# Gravity

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## What is Gravity?

Gravity refers to the force which governs every single object containing mass in the universe. It is the force that pulls objects close to each other, which is how celestial organizations such as solar systems, galaxies, etc. come together to exist around each other. Each body has its own gravitational force, even the Earth. It was examined by Isaac Newton when he saw an apple falling off a tree and became interested in the same.

### Newton’s Law of Gravity

The concept of gravity was first theorized by Sir Isaac Newton, a renowned physicist. To understand the gravity IIT JEE, we must first understand Newton’s Law. Before Newton, there were many Greek and Roman theories about gravity, without naming it anything but ‘natural motion.’

Newton figured out the concept of gravity when an apple fell from a tree - he thought that there must have been some of the other forces that made an object like an apple move from rest. He further corroborated this idea with himself by wondering about how the moon might fly away from the Earth if the Earth did not have some force keeping it close to itself.

Sir Isaac Newton and his game-changing apple

Upon discovering this, Newton named this force “gravity” and also applied this concept of gravitational force to other objects too, from something as small as an atom to something huge like celestial bodies.

### How to Calculate Gravity?

The SI unit for Gravity is m/s⁻² and the gravitational force on the Earth is 9.807 m/s².

We calculate the force of gravity using the following formula:

F=( Gm₁m₂)/ d²

Where,

F = the force of gravity

G = the universal gravitational constant

M₁ = mass of object 1

M₂= mass of object 2

d (or r) = distance between the centers of both objects

Mass is calculated in kg and distance is calculated in meters.

• The universal gravitational constant is 6.674 * 10⁻¹¹m³.kg⁻¹.s⁻²

• Mass of objects 1 and 2 can be determined by weighing them or looking it up online.

• Determining d or r requires you to measure the distance from the center of the earth.

• The distance from the surface to the center of the Earth is 6.38106 m

• After finding out the components, put them together in the formula to find the force of gravity of an object.

### Escape Velocity

We know that velocity refers to the speed at which an object moves in a specific direction. Now, to understand escape velocity, we must apply the concept of velocity to objects that are trying to leave a specific gravitational field.

The best example of escape velocity is that of a rocket taking flight from the Earth. The speed at which it must blast off from the surface of the Earth is what we call the escape velocity of the rocket. We measure this in the same SI unit as velocity and speed - km/s.

Different objects and bodies have different escape velocities required.

• The Sun - 620 km/s

• The Earth - 11.2 km/s

• The Moon - 2.4 km/s

An interesting fact: the escape velocity of a black hole, or the “point of no return,” is the speed of light, which is 3 x 10$^{8}$ m/s.

Gravitational Potential (V)

For gravity IIT JEE preparations, the gravitational potential is an important topic. The gravitational potential of any object is a measure of the work that is required to be done per unit mass to bring that object from one point to another. There is a fixed decided starting point and a fixed reference point for where to move the box from and to.

We use this following formula to calculate gravitational potential:

V$_{G}$ = mgΔh

Where,

V$_{G}$ = gravitational potential or work to be done
m = mass
g = acceleration due to gravity
Δh = distance above a surface

The SI unit for gravitational potential is J/kg.

### Gravitational Potential Energy (U)

Gravitational potential energy is also important for gravity IIT coaching and preparations. It refers to the work done to bring an object from infinity to any given point.

The formula for gravitational potential energy is:

U = - $\frac{GMm}{r}$

Where,

U = gravitational potential energy
G = universal gravitational constant
M = mass object 1
m = mass object 2
r (or d) = central distance

The negative sign in the formula denotes the inverse relationship between gravitational potential energy and distance.

We also calculate gravitational potential energy from a certain height, using this formula:

U = - $\frac{GMm}{R}$ + h

Where,

U = gravitational potential energy
G = universal gravitational constant
M = mass object 1
m = mass object 2
R = distance
h = height

The SI unit of gravitational potential energy is kg m$^{2}$ / s$^{2}$ same as other forms of energy.