Question

The Earth pulls on the Sun with the same magnitude force that the Sun pulls on the Earth. If these forces are equal, why does Earth go in orbit around the Sun? Why does Earth experience a great centripetal acceleration, while the Sun doesn't?

Answer 1

For every force there is an equal and opposite reaction force.

For instance, if one wants to find the acceleration of a person standing on a scales, he uses the force exerted by the scales on the person,

One doesn't consider the reaction force of the person on the scales.

Likewise for the force of the sun on the earth

m v^2 / R = G M m / R^2 descibes the force acting on the earth to produce the centripetal acceleration of v^2 / R

The sun experiences the same centripetal acceleration as the earth, but since the mass of the sun is about 333,000 times the mass of the earth the acceleration can be ignored for most purposes.

When a satellite experiences an acceleration of v^2 / r, the earth is undergoing the same centripetal acceleration. However since the mass of the earth is much greater than that of a satellite and the centripetal acceleration of the earth is ignored.