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

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Discussion Overview

The discussion revolves around the comparison of how much longer an atomic clock would run on the Moon compared to one on Earth, focusing on the effects of gravitational and kinematic time dilation. Participants explore the theoretical implications without reaching a definitive conclusion.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant, rowbot555, inquires about the duration difference of an atomic clock on the Moon versus Earth, seeking a specific value or equation.
  • Another participant mentions the gravitational time dilation factor, suggesting it can be approximated using the formula involving gravitational potential differences.
  • A different participant introduces the concept of kinematic time dilation, noting that while it can be calculated, its effect may be minor compared to gravitational time dilation in this scenario.
  • Another contribution emphasizes the importance of defining time dilation, explaining that observers at different locations may perceive time differently based on their relative positions and motion.

Areas of Agreement / Disagreement

Participants express various viewpoints on the factors affecting time dilation, but no consensus is reached regarding the specific duration difference or the relative significance of gravitational versus kinematic effects.

Contextual Notes

Participants highlight the need for careful definitions of time dilation and the assumptions involved in calculations, particularly regarding the perspectives of different observers.

Who May Find This Useful

This discussion may be of interest to those studying relativity, gravitational effects on time, or the practical implications of timekeeping in different gravitational fields.

rowbot555
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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
 
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welcome to pf!

hi rowbot555! welcome to pf! :smile:

the gravitational time dilation factor is approximately 1 - ∆U

where ∆U is the change in the gravitational potential,

in this case (Mearth/Rearth - Mmoon/Rmoon)2G/c2 :wink:
 
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.
 
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.
 

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