Gravity
| This is an AoPSWiki Word of the Week for March 1-7 |
Gravity is defined as the force of attraction between two bodies with mass as a result of the curving of space-time about them. It is the weakest of the four forces (gravity, the weak nuclear force, the strong nuclear force, and electromagnetism), but it is the only one which is always attractive, which means it is much more noticeable than the others.
History
The concept of gravity was first suggested by the ancient Greek thinker Aristotle, whom suggested that every object's "natural tendency" was to be at rest on the ground, which was why objects fell. He called this concept gravity. In the seventeenth century, this was improved on by Isaac Newton, who developed an intricate theory of gravity which applied use of his just-discovered branch of mathematics now known as calculus. He suggested the force that kept planets in orbit about the sun and the moon about the earth were the same that caused objects to fall. In the twentieth century, Albert Einstein refined Newton's theories by suggesting that the reason gravity was attractive was the bending of space-time, and refined Newton's formulae so that they covered slight discrepancies with actual results. This is the theory generally accepted today.
Related Formulae
- The attractive force in Newtons between two bodies with masses
and 
that are distance 
away from each other is
and 
that are distance 
away from each other is![\[G\frac{mn}{d^2}\]](http://latex.artofproblemsolving.com/e/7/e/e7e0dbe4f8824bacf82ce5a18cc327eeb15e7a23.png)
where 
is the gravitational constant. The gravitational constant is approximately equal to 
. Note that this means the gravity between two bodies is directly proportional to the masses of the bodies, and is directly proportional to the square of the distance between them as well.
