Path to a distant star Suppose we have a space ship that can go fast enough (0.9c) and we have plenty of time, and we want to travel to a star on the other side of the galaxy. How do you plot a path to navigate to that star? Given the distances and the number of stars in the way, which all affect the shape of the gravitational field, is it even possible to compute a reasonable path to follow? Do we know the trajectories and masses of the stars along the way with enough precision? Should we shoot outside the galactic plane and come back closer to it again as we get closer to the star? Stay in the galactic plane? Something else?  
 A: If you are flying about our sun at 1 AU (i.e. the same distance as Earth) you will get away at hyperbolic trajectory if you have a velocity of just 42.11 km/s. This is over 6400 times less than 0.9c. That means that with very high precision you may describe your trajectory as a straight line. Even if you touch the surface of the sun you will be deflected only by about couple arcseconds. However the galaxy is rather empty and unless you are VERY unfortunate so that the target will be almost eclipsed by some other star you will never approach anything massive closer than thousands AU and may basically forget about gravity altogether. Even in the worst case scenario in which your target is eclipsed by Proxima Centauri, starting an arcsecond off course will get you at the distance of 0.2 AU where you will not be influenced by its gravity at any significant measure. You may still need to account for a galactic gravity but we're still talking about small corrections to the initial angle. So don't expect any fancy maneveuring, your path will be almost ideally straight. All you really have to worry is to know the velocity of the star with enough precision to predict its trajectory over the years but if you're really able to do fancy maneveuring at 0.9c all you will have to do is to slightly change your angle as you get closer based on more recent data.
A: If you travel close to $c$ you will basically follow the same path as a light ray. This will indeed be bent by gravity, but for most paths through the galaxy this is not close enough to a star that there will be any effect (stars are lightseconds across, distances between them lightyears - and since it is cross-sections we care about, you get to square this ratio). 
If stars were just moving linearly, the aiming problem would be simple: the position would be $\mathbf{x}(t)=\mathbf{x_0}+\mathbf{v_x}t$, the position of the spacecraft would be $\mathbf{y}(t)=\mathbf{y_0}+\mathbf{v_y}t$, and you would just have to solve $\mathbf{x}(t)=\mathbf{y}(t)$ to find $\mathbf{v_y}$ and $t$ - a set of 3 linear equations with 4 unknowns, so you have some freedom to select velocity and arrival time (other constraints such as relativistic time dilation and fuel cost obviously would matter). 
But stars are orbiting, so $\mathbf{v_x}$ is changing over time. In the solar system where planets and spacecraft follow conic sections finding a trajectory that ends up at the destination is a nonlinear problem with a somewhat messy solution. The galactic version is essentially the same, but now with a different gravitational potential. Presumably there is a similar solution, 
One can imagine sending out a bundle of possible trajectories with slightly different velocity vectors; at any given time they form a surface or volume $\{\mathbf{y}_{\mathbf{v}_y}(t)$}. The star follows a curve through spacetime, $\mathbf{x}(t)$. Whenever the curve intersects the surface/volumes there is a possible solution. In reality this is solved using numerical methods. 
These methods in the solar system take gravitation from other bodies into account; the galactic version would have to do something similar. This might require estimating the effect of dark matter blobs, which we currently are bad at. But as we map the galaxy more we will be able to plot trajectories better. 
