Lost in the Milky Way scenario

[nikkkom]

You would need support from the Earth for this one. I say that for a reason... even if you could find your way back to our star, you would be stuck around a large number of planets, moons, and anything else that chooses to get in your pathway.

Yeah, it's a miracle Voyager managed to wiggle its way out of Solar System without hitting your "planets, moons, and anything else".

Yesterday, I was barely able to see the Sun, moons were repeatedly obscuring it. ;)

 

[.Scott]

Assuming the crew possesses all of our current knowledge of the galaxy, and time was not a factor, would they be able to locate where our Sun is, and travel back to it?

I think the "travel back to it" is a lot more challenging than locating where you are. Even if "time was not a factor", propulsing yourself back to sol with current technology would be daunting. Your random place in the galaxy is likely to be over 40,000 light years away. If time is not a factor, then we are not worrying about aging the crew, aging the ship, or aging our solar system and its civilizations. But you still have a current-technology craft that will need to be fueled and perhaps refueled.

Also, you not only need to know where you are, but what kind of a trajectory (gravity-assisted) you will need to get back, and where the solar system will be when you finally reach it (in some number of tens of millions of years - that are not a factor). I would guess you would set up roots in whatever neighborhood you found yourself in and spend a few decades planning you journey back.

I think my first thought would be reverse engineering that worm hole.