Different points in earth are at slightly different distances from the sun and hence experience different forces due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the c.m. (centre of mass) causing translation and a net torque at the c.m. causing rotation around an axis through the c.m. For the earth - sun system (approximating the earth as a uniform density sphere)

if we consider earth and sun as a system, the earth experiences a centripetal force due to gravitational force of attraction of sun, and thus revolves around the sun in a circular orbit.

We know that,

Torque of any force F about a point is defined as

.(i)

Where,

r⃗ = distance of point of application of force from the point about which torque is to be calculated.

Since earth is symmetrical in shape, the net force due to sun acts on the centre of earth and since gravitational force is along line joining the centre of mass of earth and sun, the angle between r⃗ and F⃗ becomes 0°.

Therefore from eqn.(i)

τ = 0