Apollo 13 was in the hybrid orbit at the time of the accident, which takes you around behind the moon at a low altitude but is not a true free return. The panel likely went into a high orbit around Earth. May still be there.
I agree, and in fact I hope it is. Had it followed the Apollo 13 trajectory according to AMSO and a relatively recent news story, it would slam into the earth's atmosphere over the atlantic almost perpendicularly on the third orbit (the article and the orbiter simulation agreed pretty well considering that AMSO's scenario didn't account for any delta-V due to the explosion as far as I'm aware). Just for fun I tested to see what would happen if you added some delta-V with a short burn in the direction the bay 4 panel is facing at the start of the AMSO A13 scenario just before the explosion. The result was that the new trajectory continually orbited the earth with regular perturbtions by the moon. It didn't seem to result in any collisions until at least 1971, but I didn't run the simulation any longer than that. What it showed me was that if propelled in certain directions, it's entirely possible that the Apollo 13 panel could indeed still be out there in high earth orbit. Since it's quite small it would be hard to spot just about anywhere along the orbit until it gets near periapsis (my quick and dirty test resulted in a periapsis that varied between 40,000km and about 100,000km), so it could easily remain undiscovered for 40 years. Even if it did re-enter the atmosphere a long time ago it would still be nice to know that that was its most likely fate based on knowing the rough trajectory it took.
---------- Post added at 10:03 PM ---------- Previous post was at 09:39 PM ----------
Quick update, something struck me and it wasn't the missing panel. In the movie Apollo 13 I remember them instructing Swigert to assume a certain attitude and "null your rates" which I believe would mean that they were NOT in the barbecue roll at the moment of the explosion. That's just the movie though and we all know it's far from reliable when it comes to those technical details. Looking through the actual mission transcript online I see that on page 166 of the pdf they do tell Swigert to "roll right to 060 and null your rates for photography of Comet Bennett."
http://www.jsc.nasa.gov/history/mission_trans/AS13_TEC.PDF
At 02 07 50 12 Swigert states he's "going to maneuver to 060, 090, and 0." This looks like the key to me, 060 must be the roll angle, so is 090 pitch and 0 yaw or the other way around? The explosion occurs only 5 minutes later as they're taking care of the other house keeping measures, so I think it's safe to assume they have not resumed the barbeque roll by then. If that's true, it should be easy to figure out at least what direction the bay 4 panel was facing at the moment of the explosion. Does anyone know what the standard protocol was for reporting those attitude numbers? If I can find that out I can at least come up with some reasonable numbers for delta-V using the previously posted report as a guide. I figure I'll sim a range of possible delta-Vs out to the present, translate them all to TLE's, and fish around in those areas one by one to see if I can find anything. I can easily knock out a couple dozen possible TLE's and their surrounding areas each night with clear weather when the missing panel should be close to earth. Even if the TLE is off by several minutes I can follow each possible track forwards and backwards by that amount to see if anything is there.
One more update, according to Apollo 11's transcript, it looks like the standard attitude for the barbecue roll would be pitch 090, yaw 0, so I suspect Swigert was saying he was rolling to 60 degrees with a pitch of 090 and a yaw of 0. I'll have to do some more research to find out how to match those angles in orbiter, something I should probably already know how to do
.