Inverse Square Law and Gravity

Isaac Newton was curious as to how gravity acted on objects such as an apple compared to other things such as the moon. Why doesn’t the moon come crashing down to Earth? Newton tested his theory using cannons. If you fire a cannon in an area without gravity or air resistance, the cannonball will continue in a straight path continuously unless acted upon by another force. If you were to fire a cannon on Earth with both of these factors, the cannonball wouldn’t travel in a straight line. It would actually travel in a parabola and the cannonball would eventually hit the ground due to the mysterious force of gravity. (Remember, gravity wasn’t discovered yet.) If you fired the cannonball so that it had a greater velocity, the cannonball would travel further before hitting the ground. He then theorized that if he could launch the cannonball at a fast enough speed, it would travel along the curved edges of the Earth. It would continue to circle the Earth, but never land on it. Newton thought that it was this same mysterious force that kept the moon in orbit with the Earth.

Hooke’s letter, as mentioned before, hinted towards planetary motion involving inverse squares. This was the missing piece Newton needed. He theorized that the force of gravity, F_g , was inversely proportional to the square of the distance between the objects, d². This can be denoted as: F_g  1/(d² )

Basically, this means that the farther away an object is, the less that gravity acts on that object. If an object is attracted to an object at a force of 16N, and the distance is doubled, with how much force will the objects be attracted? Well we can use the previous formula. if we substitute 2d in for d, then we know that the force will be one forth of what it was before. 16 (1/4) = 4, so the two objects will be attracted by a force of 4N.

It is for this reason that an apple falls to the ground, but the moon doesn't come crashing to the Earth and why we (being on the Earth) don’t crash into the Sun. The Earth exerts much less gravity on the moon than the apple since it is much further away. Gravity is also the mysterious force that keeps the Earth and other planets circling the Sun. This is what Newton determined during his experiments with gravity.

Here is a link to a youtube video that describes how the inverse square law works. This example is about the inverse square law in general, not just how it pertains to gravity.

_{https://www.youtube.com/watch?v=F-xNMdIXJIs}