In one of my stories, I have a pile of people on a spaceship, heading to create earth's first planetary colony. Because they'll be going close to the speed of light for a long distance, they all know that by the time they arrive, everyone they left behind on earth will be long dead. And they've accepted it. But... They've just barely got going when the earth is suddenly destroyed. They suddenly have to deal with knowing that they're all that's left of humanity, and everyone they left behind is suddenly dead. How do you think people would react to that?
Ever watched (the newer) Battlestar Galactica? That's almost exactly what happens. Mechanics, setup, and premise are a bit different but the fallout is the same. Also, how did the colonists know Earth was destroyed?
I don't think there would be any one single way they would engage this knowledge. Firstly, they would all have had to find a way, prior to the Earth's destruction, to canalize the fact that the Earth is gone to them for all intents and purposes. I think some, for whom this canalization process is perhaps tenuous, would be hit hard by the knowledge. Others will come to the conclusion that it doesn't really change their reality at all since the Earth was not something they were ever going to engage again anyway. In other words, I think there will be a spectrum of engagement of this knowledge.
Well: Somebody could have sent a message via radio shortly before they died. The message would have outrun the ship at some place, albeit with a veeeeery low frequency. And if the planet is destroyed, a good telescope/analythical instruments could pick that up once they arrive at their destination.
They would be uber pissed and sad, but what can you do except move forward. Life will continue even when the Earth is gone. Also traveling C. would still be considered slow. As for science, even a fusion capable civilization would be barely able to go 10% C. So they would be mass exodus generational ships, unless they have found a way to live far longer than the average humans.
My logical mind would be aware (before the destruction) that there was no way of returning... but my illogical whimsy would hold the hope open that via some science fiction (wormholes or time-travel) I would be able to find a way to return. The destruction of Earth would shatter that whimsy. The nearest equivalent I can think of is that moment in your career when you realise that you are stuck doing this shit to pay the bills until the day you die (lets face it, this generation can no longer rely on pensions). You are not going to get rich quick, and even if you earn a very good wage- it is unlikely to be enough to grant you freedom from wage slavery. That realisation was met with a sense of melancholy and resignation. That idea that there are powers at work that dictate your future, and you are powerless to alter them. I think you almost become subjugated by this realisation. It just becomes a cold, hard fact of life. On this issue, I read some article by one of those Dragon's Den people (I'm doing some work with him on a residential development); in which he said that anyone can earn £100m. I have never raised this with him, because he is a client, but if everyone earned a £100m, it would barely cover the cost of a sandwich. Anyway, that is the nearest I can get to the reaction I would have, that shattering of those childish fantasies you hold onto.
Each colonist may have a different reaction. It would be cool - and probably cliched - if one (or more) of the colonists is responsible for the destruction of the Earth. Perhaps the commander of the colonists did it. Earth's destruction would not necessarily be a surprise to all of them...
Careful. Saying anyone can earn $100m (switching to dollars for keyboard convenience) does not mean that everyone can earn $100m.
I think many people would grieve for those whom they left behind. Even if they knew they would never see them again, they probably wished them a happy life. Depending on the nature and speed of the planet's destruction, the people left behind might have suffered a lot. Those on the ship now are sad because of that and they probably also find it hard to deal with the uncertainty. Now knowing how their loved ones died or whether or not they have suffered. Also, survivor's guilt. "Why did I go on this ship and not my cousin? I am alive and she is not. Could I have changed something?"
Maybe the colonists would take on a no-risk, preserve-the-traditions approach. They're all that's left of humanity, so I wonder if they'd work hard to try and preserve the notion of "traditional" humanity, and all its familiar notions. Not that they'd necessarily succeed, or that trying this would even be the best idea. But I can imagine "We're all that's left. If we change, humanity really will be dead." Then other people would argue that it's human to evolve and move on, and becoming stagnant to preserve the past is more of a death than leaving behind tradition.
Hmm I think it would be interesting if one of the characters had a miserable childhood and already felt disconnected with earth society. They could get a certain amount of schadenfreude from it's destruction. Plus that's guaranteed to cause some drama and friction with the other crew members. Maybe even start a dialog about what aspects of human society they should preserve and what needs to be discarded.
Maybe some of them would throw themselves into Science Fiction writing to try and cope with their grief. Some of them might turn to drink, if they have drink there in the future.
Oh, I was away from my work and completely forgot that there's a wormhole involved! That's how they get to another planet in a single lifetime. Anyway it's more just an excuse for the plot, I'm not into hard sci-fi because it gets dated so fast.
Also, some of them might just give up. I mean, that is a pretty big thing - the almost total destruction of your species. Not everyone would be able to handle that, and some people shut down in the face of overwhelming stress. Also, depending on how the planet was destroyed, other extreme reactions might result. An example from some fiction comes from the Bobiverse series (which is totally rad, by the way), where a group of people actively start sabotaging colonization efforts to escape the dying earth, because they figure that since humans killed earth, they'd kill any other planet they could get to, and so they should just go extinct for the betterment of the universe. Something like that. I mean, ultimately it's your story, so you get to decide what kind of people are on the ship and how they react. Hell, they might get really lucky, and all just be mentally and emotionally tough sons-of-bitches that manage to shrug off the loss of our homeworld and soldier on. "Keep calm and Reignite the Fires of Humanity." Or something like that.
Or maybe they are all maudlin, sentimental types, and they all commit suicide and/or go insane. Or maybe they meet a similar race of humanoids and integrate into their society.