# Gravity

## Newton's Law of Universal Gravitation

Newton devised a formula to determine the gravitational force between any two given bodies.

"Any two bodies in the universe attract each other with a force that is directly porportional product of the masses of the two bodies and inversely proportional to the square of the distance between them."

${\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}\,}$

Where

${\displaystyle F\,}$= gravitational force ${\displaystyle (N)}$

${\displaystyle G\,}$= gravitational constant ${\displaystyle (6.67\cdot 10^{-11}{\frac {N\cdot m^{2}}{kg^{2}}})}$

${\displaystyle m_{1}\,}$= mass of the 1st body

${\displaystyle m_{2}\,}$= mass of the 2nd body

${\displaystyle r\,}$= distance between the center of object 1 and center of object 2

## Earth's gravity

To understand what is going on, one should be clear about the concept of mass. So what is mass? Nothing but one of the properties of any particle. Then what are the other properties? There are many other properties that have been discovered by scientists. Some of these are Mass, Electric charge, Strangeness, Spin, etc.

Everything in the universe is a collection of particles. And some particles couldn't exist without others. Whatever we see (or can't see) is just a collection of particles. Earth is also a collection of particles, as is a stone. By Newton's Law, both of these should attract each other with a force of magnitude proportional to the product of their masses and inversely proportional to the distance between their centers.

Take that stone. It's attracted toward earth's center with a constant force as neither mass nor distance changes. You can now see what happens if you throw a stone away from the center of earth. The stone is attracted toward the center with variable force as the distance changes. The distance between centers is ( radius of earth + distance of stone from ground + radius of stone ). The mean radius of Earth is 6731.0 kilometers.

If we compare the radius of the earth to the height and radius of the stone, we'll find those to be negligible. But only if we've guessed a suitably large value. Calculate the force between the earth and the stone by substituting into the above equation.

We know that force applied is the product of mass and acceleration (F=M*a). Force between the earth and the stone is the equivalence of the equations (F = m*a = G*M*m/r^2 ). Now we will find the acceleration of the stone toward center as G*M/r^2 which we denote as 'g', the acceleration due to gravity. It can be considered constant at the height to which one can toss a stone.

## Gravitational Potential Energy

Gravitational potential energy can be expressed as

${\displaystyle P.E.={\frac {Gm_{1}m_{2}}{R_{f}}}-{\frac {Gm_{1}m_{2}}{R_{o}}}\,}$

## Commentary

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