How does the gravitational field inside a sphere differ from outside?

Inside a sphere, the gravitational field is proportional to the distance from the centre.

When considering the gravitational field inside a sphere, it is important to note that the mass of the sphere is assumed to be evenly distributed. This means that the gravitational field inside the sphere is proportional to the distance from the centre, and is inversely proportional to the square of that distance. This can be expressed mathematically as F = Gm(r)/r^3, where F is the gravitational force, G is the gravitational constant, m(r) is the mass enclosed within a sphere of radius r, and r is the distance from the centre.

In contrast, outside the sphere, the gravitational field is proportional to the distance from the centre of mass of the sphere. This means that the gravitational field outside the sphere can be treated as if all the mass of the sphere is concentrated at the centre. This can be expressed mathematically as F = GmM/r^2, where M is the total mass of the sphere and r is the distance from the centre of mass.

Overall, the gravitational field inside a sphere is different from outside due to the distribution of mass within the sphere. Inside the sphere, the gravitational field varies with distance from the centre, while outside the sphere, the gravitational field varies with distance from the centre of mass.