Dear All,

Can someone please provide me with a quantitative answer to this question I have been thinking about for a while. As a complete non-physicist I have no idea how to start to work this out, or even if my question makes sense. The question is this:

GR predicts (I think from what I have read) that time will appear to move a different rate in stronger gravitation fields. I know that the local gravity is different on the surface of the moon relative to the surface of the earth. Therefore, as measured from the earth, would time on the surface of the moon appear to progress faster or slower to earth time? If so, by how much? Do you need to consider the gravity from earth,moon and sun in this calculation? If you need to consider the sun as well, would that mean that any difference in the passage of time on the moon as measured from the earth would in fact be very small?

Any help gratefully received at this point, I have given up trying to work this out.

Regards,

sqrt(1-(v^2/c^2)) is the equation for the slowing of time of an object moving at a velocity v
I am guessing that the effect of gravity might be modeled by v=escape velocity
however this is just a guess

as far as the sun is concerned the difference caused by it would vary as the moon orbits the earth, however, the difference is probably negligible and would probably cancel out

also if you are going to determine the passage of time in relation to that on the surface of the earth you will nedd to factor in the relative velocity of the moon (its orbital velocity as well as the effects of each objects' spin)

if I am correct about the escape velocity/time relationship then the difference is very very roughly (i did this from memory), .000000002% this roughly equates to one second every 300000 years

this would mean that the apollo astronauts came back 4.5 microseconds younger and in 3 billion years the moon would have aged between 2 and 3 hours more than the earth (neglecting rotation which might make a little closer to 3 hours)