Some ideas are:
- You branch off into another timeline and your actions make no difference to the previous timeline
- You’ve already taken said actions but just didn’t know about it so nothing changes
- Actions taken can have an effect (so you could suddenly erase yourself if you killed your parents)
- Only “nexus” or fixed events really matter, the timeline will sort itself out for minor changes
- something else entirely
I like the one where the motion of the universe is not accounted for, so the travelers drop into empty space. But someone figures out how to use that to travel through space.
Time Wars are fun though. Each prime timeline moving others toward them.
Be a potentially energy-efficient way to exit a gravity well in a spacecraft if you could exploit that and it doesn’t require too much energy. Instead of launching a spacecraft, just send it back in time to when a point was no longer in that well.
EDIT: if the above conditions hold (it’s possible and requires less energy than launch), you also have an infinite-energy-production machine, because you can obtain more potential energy than you are expending energy to time-travel.
If you screw up the calculation, your time machine can also end up deep under the mantle of the Earth. That would be a pretty spicy way to travel.