That is the dreaded question. You can imagine on a journey of thousands of years and potentially a population some of which can live indefinitely how often it will be asked.
They will ask a little more nicely than our kids ask it. What is our expected time of arrival?
With some relatively basic math and an idea of how fast specific forms of propulsion will go you can come up with estimates of how long it will take to get from solar system to solar system.
Is that then the end of it? Your journey will take 13,000 years round trip plus a few years to stay at your luxurious destination.
Well, no, I don’t believe that is it.
Technological progress will continue while the generation ship is in transit. It will happen on Earth, but as I have indicated in previous articles we need a sizable population on the generation ship to ensure that knowledge is propagated and to maintain the culture.
The whole population doesn’t need to be geniuses. Some of population will be really smart people. Really smart people with an extended lifetime (we can hope). People without a profit motive to withhold their gains in knowledge and every reason (to get there and back again like Bilbo, but faster than anticipated).
In addition, there will most likely be codops (Computerized Doppelgangers) on board the ship – the number of them may certainly exceed the number of physical humans. If you are taking a generation ship – you would want codops of all the top minds in their fields on board.
This means that there needs to be research facilities on board the generation ship. People and codops will be actively researching and modelling ways of going even faster. Over hundreds or thousands of years it isn’t a question of if they will be successful, but when, and how much of a performance increase can really happen.
We could even throw together a sort of schedule (for the benefit of our science fiction with the generation ship) and figure out how much faster and when. Perhaps there will be incremental increases slowly tipping the speed faster from 3.5 million miles per hour and faster. Each increase in speed reducing round trip time. It may well be that increases through scientific discovery might slow down – starting at (for example) 1 year for a .1 of light speed, then 2 years for another .1 of light speed – and so on. Even so, with these distances, even small increases in overall peak cruising speed will have results in how long it takes overall.
There would be a real reason for a codop or person to periodically ask – “Are we there yet?” or more likely, “Has our scheduled arrival date changed?”
I look forward to a future where we have generation ships and a part of humanity – at least 200,000 physical people strong and who knows how many codops – goes there and back again. That ETA for returning to Earth – it isn’t etched in stone.