newtonian mechanics - What would happen to the orbital radius of the Earth if the radius of the Sun is decreased but without any loss of its mass?

What would happen to the orbital radius of the Earth if the radius of the Sun is decreased but without any loss of its mass?

According to Newtonian gravity the acceleration due to gravity will increase when the radius is decreased? And the orbital radius will decrease. But then this seems to easy and simple. Can anybody help?

Answer

The gravitational attraction between two bodies depends on the mass of each body, and the distance between them. This increases as the product of their mass increases, and decreases exponentially as the distance between each body's center of gravity (aka centre of mass) increases (inverse square law). This calculation using their masses and separating distance is then multiplied by a constant to make the dimensions consistent and the numerical result match observation. Since your question says that only the radius of the sun decreases without any loss in mass, the only thing that changes is its density. Its center of gravity does not change, so the force of gravity won't change either. The only thing in your question that changes is the sun's density, and this does not have an effect on orbiting bodies. Your perception of being "easy and simple" is indeed correct.