15 light years is a distance so vast that we don’t have a hope of doing anything about it with current technology. Sure, we could invest huge sums in a highly risky project that would take several human lifespans to get there, then hope it was still operating at the end of the trip, and that it could successfully navigate its way to an orbit around the planet, and that it could successfully explore the planet and transmit findings back to us.
But we’ll never do it. Too much risk, too much cost, too little payoff in too long a time.
But there’s a better solution - telescopes. Big mother-freaking telescopes. Huge interferometry arrays in space or on the moon. Theoretically, we could build a telescope array large enough to let us resolve details the size of mountains or even smaller on a planet in another star system. We can certainly build telescopes powerful enough to examine the atmosphere for bio markers. We could build huge radio telescopes fixed on the distant system that could pick up signals equivalent to our radio broadcasts.
That’s what we’d spend the next 50 years doing. We already plan to do stuff like that, starting with next year’s Kepler mission, which is designed to discover exactly the kind of planet you’re talking about.
Five years from now, the Terrestrial Planet Finder programs will be able to catalog the nearest terrestrial planets and measure the composition of chemicals in their atmospheres.
Going out past 2020, there are already tentative plans for the Life Finder, a telescope array that could take very detailed spectroscopic measurements of the atmospheres of nearby planets, measuring things like levels of pollutants, ozone, methane, etc.
Then there’s the Planet Imager, which is currently funded at the ‘study’ level. An interferometry array 6000 km across with a starshield the size of a football field to block the light of the star, the Planet Imager would be able to directly image nearby planets to about 25 X 25 pixels, which for an earth-sized planet would give us a resolution of about 300 miles per pixel - not enough to see artificial structures, but big enough to see continents and oceans and perhaps rainforests and deserts.
That stuff is all do-able today with enough funding. We’ll be doing it, but we probably won’t see something like the Planet Imager for maybe 40-50 years. But if we discovered a nearby planet with oceans, we’d probably accelerate such projects dramatically, and maybe even take on bigger ones.
Theoretically, it’s possible to make interferometry arrays much bigger - even the size of the orbit of the earth, which could theoretically resolve details as small as a foot across on planets around the nearest stars. I’m sure practical limitations would come into play here, as well as limits imposed by quantum effects and the need to collect enough photons from the target (and sort them out from the photons arriving from the background, other transiting planets, the star itself), but I could imagine arrays the size of the earth-moon system, capable of resolving cities and agriculture on planets near us.
And of course, with a telescope like that we could examine thousands of other planets. And if we found another earthlike planet that close, the odds are very high that there would be hundreds of them within reasonable resolving range of such a telescope. So we wouldn’t be putting all our eggs in one basket.
And a telescope like that could be used for many other observations. It could actually resolve Jupiter-sized planets anywhere in our galaxy, and see right back to the earliest moments of the universe’s creation, and in significant detail.
That’s where the bang for the buck will be, and where the best chance is to learn more about such a planet, at least for our lifetimes. We won’t be sending any probes.