**T**he
Law of Gravity was published by Sir Isaac Newton in 1687. He devised it
to explain the mutual attraction experienced by all bodies of matter,
such as an apple dropping to the Earth when the tree lets go of it. Newton
suspected that the force pulling the apple down was the same one holding
the Moon in its orbit. He went so far as to calculate the strength of
this force at the distance of the Moon. In doing so, he determined that
gravity falls off as one over the square of the distance to the center
of the Earth.
This relationship is known as the inverse-square law of gravity, and
is expressed

Force = G m_{1}m_{2} /d^{2}.

Here, m_{1} and m_{2} are the masses of the two objects,
and d is the distance between them. G is called the gravitational constant.
Newton
showed that an object moving under the inverse-square law of gravity
follows an elliptical path. Since Johannes Kepler had discovered that
the planets move in ellipses, Newton concluded that they also obeyed
his law of gravity. The force that made apples fall to the ground was
the same that affected the planets. In a bold leap, Newton then conjectured
that the law of gravity was valid throughout the universe.

The inverse-square relation also applies to light and sound. The intensity
of light or sound falls off as one over the square of the distance from
the source. For example, doubling your distance from a disturbing noise
decreases its intensity (and presumably your annoyance) by a factor
of four. A useful fact to remember.

## Gravity and the Moon

Using Newton's
Law of Gravity, we can determine the force that the Earth exerts on the
Moon.
In the metric system, the masses are in kilograms, the distance in
meters and the value for the force is given in Newtons. The Gravitational
constant G is 6.67 x 10^{-11} N m^{2} kg^{2}
(0.0000000000667 Newton meters squared per kilogram squared). The mass
of the Earth is 5.975 x 10^{24} kg; the mass of the Moon is
7.35 x 10^{22} kg; the average distance between them is 3.84
x 10^{8} meters.

Plugging
these values into the equation for Newton's Law gives us a force of
1.99 x 10^{20} Newtons.

How does this compare to anything familiar? If an apple weighs about
a third of a pound, then the force acting upon it at the surface of
the Earth is 1.34 Newtons. The force needed to hold the Moon in its
orbit is about 200,000,000,000,000,000,000 Newtons. Something to consider
the next time you're weighing apples at the grocery store.

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