Question:
I have read the weight of the moon is about 81 billion
tons. How is this calculated?

Replies:
Sir Isaac Newton calculated that the gravitational force between objects
(say planets, or anything else) is proportional to the square of the
masses, and inversely proportional to the square of the distance between
them. Cavendish measured the constant of proportionality. It is known as
follows:

f = GMm/r^2

By using a body's mass, knowing the force (mg) and the radius of the earth,
the mass of the earth can be calculated.

Now, knowing the mass of the earth, and the orbital radius of the moon, and
the acceleration of the moon about the earth, the mass of the moon can be
found.

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