Equation for Gravity Going to Zero at Finite Distance?

[jaketodd]

Seeking an equation for gravity where gravitational force goes to zero at large distances

I realize the Newtonian formula has trouble with this. And I've heard gravity never goes to zero in relativity. So, maybe a quantum gravity one, that isn't too complicated? Thanks!

 

[PeterDonis]

I realize the Newtonian formula has trouble with this.

Why would you think so? The standard Newtonian formula for gravitational force gives zero as $r \rightarrow \infty$.

I've heard gravity never goes to zero in relativity.

Where have you heard this? Have you looked at any GR textbooks?

 

[PeterDonis]

maybe a quantum gravity one

There is no accepted quantum gravity theory, so there's no way to provide this.

 

[jaketodd]

Why would you think so? The standard Newtonian formula for gravitational force gives zero as $r \rightarrow \infty$.
Where have you heard this? Have you looked at any GR textbooks?

Well, I need an eq that has gravity going to zero at a reasonable distance (not infinity). Like my pencil does not attract my pen, on my desk here, a few cm apart. Even if there's no big, popular quantum gravity equation, there must be some that aren't too complicated, and are somewhat accepted. Can you guys help?

Thanks

 

[PeterDonis]

I need an eq that has gravity going to zero at a reasonable distance (not infinity)

There isn't one. But you can easily run the numbers to show that, for example, the gravitational force between your pen and your pencil is way, way, way too small to matter. Which is quite good enough.

 

[PeterDonis]

Moderator's note: Thread moved to Classical Physics forum since the basic question has nothing to do with quantum physics, and doesn't even require relativity.

 

[jaketodd]

There isn't one. But you can easily run the numbers to show that, for example, the gravitational force between your pen and your pencil is way, way, way too small to matter. Which is quite good enough.

Well, now that we get a bit into detail, it's not for a pen and pencil. I want to use it for masses such as the Planck mass, separated by a very small distance. No such equation huh? So gravity does indeed go to infinity in relativity? Thanks

edit: Sorry, I should not have said "large distances" in my original post.

 

[Dale]

Even if there's no big, popular quantum gravity equation, there must be some that aren't too complicated, and are somewhat accepted

There are none yet.

 

[PeterDonis]

I should not have said "large distances" in my original post.

Indeed.

I want to use it for masses such as the Planck mass, separated by a very small distance. No such equation huh?

There is the Newtonian equation, but of course it has not been tested on anything like such distance scales.

There is relativity, which mathematically has no restriction on how small distance scales can be, but which has other issues with a question like yours. See below. (Also, of course, relativity has not been tested on anything like such distance scales either. Nothing has. The smallest distance scale we can currently probe experimentally is a good 15 orders of magnitude or more larger than the Planck length.)

So gravity does indeed go to infinity in relativity?

If you mean, at small enough distances, no, for two reasons.

First, relativity has issues with treating objects as point particles, because that would require the object to be of infinite density and would therefore create infinite spacetime curvature at the object's location, which breaks the model.

Second, in GR, if a massive object gets compact enough, it will be a black hole, not an ordinary object. And the "acceleration due to gravity" above a black hole increases without bound as the hole's horizon is approached, not as "zero distance" is approached. So the intuitive model you appear to have in mind, of having a "gravitating mass" that is arbitrarily small and can be approached arbitrarily closely, is not really possible in GR.

 

[PeterDonis]

Moderator's note: Thread moved to relativity forum now that the OP question has been clarified and does indeed involve relativity.