Not too far off in the future, maybe 20-50 years from now, an anomaly is detected a little ways outside our solar system and it's like nothing we've ever seen before. Researchers begin studying it immediately and soon it becomes clear that whatever it is will destroy our planet in less then 500 years. Independent teams around the globe who also have been studying the anomaly begin to confirm the initial reports and it seems that earth may be in serious trouble.
However amidst the panic a team of scientists announce that they may have a way to save earth from it's impending doom. But there's only one problem, they would need a spaceship capable of bringing a team to the anomaly for the plan to work. With current spaceflight technologies it seems impossible, we can't even get to mars yet without frying astronauts! Plus current thruster technologies would mean a generation ship would be needed to make it to the anomaly.
The only way this could even works is if every country on earth poured every spare dollar into spaceflight research, and even then you'd need to cut funding from every program you could to ensure you were putting as much as you could into research. But if earth is just going to be destroyed anyway there's not much point in spending money anywhere else is there? If we all just worked together on this project for even the slightest chance of saving the planet, would we all give it a shot and work together on one massive generation ship?
Here's a proposal;
Form a Global Space Agency, instead of each independent group working on their own separate design everyone works together and shares tech and research. Groups would be formed to work on individual components that would be needed, like propulsion, design, radiation shielding etc. Also any useful tech must be divulged to the GSA.
Stop fighting, everyone calling a truce means military funding could be diverted to spaceflight research. No hostile actions can be made towards any other member contributing to the Global Space Agency.
Basically just try to get along.
Would everyone do it? Would it just take some time to convince everyone? Or would anyone even care with it being so far off in the future, just figuring that the next generation can deal with it when it's a more urgent problem?
The entire world all recognizes the anomaly as a real threat, everyone knows that it will destroy earth within time frame researchers have estimated. No one thinks it's just some ruse to try and convince them to reveal top secret technologies or anything like that.
They have current a current technology level of what could be reasonably expected in 20-50 years, but spaceflight advancement has been somewhat slower than you might expect. The first manned missions to mars have been continuously delayed as there hasn't been sufficient advancement in radiation shielding or propulsion tech to get a crew to mars without cooking them.
If people wouldn't be worried about what's going to happen down the road enough to do anything about it is there something that would make them concerned enough to pay attention? If the anomaly posed a more urgent threat, would that make a difference? For example if every 30-50 years it released a powerful enough EMP to affect earth and cause widespread damage would that get more people's attention?