## Center of mass of the earth and the moon

Thanks for several interesting replies, the technical level is a lot higher here than at comparable forums.

It's true that I ignored the acceleration of the earth. Two hypotheses seem to be offered in the discussion. That the pendulum will show a much smaller deviation or that the deviation will be exactly zero. The existence of tides makes me doubt that the sum of all graviational forces (mentioned and unmentioned ones) on the pendulum would stay unchanged over time.

However, the tides is a topic where I've tended to mess up the explanation, so I will not try to justify this hunch :-)

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 Quote by Labrodor The center of mass of the earth is approximately at the center. The center of mass is also where the force vector of the gravitational force is pointing. (down that is). Now the total gravitational force excerted on me should be the sum of the force excerted by the earth plus anything else, especially the moon. With the sum of these two vectors being what I feel as "down", should the direction of down change as the moon's position in the sky changes? ..... Is this enough to measured? Since we've got the ratio of the lengths in the triangle, we quickly find that if we have a pendulum hanging from a 300 meter long string (say, from the eiffel tower) it will deviate by 1 millimeter. That is, a change in 2 millimeters as the moon passes from one side of the horizon to the next.
The direction of gravitational force is not towards the center of the Earth (as other's have mentioned).

It does remain in a virtually constant direction provided you're remaining at the same location on the Earth.

Since your goal is to measure how the Moon changes the direction of down (regardless of what direction that may be), then Yes, that will work provided your pendulum is long enough that you can measure the deviation.

The main complication would be cancelling out the noise from the Sun and the planets since their geometric configuration will affect the direction of "down" as well. In practice, screening out the unwanted noise to measure the desired attribute is just part of the challenge (often the largest part of the challenge).

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