Suppose that our random heroic brave interstellar expedition is returning to Earth from Alpha Centauri at 60% of the speed of light, but there was an accident in the nuclear reactor, forcing the captain of the ship to jettison the whole propulsion section in order to evade the nuclear explosion. The ship has lost all propulsion power whatsoever and is on a course that will pass straight through the solar system (the ship was supposed to brake during the last stage of the mission) and leave it again, to become eternally stranded in deep space, ultimately leaving our galaxy.
We still have got life support (that will keep functioning for 5 years) and that our current distance to Earth is 2 light years, which means that we are supposed to pass our home planet in 3 years and 4 months if our speed does not change before we will head into space again. The ship has two shuttles which are designed for reentry and landing on Earth.
The signal will take (you guessed it right) 2 years to reach earth, which means that we have 1 year and 4 months until the closest passage. At the time when the signal will reach Earth, the distance between the ship and our planet will be 0.84 ly.
If we take time dilation into account (+25% for the observer at 0.6c, that's why I chose this speed), the Earth has actually 1 year and 8 months until the closest passage.
As said before, if no change in velocity happens, we will shoot out of the solar system again at 0.6c with a minimal course correction induced by solar gravity.
My question is:
- How can the ship (or at least the crew) be saved within a reasonable time period (there are 3 years of life support left)?
- By "saved" I mean that the ship must be slowed down into a solar orbit where it can be accessed by rescue vessels.
- Bonus points for making it head towards earth or into an earth orbit so that the crew will only have to board the shuttles.
- No propulsion whatsoever may come from the ship itself unless you decide that sending a new nuclear reactor and propulsion module for rendezvous at relativistic speeds.
- You can use anything else as long as it is feasible in the year 2100 in a hard sci-fi setting.