Basically, exactly what it says on the tin: Find a POD after 1960 (even better would be after 1966, but 1960 is fine) which allows Apollo to continue and be the main human-launch capability of NASA (much like Soyuz).
My money is that the best POD is not escalating the Vietnam war, by staying with advisers, say. The stress of funding a war (critically, one that was exercising a fair bit of aerospace knowledge and funding), the Great Society, and NASA simultaneously led to the failure (in whole or in part) of all three. Without the war, more resources will be available for NASA, and perhaps without the actual martial competition going on cold warriors will feel more inclined to engage in virtual competition (even after we win the first round).
This is unlikely to result in early Mars landings, though, since the technology just wasn't good enough. In fact, it may not be terribly plausible to even keep going to the Moon much longer. A retrogression to LEO and space station competition might happen, unlike in OTL where the US was at best half-hearted in it's efforts to launch and maintain stations until well after 1991. That *might* still be enough to keep the Saturn V production lines open, at least a little longer, but with the 'wet workshop' concept and modularity, I wouldn't count on it. Even so, we would probably come out rather ahead of where we were, since we wouldn't be wasting resources on an ineffectual Space Shuttle, nor would we have a 10-year gap between manned space missions. I suspect robotic probes would actually come out a little less shafted here than IRL, since the burden and expense of developing a whole new space flight system just wouldn't be there, and the total NASA budget might be a little greater overall. We might see an actual TOPS! Or Voyager! *squees*
My money is that the best POD is not escalating the Vietnam war, by staying with advisers, say. The stress of funding a war (critically, one that was exercising a fair bit of aerospace knowledge and funding), the Great Society, and NASA simultaneously led to the failure (in whole or in part) of all three. Without the war, more resources will be available for NASA, and perhaps without the actual martial competition going on cold warriors will feel more inclined to engage in virtual competition (even after we win the first round).
This is unlikely to result in early Mars landings, though, since the technology just wasn't good enough. In fact, it may not be terribly plausible to even keep going to the Moon much longer. A retrogression to LEO and space station competition might happen, unlike in OTL where the US was at best half-hearted in it's efforts to launch and maintain stations until well after 1991. That *might* still be enough to keep the Saturn V production lines open, at least a little longer, but with the 'wet workshop' concept and modularity, I wouldn't count on it. Even so, we would probably come out rather ahead of where we were, since we wouldn't be wasting resources on an ineffectual Space Shuttle, nor would we have a 10-year gap between manned space missions. I suspect robotic probes would actually come out a little less shafted here than IRL, since the burden and expense of developing a whole new space flight system just wouldn't be there, and the total NASA budget might be a little greater overall. We might see an actual TOPS! Or Voyager! *squees*