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Why “super” for supersynchronous orbits? Why not “trans”? and discussions and answers there got me wondering:

Question: What was the first spacecraft intentionally placed in a supersynchronous Earth orbit where supersynchronous means having an orbital period longer than one sidereal day (23 hours, 56 minutes, 4+ seconds)

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Depending on exactly what you want, I've found two plausible candidates.

Luna 3 was (briefly) in a highly elliptical orbit in 1959. It spent at least a few months in space, and had an orbital period of ~360 hours. It was assumed to have burnt up in the atmosphere in 1960, so it must have made a few orbits in that time. Given that the perigee was quite low, and it only needed to swing by Earth once to offload its images and then its mission was over, it seems tenuous to suggest it was in a deliberate supersynchronous orbit before it re-entered, but if you have sufficiently relaxed standards it might just pass.

More convincingly, Vela 1A was in a nice roundish high Earth orbit in 1963. According to wikipedia, it had a perigee of ~101000km and a period of ~375 hours. It is still there, if you wanted to visit.

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