I don’t know if this project is comparable to finding a needle in a haystack. Maybe more like finding a particular grain of sand on a beach.
I’m a bit of a math geek but the prospect of finding a 42-year-old Lunar Module cast away to orbit the Sun boggles the mind. It can probably be done as we have a pretty good handle on orbital mechanics. Limiting the variables will be a problem. To my amateur’s mind, the big questions would be getting precise enough data on the LM’s orbital elements after they left it behind, and what kind of other weird cosmic effects may have pushed it around over the last four decades. Solar wind and gravity gradients are way beyond my layman’s knowledge.
Apollo 10 was a dry run for the first landing mission, Apollo 11. Their orbit took them pretty darn close the the Moon’s surface, and they did everything but actually land. But even if the crew had grown a wild hair and decided to go for it, they would’ve been in for a long stay. The Lunar Module for the dry-run mission was used precisely because it was too heavy for a landing attempt. Grumman had embarked on an aggressive weight-reduction program for the landers, and apparently this one (LM-4, named “Snoopy” by the crew) didn’t make it to the scales in time.
But don’t feel too bad for the guys who almost made it. Two of the crew (Gene Cernan and John Young) ended up going back as mission commanders. Of the very few men who’ve been to the Moon, they’re part of the really select few who have done it twice. The third, Jim Lovell, flew around it twice on Apollo 8 and Apollo 13.
You’ve probably heard of that last mission. I would imagine his frustration at not landing was tempered by the relief of just getting back alive.
And in case you’re wondering, Apollo 10’s Command Module was named (you guessed it) Charlie Brown. Not sure where Lucy and Linus fit in here, but Snoopy actually has a long history with the space program, particularly during the 60’s when both the agency and the comic strip were at their heights. The Silver Snoopy is still a prized award within NASA ranks.