Question

Why does the earth revolves* around the sun?

Answer 1

If it did not it will fall in to the sun.

Explanation:

There are two balancing forces acting on earth when it revolves around the sun.

[Source:mathworks.com]

Gravitational force of attraction.
Law of Universal Gravity states that every body in this universe attracts every other body with a force which is called force of gravity. The force

`F_G =G (M_1.M_2)/r^2`

Where `M_1 and M_2` are mass of two interacting bodies, `r` is the distance between the two and `G` a constant.

It has the value `6.67408 xx 10^-11 m^3 kg^-1 s^-2`
In our case, one is the sun and other earth.

Centrifugal force.
Centrifugal force is a 'fictitious' force that appears to act on all rotating objects and is directed away from the axis of rotation.
It is given by the expression

`F_(centri fugal)=mromega^2`

where `m` is the mass of rotating object, `r` the radius of circle of rotation and `omega` its angular velocity.

These two forces balance each other and keep the sun-earth system in equilibrium.

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*in the question 'revolves' is preferred word as earth 'rotates' around its axis.