I was reading fastest trip to the moon and that question got me in the mood for asking "what's the record for X" style questions. I thought of 5-10 but I'll limit myself to one because they're not particularly... well thought out or researched. Anyhow, I want to find the longest operational surface probe judged as follows:
- Anything (rovers, probes, cameras, sensors, etc...) counts as long as it's on the surface of another body and is able to transmit data back to Earth.
- Only the time after the object has landed on a foreign body should count towards the time.
- Impacting is not counted as 0 seconds, the probe must soft land on the body.
- Transit time from Earth to X does not count, even atmospheric entry.
- Only objects that are functional count, if a probe stops transmitting, that's its end time.
If there is a period of time the probe was not functional, just make sure to mention it. But you don't need to do calculations to remove that amount of time unless you want.
I'm guessing it would be one of the Mars rovers for longest and a Venus or the Huygens Titan probe for shortest, but I'm ready to be surprised as well :).