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.

 

[pmacias]

Hello rowbot555,

Thank you for your question about gravitational time dilation. This is a fascinating concept in physics that has been studied for many years. To answer your question, we first need to understand what gravitational time dilation is.

Gravitational time dilation is the phenomenon where time moves slower in a stronger gravitational field. This means that time on the surface of the Earth moves slower than time on the surface of the Moon. This is due to the fact that the Earth has a stronger gravitational pull than the Moon.

Now, to calculate how much longer an atomic clock will run on the Moon compared to the Earth, we can use the equation t' = t√(1 - 2GM/rc^2), where t' is the time on the Moon, t is the time on Earth, G is the gravitational constant, M is the mass of the Earth, r is the distance between the Earth and the Moon, and c is the speed of light.

Using this equation, we can calculate that for every second that passes on Earth, approximately 0.999999999983 seconds will pass on the Moon. This means that the atomic clock on the Moon will run about 0.000000000017 seconds longer for every second that passes on Earth.

I hope this helps answer your question. If you have any further questions, feel free to ask. Thank you for your interest in gravitational time dilation.

Best regards,