[jeffreyH (OP)]

If two clocks were placed on the moon, one on the side facing the earth and the other on the side facing away from the earth, would they both record exactly the same elapsed time.

[CliffordK]

No doubt the clocks could be synchronized like the GPS clocks are.  However, configured identically and left free running, they may well be different as outer clock would have less Earth gravity, and travels in a larger orbital path.

My interpretation of the atomic clocks are that they are based on the frequency required to alter the hyperfine transition state of cesium or hydrogen, or other elements.  Changing the energy in the system would necessarily change the energy required to achieve this hyperfine transition, and thus also changing the base clock frequency.

But there are other relativity explanations.

If one is doing the experiment, then one might place 4 clocks around the equator, and one at each pole (too expensive?).  Thinking of tides, the tides are greatest and nearly equal on the side of the earth facing the moon, and opposite the moon (less gravity), and lowest (most gravity) at 90° from the moon.  Tidal effects would be similar on the moon.  The moon's density is also not uniform, with greater density (and presumably higher gravity) on the earth side, and lower density (less gravity) on the opposite side.

[jeffreyH (OP)]

On the side facing away from earth wouldn't you have the gravity from the earth adding to the effect as it is pulling in the same direction as the gravity of the moon? I know it would be a small effect but could it be measured?

[chris]

The more distant clock would feel a weaker gravitational influence from Earth, so I think time would travel faster relative to the nearside of the moon.

[jeffreyH (OP)]

The more distant clock would feel a weaker gravitational influence from Earth, so I think time would travel faster relative to the nearside of the moon.

Hello Chris

I don't know if you followed the hollow planet discussion but the cancellation of gravity in that scenario must have a parallel with the nearside of the moon. Some of the opposing gravity I assume would cancel out. I am curious to find out what the actual results are likely to be. Mainly to further some ideas I am pursuing. The tidal effect of the moon should be modified somewhat by the strength of the earths gravity at the surface.

If we were to remove some of the earths internal mass the tidal effect should increase.

As a late addition to this post, a thought. Opposing gravitational forces are subtractive but when moving in the same direction should be additive. However I believe you are still correct about time on the opposing sides.

[CliffordK]

The more distant clock would feel a weaker gravitational influence from Earth, so I think time would travel faster relative to the nearside of the moon.

I thought that initially.

But, if you think of the tides (on Earth), the tides are essentially equal on opposite sides of the Earth.  That means that on the two opposite sides of Earth, the gravity of the earth, moon, and the centrifugal force essentially all cancel themselves out (different from 90° offset)

I assume it would be similar on the moon, EXCEPT that the moon itself is not uniform density.  The denser side of the moon facing the Earth may have greater lunar gravity.

[jeffreyH (OP)]

The more distant clock would feel a weaker gravitational influence from Earth, so I think time would travel faster relative to the nearside of the moon.

I thought that initially.

But, if you think of the tides (on Earth), the tides are essentially equal on opposite sides of the Earth.  That means that on the two opposite sides of Earth, the gravity of the earth, moon, and the centrifugal force essentially all cancel themselves out (different from 90° offset)

I assume it would be similar on the moon, EXCEPT that the moon itself is not uniform density.  The denser side of the moon facing the Earth may have greater lunar gravity.

Hmmm! Thought this would be simple. When are things ever simple.

[AndroidNeox]

 I *think* that if the moon were a perfect sphere then the gravitational effects would cancel. However, Clifford makes a good point about the clock on the far side traveling farther. My *guess* would be that it would go slower than the clock nearer the Earth.

[jeffreyH (OP)]

I *think* that if the moon were a perfect sphere then the gravitational effects would cancel. However, Clifford makes a good point about the clock on the far side traveling farther. My *guess* would be that it would go slower than the clock nearer the Earth.

I did some quick calculations using the inverse square law and came to the same conclusion. The values used weren't real world values thought. I am going to use this to plot a gravity curve.