The gravity associated with any object is
not related to the origins of the object, so
even if the moon was originally part of Earth
(something which is still unclear), there is no
reason it would have the same gravity as the
earth. Instead, the attractive force of gravity
between two objects depends on the masses of
the objects and the distance between them, and
is given by the equation F =
where m1m1 and m1 are the
masses of the objects, r is the distance
between them, and G is a constant called
the gravitational constant.
m3/(kg-s2). Note that this
is different from the better-known acceleration
due to gravity g=9.81 m/s2.) So we can
see that objects with more mass will exert more
force from gravity, but that force will decrease
as the separation distance increases. By comparing
the mass and size of the earth and the moon, we
can see why the gravity acts more strongly on
something on the surface of the earth than on the
moon. The mass of the earth is ~100x that of
the moon, but the radius is only ~4x that of
the moon. The higher mass offsets the increased
distance, and the force of gravity is greater on a
person on Earth than on the moon (by ~6x).
So the really short answer is that gravity
is higher on earth than on the moon because
the earth has a lot more mass and is only a little
bit bigger across.
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