In 500 million years, hopefully humans (or whatever humans have become at that point) will be able to modify the Earth's atmosphere to deal with the increased luminosity of the Sun.
We might be lucky enough to do that, but it could have easily taken intelligence another 500M years to evolve on another planet. First animal fossils are something like 700M years old, so it took 2-3G years to just any animals.
The problem is that there are just so many planets. Sure, another planet could be 500My slower, but with a billion planets, some of them should be 500My faster instead.
It's possible we are absolutely one-in-a-billion uniquely lucky - after all, someone has to be the first and the luckiest. But every year we find indications that our planet is completely typical.
We'll have colonized the galaxy in 10 million years. In 200 million years, I'd expect that some future historical society could undertake a project to clean out the heavy elements in the Sun to keep it going.
Yeah, but if humans exist by the time the sun fails us, they wouldn’t really be the same species as us, and they’d hopefully have progressed to the point that they could escape the Earth.
You're saying we wont maintain tradition and our "humanity"?. I like to be a little more optimistic and believe in us as a species transferring values until the end.
Look at all types of mammal that exist, from us to platypuses to bats to whales. Evolved in a few hundred million years. Modern humans have been here for a few hundred thousand.
In 500 million years absolutely anything could happen (if we survive this century).