Measuring the tidal effect of the moon on the earth

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An undergraduate physics major seeks to measure the tidal effects of the moon and sun on gravity at different times of day, estimating a gravitational difference of about 10^-6 m/s^2 from the sun and three times that from the moon. The challenge lies in accurately measuring such small differences in gravity, as conventional scales cannot handle the required mass. Suggestions include using a pendulum, which is sensitive to minor gravitational changes, or a seismometer, though the latter requires extensive calibration. Laser interferometry is also proposed as a precise measurement method. The experiment presents significant challenges but offers an intriguing opportunity for exploration in gravitational physics.
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I'm an undergraduate physics major and I want to create an experiment where I measure the difference in gravity between sunrise, noon, sunset, and midnight (and everything in between for that matter) due to the tidal effect from the moon and sun. I did some calculations and I expect the difference in gravity due to the sun to be on the order of 10^-6 m/s^2 and due to the moon to be about 3 times that.

My dilemma is how to measure that tiny difference in gravity.

I have yet to come up with a good way. Any scale I could get that's accurate enough couldn't handle the large mass needed to generate a tiny difference in force. I've thought a little about using interferometry to try to measure small variations in the deformation of a wire or a bar or something, but that still seems complicated because I'd have to know the exact properties of the material I am using.

Any ideas?
 
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That's an interesting experiment you're trying to carry out! It certainly seems like a difficult task. Have you considered using a pendulum or a seismometer to measure the gravitational changes? Pendulums are particularly sensitive to small changes in gravity and can be relatively easy to set up. Seismometers can also be used to measure gravitational changes, although they require more calibration and may not be as precise as a pendulum. Alternatively, you could look into using lasers to measure the difference in gravity. There are a few different methods available, including laser interferometry, which can be very accurate. Good luck with your experiment!
 
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