There's a good chance this question won't make sense, or be moot, but just curious.

Time dialation has been confirmed by atomic clocks aboard planes, and well observed in the GPS satelite systems, etc. My question is this:

According to what I read, the moon orbits the earth at approx 1km/sec, which converted roughly to 2,237 mph. The effects of time dialation on a plane flying approx 600 were minisucle, but noticeable. This is roughly 4 times faster. Granted the effect would still be small. But wouldn't that add up over the few billions of years the moon and earth have been around?

Not that it matters, unless the face on the moon really is a man. Then that guy gets to age slower than us here on earth.

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I'm like one of those idiot savants...well, except for the savant part.
"In order to increase awareness of the homeless, security have been given binoculars."

Let's keep the math simple and say a few billionths of a second times four times 365 days times 4.5 billion years = not much! Dont' you have wares to peddle?

I couldn't find on a quicksearch what the clock differences were at 600mph. and with the invention of the winblows OS, i can't multitask-peddle wares and to BAUT (v.): To spend time posting inane questions on a scientific web forum. Generally applies to posts by Fazor

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I'm like one of those idiot savants...well, except for the savant part.
"In order to increase awareness of the homeless, security have been given binoculars."

There are also gravity effects, but to get the general ballpark, we can just say that the Moon ages at a rate that differs from the Earth by about (v/c)^2, which is about 1 part in 100 billion. So even after 4.5 billion years, the Moon (neglecting the fact that it used to be closer and faster) would only be a couple weeks younger than the Earth. It might actually be a couple months if you do it right, but still, that's not much for a planet.

no but i just thought it's kinda cool to think of it that way. *shrugs*

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I'm like one of those idiot savants...well, except for the savant part.
"In order to increase awareness of the homeless, security have been given binoculars."

Hey if the earth is going round the sun at (93 million miles times pi) per year does that make the sun or the earth the older?

If you all want to do some ballparking. In GR's weak field, low velocity limit, we can write this for clock rates:

dT/dt = sqrt(1 + 2(phi)/c^2) * sqrt[1 - (v/c)^2 ]

The first factor is the gravitational effect, and the second is the SR gamma effect. 'Phi' is the Newtonian gravitational potential (which will be negative, don't forget that, and its important that Phi be normalized to a reference of 0 at infinity for that to work).

That gives the clock rate relative to a fixed clock at infinity (where the potential is 0 ).

I stress the above is accurate only in the weak field and low velocity limit. The SR gamma factor in strong fields would become something that was actually the "local gamma", depending on the metric, and the g_00 term would be different that just the sum of the the inverse square potentials (that's the non-linear aspects of the field equations, there -- in the weak field limit, it becomes linear).

So if you want to compare clock rates, say for clocks on the surface of Venus vs the earth or moon, add up all the Newtonian potential terms, that of the sun, and the body you're on (you can ignore other far way bodies, as they will be very small indeed. For the earth-moon system, use both if you like). Then calculate the first factor above. Then get the orbital speed and calculate gamma.

-Richard