Since the transit method of detecting exoplanets requires perfect alignment of orbits, would a Kepler-type telescope yield more exoplanet detections if sent out of our solar system even to relatively realistic interstellar distances (say, 0.1-0.5 light years)? Essentially, what I mean is changing the coordinates at which we'd do the observing.
@SF. is right. It is true that a location far from Earth could have access to different orbital planes and thus potentially see a different set of occultations an transits, you would have to move very very far away from the Earth to make any difference.
The same budget and time would be much better spent developing a next generation optical space telescope which uses mirror segments that are no longer even part of the same spacecraft, but instead are separated by tens or hundred of meters from each other but can still combine their signals (optically or otherwise) to synthesize an extremely high resolution optical aperture as big as the distance between the segments. This is the same principle used by radio telescope arrays.
With a larger effective aperture you can resolve objects farther away, which opens up a much larger volume of space for direct imaging of solar systems instead of relying on geometry for transit measurements alone. Right now only a handful of systems close to the Earth have any kind of direct imaging data.
There are several problems with that idea:
- As mentioned by uhoh and SF, reaching a point far enough away from our solar system to make a different observation than Kepler's takes so much time, that the telescope and the data will in fact be antiquated by the time they reach that point - even IF (and that's a very very big IF) we could even manage to build it that it would still work in that distance (power source, transmission array, controlling the telescope's orientation etc.), it would be of limited use.
- The angle to watch would still be the same. Yes, you would be far out in space, but you would STILL only be able to detect most planets with a transit method, simply because now that you might be a little closer to the Alpha Centauri System, you would still be light years away from almost any other star and still face the same problem as you face on earth. You might detect a few different planets, due to a slightly different angle, but they wouldn't be that much different unless you consider moving hundreds of light years - which would take millions of years with our current technology.
- Direct detection by visual imaging with current technology is out of the question unless you get very close to a star system or the planet is sufficiently large and far away from its parent star. The limiting factor in this is, that the parent star is so bright, it outshines the reflected light of its planet by several orders of magnitude. If they are close to the parent star, the star will be too bright for them to be imaged directly (be it in microwave, IR, visual or UV range). If they are far away from their parent star, the reflected light is far too faint to be detected unless that telescope would be close to the star system observed - and then it could only detect the planets of that specific star system.
Somebody else can tackle the detailed maths, but the longer your baseline, and the more observatories, the more complete the coverage. Two observatories in the same orbit as Pluto but on opposite sides of the sun would still only be 0.0012 of a light year apart. Three would be better and they would still be close enough (just) to allow for the communication necessary to allow coordinated observations necessary for parallax type measurements and comparisons. Going much further doesn't actually help since there would be no way to get the information back to Earth to be useful.