[Little Bang]

Moderation note: This thread was extracted from “Origin of the Universe,,,,Bang or no Bang”, because it is primarily a discussion of relativity, not the Big Bang Cosmological model

Pluto, do believe that a clock on earth runs slower than one in a geo-stationary orbit?

[Moontanman]

Originally Posted by Little Bang

Pluto, do believe that a clock on earth runs slower than one in a geo-stationary orbit?

I can't speak for Pluto but if Einstein was correct it would have to run slower. If not then we need to find out where the theory went wrong.

[Little Bang]

Albert has already been proven right, I just want to see pluto admit to that fact.

[CraigD]

Originally Posted by Little Bang

Pluto, do believe that a clock on earth runs slower than one in a geo-stationary orbit?

According to Relativity, yes, a clock on Earth’s surface, at the equator, does run slower (about 1.0000000002437 times, by my calculations) than one in a circular geostationary orbit (about 35786 km above ground level).

A clock on Earth’s surface at the equator, however, runs faster (1.0000000003253 times) than one in a lower circular orbit (say a typical low-earth orbit of about 200 km AGL).

A fun exercise is to calculate the altitude at which the clock on a satellite runs at the same speed as one on the surface. Everything need for the calculation can be found at the wikipedia articles “Earth”, “orbital speed”, “standard gravitational parameter”, “time dilation”, “gravitational time dilation”, and “speed of light”.

[Little Bang]

Craig, I do not understand why you are trying to confuse a simple statement. I never made any attempt to delve into the relativity aspects of time. Either a clock slows as it falls into a gravity well or it does not. Now if you have evidence that it does not please enlighten us.

I notice that Pluto did not respond.

[modest]

Originally Posted by Little Bang

Craig, I do not understand why you are trying to confuse a simple statement.

Your situation unfortunately complicates itself.

Originally Posted by Little Bang

I never made any attempt to delve into the relativity aspects of time.

Which is the first complication. All differences in proper time are matters of relativity, are they not? There are two types of time dilation and Craig is accounting for both. A satellite (even one in geosynchronous orbit) has a different relative velocity from some earthly reference - it must be accounted for. But, even if it is temporarily ignored, the following sentence still isn't quite right:

Originally Posted by Little Bang

Either a clock slows as it falls into a gravity well or it does not.

It does not. Not as you state it here. It must slow compared to something because it surely won't slow compared to itself.

If there is no difference in velocity between two observers who are situated higher and lower in a gravity well then I would agree that the lower observer has a slower proper time compared to the higher observer. Is this ok?

-modest

[Little Bang]

Yeah, that's just fine.

[CraigD]

Originally Posted by Little Bang

Craig, I do not understand why you are trying to confuse a simple statement. I never made any attempt to delve into the relativity aspects of time. Either a clock slows as it falls into a gravity well or it does not. Now if you have evidence that it does not please enlighten us.

I’m not trying to confuse your statement (“Pluto, do believe that a clock on earth runs slower than one in a geo-stationary orbit?”, in post #171), but to encourage you and other readers to consider it more carefully. In particular, I think it’s good for people to actually go through the exercise of using the equations of relativity to calculate their own results, rather than accepting the results of others on faith or intuition. With practice, it’s not difficult, and the results can be surprising, often revealing significant flaws in our intuitive grasp of physics.

In the example you gave - a clock A on the surface of Earth, compared to a clock B in orbit - there’s more to consider than just their difference in altitude (In the case of a geostationary altitude, about 6378 vs. 42164 km from the Earth’s center). They are also moving at different speeds (about 465 vs. 3075 m/s). So both gravitational time dilation and time dilation due to speed must be taken into account. In the geostationary orbit case, the relative gravitational time dilation (, the clock on Earth runs slower) is larger than the relative speed time dilation (, the clock on Earth runs faster), so the net relative time dilation results in the clock on Earth running slower. If clock B is in a lower orbit, however, the relative speed time dilation is larger than the relative gravitational time dilation, and the clock on Earth runs faster than it.

If you could eliminate velocity (for example, by raising clock B using a mast set at the geographic North or South Poll, rather than orbiting it), or eliminate mass (for example, have clock A and B fly in their usual circular paths far out in space), then their relative time dilation could be explained using only one of the time dilation equations. For a real-world example, however, both must be used.

PS: This discussion of relativity seems to me off-topic, so if there are no objections, I’ll move it and perhaps other off-topic posts to a separate thread.