acceleration. [latex]mv^2/R[/latex] is the force.

 

[Just thinking]

Ok, I have a few questions and I am going to try to write it out in the correct fashion.


There are 2 planets in 2 identical solar systems but not connected and both are in seperate vaccums.

If one planet was earth and the other planet was identical to earth but rotated on its axis slower would the gravitational force the planet exudes increase?

Basically, no.

If one planet was earth and the other planet was identical to earth but 10 times larger in every aspect to include mass and rotated on its axis 10 times the speed earth rotates would the planets gravitational force be equal?

Interesting -- if the planet was 10 times larger in every aspect, including mass, you will have a very low density planet. Here's why. If the diameter increased by a factor of 10, the volume would increase by a factor of 1000 -- and an increase of mass only 10 times would mean the mass of 10 Earths in a volume of 1000 Earths. In other words, it would have the density of 1/100 of what we have here on Earth (overall mean density, that is).

Now, as for gravity -- let's examine it at the surface. For us, it's pretty much 1 G everywhere with minor variation. On this other world, we have a mass of 10 times that for holding us to the surace -- but wait. That surface is 10 times greater away from the center of mass of the planet than it would be here on Earth. Since gravitational forces are determined by ...

F = G x (m1 x m2) / (r x r)

... we get the new force as ...

F = G x (10m1 x m2) / (10r x 10r) = 1/10 that of Earth --- or 0.1 G.

And I have yet to take rotation into account. Spin this guy at 10 times the angular velocity of Earth and you won't be able to stand on the surface at the equator. But out in space, it would simply behave as a mass 10 times that of Earth.

If one planet was earth and the other planet was identical to earth but 30 times its size but had 1/2 the mass of earth and rotated as fast as earth would the gravitational force be less?

Out in space it would bahave as a mass 1/2 that of Earth. At the surface its gravity would be so weak you might be able to jump off it. It has only half the mass of the Earth in 27,000 times the volume -- and now you're 30 times as far from its center of mass as you would be here on Earth.

F = G x (0.5m1 x m2) / (30r x 30r) = 1/1800 that of Earth.

Does rotation or movement of any kind have an effect on gravity?

Only at relativistic velocities -- yours are nowhere near that.

 

[Ceritus]

So basically if a planet was rotating at the speed of light it would change its values.

Are there any celestial bodies that rotate at the speed of light?

 

[Cuddles]

So basically if a planet was rotating at the speed of light it would change its values.

Are there any celestial bodies that rotate at the speed of light?

A body can't rotate at the speed of light. Rotation is measued as angular velocity in radians/second while the speed of light is a linear velocity. Asuming you mean "Are there any rotating bodies of which any part has an instantaneous velocity equal to the speed of light?" the answer is still no. Nothing can be accelerated to the speed of light. As a particle's energy increases, it's mass increases. This means as it speeds up, more energy is required to produce the same increase in velocity. As the velocity approaches the speed of light, the mass approaches infinity and so an infinte amount of energy would be required for it to reach the speed of light.

Another way of looking at is, in the case of a rotating body, any particle traveling close to the speed of light would be thrown off into space since gravity would not be strong enough to hold on to it. If the gravity was strong enough to hold something traveling at the speed of light it would also prevent light escaping and would in fact be a black hole.

 

[Just thinking]

Relativistic velocities does not always mean at the speed of light -- merely velocities that incur relativistic effects. Usually these become appreciable at 10% of the speed of light and above, but not really noticable until even 75% of the speed of light. But it all depends on what is doing the moving and what exactly you're measuring.

Anyway -- objects that rotate at relativistic velocities are collapsed stars; usually black holes, but white dwarfs and neutron stars may qualify as well IIRC.

 

[TjW]

Also, you might want to consider the structural properties of planetary material.
After a hypothetical planet is spinning fast enough that the equator is zero gee, spinning it faster puts tension on whatever the planet is made of. It will start coming apart.

 

[Ziggurat]

Only at relativistic velocities -- yours are nowhere near that.

The effect is only easily noticeable at extremely high velocities, but it exists at any velocity. There's an experiment going on right now to test the general relativistic effects of the earth's rotation. The satellite that's testing this is refered to as Gravity Probe B, and it's a fantastically sensitive piece of equipment. What it's looking for isn't a change in the overall strength of the gravitational field (since we don't actually know exactly how much the earth weighs, so we have no reference), but instead an effect known as frame dragging, which shows up in how the gravitational field changes from place to place as the sattelite orbits earth.

 

[Just thinking]

The effect is only easily noticeable at extremely high velocities, but it exists at any velocity.

Well, of course ... but you'll notice I said "Usually these become appreciable at 10% of the speed of light and above, but not really noticable until even 75% of the speed of light. But it all depends on what is doing the moving and what exactly you're measuring." So even though every day velocities produce relativistic effects, one doesn't usually consider taking those effects into account. I did however find your link very interesting -- thanks.