Would a horseshoe orbit planet be able to travel to their partner planet?
Recently I have become obsessed with the idea of twin sapient species developing on separate planets of the same horseshoe orbit. As I was considering the technological advancement of this planet, I realized that as one planet discovered space faring technology they would most likely attempt to travel to their partner planet. But considering the way that horseshoe orbits work, it seems less than likely. Horseshoe orbit mean that 1) the planets are only close once a year and even then for a very short time and 2) when they are close the speed change of the planets would make it difficult to chase after. Would a culture with 2010 level technology be able to successfully travel to and land on their partner planet? If not, why would they fail?
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Well, we did travel to the Moon with 1960s (and some even 1950s) technology. We also had reasonably detailed plans to use the same underlying technology to make a year-long Venus fly-by mission in 1973-1974, but as we know, we never made the trip. So technology on its own likely wouldn't have been the limiting factor in a mission such as the one you propose.
A Saturn V booster packed quite a lot of $\Delta v$ (delta-v, velocity change) capability, and with sufficient motivation, it certainly wouldn't have been beyond us to build and launch several of them for a single mission. (That was one of the original ideas for how to get the US to the Moon: Earth Orbit Rendezvous. They went with Lunar Orbit Rendezvous in the end.) The tyranny of the rocket equation would have been problematic, but we probably could get to at least 15 km/s or so with just chemical rockets if we really wanted to. The return trip might actually be easier than the outbound trip. So delta-v budget likely wouldn't have been the limiting factor. Mid-course corrections can account for smaller errors, and are a common thing to do in spaceflight. (The earlier you make a course correction, the less delta-v budget is expended in the correction because the change has more time to have an effect.)
Generally speaking, when going places in space, it isn't so much a problem that the target is moving quickly if you can just calculate where the target will be when you get there. That's no different from going to the Moon, or to Mars, or for that matter to Pluto. Computers are good at solving that kind of problems, so our ability to end up in the correct place at the correct time likely wouldn't have been the limiting factor.
Since we have now concluded that none of the major obstacles -- technology, delta-v or navigation -- are likely to be factors that would limit our ability to reach such a planet, it stands to reason that we would be perfectly able to mount such a mission, given an incentive to go there. Depending on the specifics of the orbits involved, it might take some time to make the trip, so we'd likely start off by sending an autonomous probe rather than a manned spacecraft, but there wouldn't be any magic involved.
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