You meant ‘orbit around the moon’ not sun, didn’t you?
I meant sun because during the days the ship between the Earth and the moon it is in an independent orbit around the sun. Once it gets to the moon it would orbit the moon.
Some longer missions to consider are the recent trips to Mars. The probes go into elliptical orbits around the sun until they meet Mars's orbit right when Mars is passing. Then they fire the engines to match speed with Mars and enter its orbit.