Everything falls on the Earth. Books, apples, balls, etc. All objects fall on Earth
accelerating 16 feet per second every second (9.8 meters per second every second).
Just like the objects on Earth, the moon is also falling towards Earth. But how fast?
We can figure this out by using (don't be surprised) the Pythagorean theorem.
Here is a diagram of the Earth and the moon.
Here are the explanation of the symbols.
=distance from the Earth to the moon.
=the distance the moon should have fallen because of the
gravitational affects of the Earth.
=the distance travelled by the moon in a second if the
Earth was not pulling it.
So, is the distance the moon falls in a second because of
the gravitational influence by the Earth. is the distance
the moon could travel without gravity acting on it for one second.
Let's find by using the Pythagorean theorem.
Let's ignore because it is a very very small number.
Now let's solve the equation.
is the distance the moon travels in a second if it is not
influenced by the gravitational affects of the Earth.
Therefore, to find , we must first find what is the speed
of the moon travelling around the Earth.
Since the moon orbits the Earth every lunar month, we get the equation:
is the circumference of moon's orbit.
The distance from Earth to the moon is 238,855 miles.
There are 2,360,591 seconds in a lunar month.
Substituting the values into the equation we get :
So, the spped of the moon is 40,281 inch per second. Since
is the distance travelled by the moon without the gravitational influence of the
Earth in a second,
Let's go back to the equation :
When the values are substituted in and solved :
So there it is--the moon falls inch every second towards
Brilliant isn't it. This was figured out by Sir Isaac Newton in the 17th century.
To understand this more thoroughly we must understand Newton's second law of motion
and the law of Universal Gravitation.