comets move around the sun in highly elliptical orbits.the gravitational force onthe comets due to sun is not normal to the velocity of comet,yet the work done by sun on comet over the complete orbit is zero.why??

the work done over the complete orbit is a definite integral which is the sum of the work done over infinitesimal intervals around all points of the orbit. Even though the work done over all but two intervals is nonzero the sum is zero because it is positive over some intervals and negative over others in such a manner that the positive work exactly cancels out the negative work.