The Navy obtained two Lockheed P-80As from the Army and assigned them BuNos 29667 and 29668. At least one, BuNo 29668, was modified with carrier-based hardware for catapult takeoffs and arrested landing. In the shipboard trials aboard Franklin D. Roosevelt on 1 November 1946, Marion Carl made four deck runs (starting from virtually the fantail) and two catapult launches at fairly light gross weights and about 35 knots wind over deck. All were satisfactory. Landings were a bit trickier, requiring precise speed control and pitch attitude at touchdown.
I've written about the original use of 29668 in carrier trials in my modeling blog. See: http://tailspintopics.blogspot.com/2011/11/lockheed-p-80a-carrier-trials.html.
Lockheed reportedly referred to the Navy P-80s internally as FO-1s, which they assumed would be the Navy designation, F for fighter and O for Lockheed-Burbank. However, it reportedly had been used officially for a handful of photoreconnaissance P-38s that the Navy obtained from the Army Air Forces and operated in Europe during World War II.* The next Lockheed fighter would therefore have been the F2O. In any event, the Navy apparently didn't assign its designation to the aircraft, always referring to them as P-80As.
BuNo 29667 was reportedly stricken on 13 February 1947 and 29668, on 4 June 1947. Lockheed proposed carrier-capable P-80Bs to the Navy in 1947 as the FO-2,
consistent with its referring internally to the Navy P-80As as FO-1.
The Navy, however, declined the opportunity in favor of production of
the jet fighters it had developed, the Grumman F9F Panther and the
McDonnell F2H Banshee.
The Navy did procure a third P-80A (Army Air Forces serial number 44-85235, Navy BuNo 29689) and a P-80B (Army Air Forces serial number 45-8557, Navy BuNo 29690). These were assigned to the Navy’s missile test facility at Point Mugu, California as a chase and safety aircraft. In the event that a missile went astray, the P-80 pilot was to shoot it down with his machine guns. Both of these P-80s were eventually painted Navy gloss blue. (689 was originally pearl grey like the Army Air Forces' P-80s.) Since these were not operational airplanes, the Navy did not bother to assign them Navy designations and they were referred to officially as P-80s. For more on these two P-80s, see http://herschpahlbooks.com/dedications/cliff_weirick.htm
In early 1948, however, the Navy realized that they couldn't get jet fighters from Grumman and McDonnell fast enough to meet its near-term needs for both jet transition training and operational squadrons. (This shortfall might have been caused, at least in part, by schedule delays in the production of Vought F6Us) The solution was to buy 50 P-80Cs from the Air Force to “train pilots and maintenance personnel in operation of jets.” These were stock 50 P-80s (49 P-80C-1-LO and 1 P-80C-5-LO), designated TO-1s since the Navy considered them to be trainers and they were not carrier capable. They were assigned BuNos 33821-33870. “To simplify problems of maintenance and logistic support”, all were initially based in the San Diego area. Of the 50, 36 were assigned to two squadrons and the rest were held in reserve for attrition.
VMF-311 received 12 and operated them from MCAS El Toro, California.
VF-6A, to be redesignated VF-52, initially received 24, supplementing its North American FJ-1 Furys. A handful of VF-52 pilots completed Air Force jet transition training in the P-80 at Williams Field, Arizona and returned to instruct the remainder of the squadron pilots; the squadron then functioned as the Navy's jet transition training unit.
The Navy also procured the two-seat trainer version of the P-80, the T-33, as the TO-2.
The Navy subsequently decided to transfer responsibility for jet transition training to the training command. VF-52 received Grumman F9F-3 Panthers and prepared to deploy. Advanced Training Unit SIX (ATU-6) at NAS Corpus Christi received its first TO-1 in July 1949. Two months later, the unit transferred to NAS Whiting Field, Milton, Florida, and was redesignated Jet Transitional Training Unit ONE (JTTU-1). The squadron's mission was extended to include training of fleet pilots. (The unit transitioned the U.S. Navy's Flight Demonstration Squadron, the Blue Angels, to jet aircraft.)
On 20 August 1951, JTTU-1 moved to NAS Kingsville, Texas and was redesignated Advanced Training Unit THREE (ATU-3).
In 1952, the TO-1 became the TV-1 and the TO-2, the TV-2 when the Navy finally decided to
recognize that Lockheed’s two manufacturing divisions belonged to
a single company.
Late in 1952, ATU-3 became ATU-200. The squadron's mission consisted of training newly designated aviators in familiarization, formation tactics, instruments and navigation using both TV-1s and 2s.
*That may be, but if the Navy did assign FO to those P-38s, it had forgotten about it by 1951, because it was then assigned to Lockheed's vertical-rising convoy fighter, better known as the XFV-1 after the Lockheed O's were changed to V's...