How much less does a ship at sea weigh during the full moon?

Hmmmm. If a ship weighs 1000 metric tons ( wild guess) this equals 1 billion grams. The acceleration of gravity at the equator is 980.66 cm/sec/sec and the centrifugal acceleration due to earths rotation is 3.4 cm/sec/sec. The acceleration due to the Moon at a mean distance of 3.844 x 10^10 cm with a mass of 7.35 x 10^25 grams is about 0.0033 cm/sec/sec.

This means that a billion gram Tanker will have a weight that varies by as much as 3.4/980.66 x 1 billion = 3.5 million grams due to its proximity to the equator where it will be lightest! As for the Moon, its gravitational acceleration is 0.0033/980.66 x 1 billion = 3.36 kilograms lighter when the Moon is roughly above the horizon or over head.

All this is approximate, but probably not too far off in order of magnitude!

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All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the
NASA IMAGE/POETRY Education and Public Outreach program.