Mdtryhht

A spaceship crew, during their interstellar travel loses control of the spaceship for a few hours due to external factors (exact factor not important). This causes the spaceship to deviate from its original course. The deviation is sudden and large (imagine the spaceship spinning(?) in space during deviation).

The question is, once the crew stopped the spaceship from spinning, how are they going to re-orient it along its original direction? What reference points can one use in space?

I think one cannot use distant stars as reference points since we only know stars by their geocentric coordinates. So, is there anyway for my space travellers to save themselves or are they doomed??

I think one cannot use distant stars as reference points since we only know stars by their geocentric coordinates.

We are smarter than that.

The Pioneer golden plaques, besides having porn, also had this:

With this you can locate the sun, by figuring out where the signals of 14 pulsars meet in a specific way.

If you can track objects of interest, you can find yourself. Before GPS was invented, US military jets of the 60's to the 90's sometimes used the position of stars to locate themselves:

In flight, the ANS, which sat behind the reconnaissance systems officer's (RSO's), position, tracked stars through a circular quartz glass window on the upper fuselage. Its "blue light" source star tracker, which could see stars during both day and night, would continuously track a variety of stars as the aircraft's changing position brought them into view. The system's digital computer ephemeris contained data on a list of stars used for celestial navigation: the list first included 56 stars, and was later expanded to 61. The ANS could supply altitude and position to flight controls and other systems, including the mission data recorder, automatic navigation to preset destination points, automatic pointing and control of cameras and sensors, and optical or SLR sighting of fixed points loaded into the ANS before takeoff. According to Richard Graham, a former SR-71 pilot, the navigation system was good enough to limit drift to 1,000 ft (300 m) off the direction of travel at Mach 3.

Also remember that in space you are always orbiting something. If you can figure your altitude from the barycenter and your orbital speed, you can calculate the shape of your orbit. Find any other two objects also orbiting that barycenter and, given database entries of those objects' orbits you may not only know where you are, but also when you are.

If you've got a math geek with a knack for astronomy onboard, they may be able to calculate that with pen and paper just like old man Kepler and his pals used to. They will use the same equations that Kerbal Space Program uses to position your spacecrafts whenever you load a saved game.

I think one cannot use distant stars as reference points since we only know stars by their geocentric coordinates.

Wrong.

We also know geometry, and if know the geocentric coordinates and the present coordinates, we can determine the displacement vector between the two, which give us the desired information: where are we in space.

One or more wide field images can help in finding known stars, and from there determine the rotation with respect the last known position. Mind that, knowing the trajectory up until before the incident, the maps are quite updated.

A lot of time in science fiction, and in real life space craft use pulsars to navigate.

X-ray pulsar-based navigation and timing (XNAV) or simply pulsar navigation is a navigation technique whereby the periodic X-ray signals emitted from pulsars are used to determine the location of a vehicle, such as a spacecraft in deep space. A vehicle using XNAV would compare received X-ray signals with a database of known pulsar frequencies and locations. Similar to GPS, this comparison would allow the vehicle to triangulate its position accurately (±5 km). The advantage of using X-ray signals over radio waves is that X-ray telescopes can be made smaller and lighter. Experimental demonstrations have been reported in 2018.

If you're relying on near-future (i.e slower-than-light) tech, getting lost in deep space would take a long, long time. The crew is on a journey of light-years, and in the worst case scenario you'll only be off course by a matter of light-hours.

For example, suppose you're travelling from Earth to Alpha Centauri. The propulsion systems that we currently have and expect to have in the near future are most efficient when they provide a little bit of thrust over a long period of time. As such, it's likely that the ship would start out at Earth and start accelerating toward Alpha Centauri until it reaches the halfway point, where it would turn itself around and begin decelerating so that it is travelling at a reasonably slow speed by the time it reaches its destination.

The best case scenario for your voyagers is that the deviation is caused by their ship spinning and the engine pushing in the wrong directions due to that spin. If that is the case the overall effect of the push will be a net zero, meaning their velocity will be the same as before they began to spin. They just need to see which way they are going, and then resume accelerating or decelerating.

Slightly worse than this is if somehow the ship got spun around, then stopped spinning and accelerated in a single unknown direction for a while before the crew managed to fix the ship controls. Their velocity now is not the same as it was before the deviation, but remember that they've been accelerating for a long time at this point (or they're close enough to the sun that they can use it as an obvious reference point). If they're close to halfway, then they've been accelerating for years - the deviation caused by even a full day of accelerating in the wrong direction would be less than 1% of their overall velocity. They can still just figure out which direction they're going, and make the small adjustment necessary to correct their velocity.

The worst case scenario is something like alien shenanigans causing them to suddenly accelerate to ludicrous speed (say, 0.99c) in an unknown direction. In this case they're probably doomed simply because the energy requirement for decelerating from that speed is absolutely ridiculous (on the scale of converting 9 tenths of the mass of their ship into pure energy for use in slowing themselves down, and doing so with 100% efficiency). However knowing where they are still isn't a huge issue - even travelling at that speed, they'd be off course by a matter of light-hours. So they'll be less than 1% off course - they would be able to take a picture of their surrounds and quickly orient themselves.

If you're relying on faster-than-light tech, you actually could be so far away from your intended path that the star field would be significantly different. In this case, you'd want to use the pulsar method that other answers have mentioned.

Since the question provides little context, a simple answer is to assume that the spacecraft will still be in contact with Earth or wherever it took off from, and/or possibly other places already colonized by humans if this scenario is assumed to be playing out in the near future (the moon, Mars, Mars' moons, maybe even a few of the most-likely-habitable moons of the giant gas planets, https://en.wikipedia.org/wiki/Habitability_of_natural_satellites).
Thus, the spacecraft would never have been lost as their position with respect to their launching point would be constantly tracked through whatever communication means the ship has with human bases on earth and/or throughout the solar system.

Albeit realistic, my first answer might seem a it trivial (and therefore not as interesting). Let's spice things up a bit and assume that there's no contact with any other humans outside of the ship. Also, since there's no specification of the speed at which the ship travels, lets assume it's only a fraction of the speed of light (as another answer assumed as well). Since control was lost for only a few hours and interstellar distances are so enormous, the position of the spacecraft would be relatively close to where they were when they lost control and not too far to the curve that traces their intended route.
They ship would VERY LIKELY be equipped with good (geocentric) maps of all the observable/known universe before they set out. Given such comprehensive 3D map models, they could easily predict what the sky should look like from any other point on the map. Thus, they could quickly run a computational search to find a match with what they are seeing. That is, they could take snapshots of what they see in different directions from their spacecraft, and then correlate their observations with predictions of how the sky would look like from different points on the map. The search for "simulated" views on the map would be quite small -they only have to generate simulated views from a narrow radius accounting for the distance travelled since they lost control. They could even figure out what new direction they're traveling in (assuming they got completely off course through propulsion/acceleration in the wrong direction when they lost control) if they took snapshots at two different time points, long enough for differences to be perceptible in at least one of the many directions they could collect snapshots from. Then, with knowledge of their new trajectory, they could easily correct course to intersect their prior trajectory at the final destination. If following the EXACT original trajectory were important, they could do that too: calculate the shortest distance from their current trajectory to the original one, and get back on track along the original route with careful manipulation of their propulsion/acceleration systems. Of course, the supercomputer on the spacecraft would do most or all of this automatically (individual pilots would not need to know trigonometry, geometry or physics themselves).