I am currently working on A Depth Study for my year 12 Physics class, and am looking at relativity and time dilation of a lunar eclipse experience on the moon compared to as seen from on Earth. From what I understand there is no atomic clock data from the surface of the moon, and especially none relating to lengths of a lunar eclipse. However, I have decided that the best idea is to find a similar past project that doesn't directly show data for my investigation, but will be able to confirm that there is definently a time dilation. I have already made predictions for the time dilation of the moon over the length of a lunar eclipse seen from Earth using general and special relativity equations. If someone has an idea on how approach this, help would be much appreciated. Thanks.
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1$\begingroup$ To clarify. On Earth, a lunar eclipse begins when the Earth's penumbra first touches the edge of the moon, and then proceeds through penumbrial, to partial, to total eclipse and then back again. How is the length of the eclipse defined. For the observer on the moon, the eclipse begins when the penumbra reaches there location, and continues through partial and total phases. How is the length of the eclipse defined for a lunar observer, since these arent the same event. The observer on the moon cant observe the penumbra reaching the edge of the moon, only when it reaches their location. $\endgroup$– James KCommented Aug 14, 2021 at 15:10
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1$\begingroup$ Most calculations of timing of eclipses use an assumption that light will travel in a straight line, but this is not the case if you are considering relativity, both the Earth and the moon will bend light. The effect is tiny, but so is the effect of time dialation. $\endgroup$– James KCommented Aug 14, 2021 at 15:21
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$\begingroup$ You have a similar question Time of lunar eclipse relativity can you add a short explanation how this one is different, and in what ways the answer there applies here? Thanks! $\endgroup$– uhohCommented Aug 14, 2021 at 22:39
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$\begingroup$ From what I understand, theoretically we say that an observer at a point on the surface of the moon, would enter darkness at that location. And so if this was observed from Earth we would start and end our timing when the light disappears and returns from that point on the moon. Even with the bending of light, theoretically a test like this would still work. This is only a high school final year project, so I can point out certain flaws in the idea, however, $\endgroup$– Callum DuffyCommented Aug 15, 2021 at 7:27
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$\begingroup$ I just need to show some calculations to show how I have used this idea to 'prove' Einstein's theory of relativity. As we know time dilation occurs on the moon the theory is obviously right, but i need some data to prove this in consideration of the lunar eclipse. I am only looking at the lunar eclipses aspect so that the project is original. $\endgroup$– Callum DuffyCommented Aug 15, 2021 at 7:27
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A lunar eclipse as seen from the moon is actually a solar eclipse (by the earth). This should definitely be better to time than the lunar eclipse from the earth (which is a very 'fuzzy' event). Still, I doubt you could even come close to the microsecond accuracy needed here. Practically any other method would be much better. You could for instance just send a light signal of known duration from the earth and record its duration on the moon. That would give you a direct measure of time dilation after you remove additional effects like Doppler shift.
