Aircraft can orbit either left or right. Either pilot can be the handling pilot but captain is usually, but not always, in the left hand seat. Autopilot has a green rating so does most of the work. Orbits orientated to get the most out of the radar system, or to get the sun out of the captain's eyes.
Many tricky decisions to make on the E-3 flightdeck, but all the time in the world to make them.