Question

what is work done by earth in completing half the rotation around the sun ?

Answer 1

$$\begin{gathered} W=\overrightarrow{F}.\overrightarrow{s} \\ W=Fs\cos \theta \end{gathered}$$
Now, if the force is acting perpencular to the displacement, θ=90^o.
Work done is zero.
Assuming circular path, gravitational attraction (F) is perpendicular to the displacement.
So, no work is done.