The aircraft departed Canberra for Merimbula on a VFR flight with a departure instruction to remain on the Tower frequency. A short time after departure, ATC instructed the pilot to call Approach, but there was no reply. The aircraft was then observed to make a right turn to intercept the outbound track to Merimbula although no transponder return was being interrogated. The aircraft was subsequently observed orbiting over the Googong reservoir. ATC tried unsuccessfully to make radio contact. Shortly after, the aircraft was observed to be returning to the airport for an approach to runway 30. On finals it was evident that the landing gear was not fully extended and a full aerodrome emergency was declared. The aircraft then made a low fly pass and the tower observation confirmed that the landing gear was not down and locked. The aircraft subsequently made a wheels up landing on the grass parallel to runway 30. When the aircraft came to rest, the sole occupant walked clear of the aircraft. During the maintenance investigation, the landing gear retraction system components were tested and found to be serviceable. The aircraft battery was found to be fully discharged.