How is the mass of the moon determined?

Answer 1

The moon doesn't revolve around the earth; instead, the earth and moon revolve about a common center of mass, and this causes a periodic wobbling in the earth's location. By making careful measurements of the positions of solar system objects, one can detect this wobbling, and determine that the center around which the earth/moon revolves is 1/81 the distance from the center of the earth to the center of the moon. That means that the moon's mass is 1/81 of that of the earth.

Also one can look at the positions of asteroids. Occasionally, one comes close enough to be significantly close to the moon to have its orbit changed by it. In this situation of two highly unequal masses, the moon is much more massive than the passing asteroid and by using Newton's laws of gravity, once can determine the mass of the moon from the observed deflection of the asteroid's orbit (having taken account of the earth's influence too)

Obviously these calculations are really very difficult, particularly when you realize that they were done before the days of calculators and computers by a French astronomer Charles-Eugene Delaunay who devoted twenty years to a study of the precise orbit of the moon, which led to accurate masses of the earth and moon being known long before humanity launched satellites into space.

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Answer 2

The mass of the Moon is determined through its gravitational effect on objects like spacecraft or other celestial bodies. By observing the orbit of these objects around the Moon, scientists can calculate its mass using Newton's law of universal gravitation and Kepler's laws of planetary motion. The mass can also be inferred from the Moon's gravitational interaction with Earth.