How Much Longer Does an Atomic Clock Run on the Moon Compared to Earth?

[rowbot555]

Hi All

I whish to know how much longer an atomic clock will run on the moon than it does on the earth. Considering time on Earth for 1 second, I know it will be very slightly longer on the moon. How much longer is my question, or maybe an equation. Don't consider the travel there, start both clocks after the one on the moon is already there.

thanks for your answer ahead of time,

rowbot555

 

[tiny-tim]

welcome to pf!

hi rowbot555! welcome to pf!

the gravitational time dilation factor is approximately 1 - ∆U

where ∆U is the change in the gravitational potential,

in this case (M_earth/R_earth - M_moon/R_moon)2G/c²

 

[bcrowell]

There will also be a kinematic time dilation, which can be calculated as in SR, but I think in this example it will be a small effect compared to the gravitational one.

 

[twofish-quant]

Also you need to be careful about defining time dilation.

You have a machine on Earth that is putting out regular pulses, say once every one second. It's getting monitored by a receiver in deep space, and the deep space receiver will see the time arrive at slightly more than once a second and that is your time dilation.

It's important to define what you mean by time dilation because someone sitting next to the pulse machine will see the pulse come out once a second.