Exploration of space

A current topic if any. I had some thoughts recently about how hard it might be, even with FTL travel to explore even small regions of space.

A hypothetical setting: a way to travel faster than light has been discovered and a stable jumpdrive-ship built. The maximum speed it can travel is roughly 1 ly / day, vastly more than the speed of light. The drive can be activated in the outer solar system, to where it takes a week or two to travel with the sublight drives.

The practical range of travels with the ship is limited to two months, after which it starts running out of food, air and fuel. 6 weeks of travel is roughly 95% safe not accounting accidents or unforeseen problems.

So around 42-56 lightyears is the maximum range of the ship. The ship can, when entering a system, survey the entire star system in a 1-3 days, depending on the system, with an average of 1,5 days.

It would be logical for the ship, being still first of it's kind, to first make short jumps to nearby systems: Proxima Centauri, Alpha Centauri, Sirius, etc. First to the Centauri system and back, a 9-10 days trip in total. Then a two-system journey, say to Sirius and then Lalande 21185. Sirius is 9 days of hard travel, then about 5-6 days to Lalande 21185 and finally back home, another 8 days. In total, the journey took 21-22 days plus a few days to survey the system.

Now the ship has spent around 5 weeks exploring and has reached 3 systems. A still longer journey is planned out: going by Barnard's Star and Ross 154 to HD 217987. Barnard's star is a little over 5 light years, getting there is 6 days. From there, Ross 154 is about the same distance, 6 days more. Then, to HD 217987, roughly 9 more days. And let us say 6 days of surveying. The total time of this star trek has been 27 days, almost a month. The ship can still travel a little less than doubly this travel, we are approaching the limit. The ship has now seen 6 systems during it's journeys and systems close to Earth are running out. And a roughly two-day survey on each system gives only a slight clue on the planets and their possible habitability. And the usefulness of each system can only be guessed at the moment. But that is not the concern of this exploration vessel.

Now an even longer trek, off first to UV Ceti, Epsilon Eridani, then Wolf 359, then Ross 128 and finally to DEN 0255-4700. The travel takes 9 days to UV Ceti, from there about 7 days to Eplison Eridani, then almost two weeks to Wolf 359, then say a 5 day travel to Ross 128 and finally a 12 day travel to DEN 0255-4700 and 17 days home. The total travel, including the surveys take about 70 days. The ship will be almost running on fumes and the crew a bit tired when they return. And now there has been almost 4 months of exploring. Not so much as such, but so far the ship has explored 11 systems out of the 50 systems within 15 light years from Sol. With the rate remaining the same, within one year there would be around 30-35 exlored systems, within 20 months all of the nearby systems would be explored. But of course the rate would drop and I'd assume that the real time spent to explore all the 50 systems would be somewhere around 2-2½ years. Possibly 3.

Now humanity has explored a roughly spherical volume of space, 15 light years in diameter. The local bubble, the next step, is 300 ly across. With a spherical volume, it would be around 94247 cubic ly. This area might contain somewhere around 10 000 solar systems and assuming rate remaining constant (it wouldn't), it would take around 300 years to explore. After this step, humanity has explored around 1/100th of the distance from the Sun to the Galactic Core.

Of course, while time progresses, there would be more exploration ships, the technology would improve and people would start building colonies and starbases further away from the Solar system. And starships could be away longer periods of time, perhaps even a few years, exploring.

Still, exploring a galaxy might take time. And of course there might be prioritizing. If the priority is in establishing new colonies, surveys might only be done to systems likely to have habitable planets. This would quicken up the exploration a great deal, but a huge portion of stars would be left unobserved.