Gravity and Time and a Fictional Setting

[ParanoiA]

Well, it's about time for one of my silly questions.

 

I had asked once before if the gravitational field strength increased or decreased as one moves from the surface of say, the earth, to its core. The answer was that it decreases, roughly linearly, as one moves to the core - finally ending up at zero.

 

Now, I can only assume this is the case as one moves from the surface of the earth, out into space, as well. From this assumption, I would conclude that the gravitational field strength is strongest on the surface.

 

Are these correct assumptions, or have I missed the boat again?

 

 

 

This is the setup for my question, in a fictional setting...

 

Let's say that in an alternate universe or whatever, the laws of physics have been somewhat perverted in comparison. Let's say that time is effected by gravity, such that it appears to move faster in a stronger field in reference to weaker fields, and this is exaggerated.

 

So, someone floating in the air 3 miles above the surface should be experiencing a lower gravitational field strength (unless I was corrected above), than someone standing on the surface.

 

My question...Would the reference frames be such that the floating dude appears to be moving in fast-motion when observed by the guy on the surface? And would the guy on the surface appear to be moving in slow motion when observed by the floating dude?

[insane_alien]

yep, gravitational field strength does decrease as you get further away from earth but not linearly.

 

and yes, clocks high above the earth do seem to run faster. we had to take this into account when we made the gps system.

 

its only a few microseconds/second out though so it doesn't look like an oldtime slapstick comedy film.

 

and the relationship is the inverse square of distance.

[Sisyphus]

 

and the relationship is the inverse square of distance.

 

Clarification: distance from the center of the Earth.

[bombus]

Well, it's about time for one of my silly questions.

 

I had asked once before if the gravitational field strength increased or decreased as one moves from the surface of say, the earth, to its core. The answer was that it decreases, roughly linearly, as one moves to the core - finally ending up at zero.

 

Now, I can only assume this is the case as one moves from the surface of the earth, out into space, as well. From this assumption, I would conclude that the gravitational field strength is strongest on the surface.

 

Are these correct assumptions, or have I missed the boat again?

 

Mmm. have you seen my thread on saltwater amphibians (and the EET). Have we a mechanism for planetary expansion?

[insane_alien]

there is no mechanism as it doesn't happen. do not hijack this thread.

[swansont]

and yes, clocks high above the earth do seem to run faster. we had to take this into account when we made the gps system.

 

One should note that this varies with the gravitational potential, though, and not field strength.

[bombus]

there is no mechanism as it doesn't happen. do not hijack this thread.

 

I'm not trying to hijack anything. You seem very sure it doesn't happen. When you have lived a few million years perhaps you can show us all proof of that.

[insane_alien]

One should note that this varies with the gravitational potential, though, and not field strength.

 

oh, didn't know that. just corrected one of my misconceptions about GR then.

 

 

I'm not trying to hijack anything.

 

well the topic you introduced is completely irrelevant to the topic at hand and will not be discussed further here. if you want to talk about it open up a new thread.

[ParanoiA]

One should note that this varies with the gravitational potential, though, and not field strength.

 

Parden me, if I may be so lazy, but what's the difference between the two? And does that impact my conclusions in the OP?

[Mr Skeptic]

The gravitational field decreases as you approach the center of the earth past the surface because of the amount of mass that is no longer attracting you toward the surface. If you are inside a sphere of mass, the mass does not attract you more in any particular direction than any other, canceling out. The mass decreases as r³ more than counteracting the increase in gravitational strength as 1/r².

 

As you leave and go above the surface of the earth, the gravitational field strength decreases as 1/r² but the gravitational field potential increases as 1/r. So long as you are outside a sphere of mass, the gravitational field would be [math]Field = \frac{GM}{r^2}[/math] and the gravitational potential (if you take infinity as zero potential, which is useful but sometimes confusing) the potential is [math]Potential = -\frac{GM}{r}[/math]. Multiply these by a mass and you get the gravitational force on the mass and the gravitational potential energy of the mass, respectively. However, for change in gravitational potential energy (which you can measure) you want to take the difference in potential energy between two points.

[ParanoiA]

Hmm...well I looked this up on Wiki and I don't understand most of the words on that page.

 

I don't understand the concepts of Potential and Field related to gravity. I can kind of follow along the equations, but I'm not inferring any qualitative value from it.

 

If any fictional setting were to utilize this twist of physics, I'm wondering if it would be better applied in reference to gravitational potential, rather than field strength. My thought was merely for objects high in the air to appear to move faster, in reference, from the ground, due to the difference in reference frames. It seemed some relationship to gravity could be responsible for that. But I never thought about (or even knew about) potential vs field strength, or etc.

[swansont]

Parden me, if I may be so lazy, but what's the difference between the two? And does that impact my conclusions in the OP?

 

Potential is the depth of the well. Field strength is the steepness of the slope of the wall. At the center of the earth you would have the largest potential, even though the field strength has gone to zero — you're at the bottom of the well, and would have to add the most energy to get out.

 

It doesn't affect your answer, because you have defined a situation where time hypothetically depended on field strength. (You'd probably run into a conflict somewhere along the line, though, if you explored the impact on physics.)