Suppose we want to send a probe to the Alpha Centauri system, about 4 light years away. It will be a simple flyby mission, just go there and take pictures, transmit them back to earth, no stopping and no coming back Let us assume we have the technolgy to quickly accelerate our ship to about 10% of light speed, so it will take about 40 years to get there. Our probe has a main propulsion system which will quickly get it up to 0.1c at burn-out, and a secondary and much less powerful engine for minor course corrections and other maneuvers. This secondary propulsion can be controlled by radio (or telecom laser) from earth, but keep in mind that it takes time (light speed) for navigational data from the spacecraft to get to earth, and time for maneuvering commands to get back. The secondary propulsion system is also low accelleration and takes a long time to give enough of a delta-v to alter the spacecraft's course substantially, so all these factors must be taken into account.

Alpha Centauri is a triple system. The A and B components are listed as 4.36 ly away at RA 14h 40m, DEC -60d 50'. The third component, Proxima, is considerably distant from the pair at 4.24 ly
from us, it is in a highly elliptical orbit around them. Its geocentric coordinates are RA 14h 30m, DEC -62d 41'. This separation is easily noticeable, even to the naked eye, Proxima and Alpha are about two degrees apart in the sky. Even though these stars are all gravitationally connected, they are also extremely close to us as stars go. By the way, keep in mind that Dec is in angular units, 360d to a full circle. RA is always given in time units, 24h to a full circle. A minute of time = 15 minutes of arc. There is a good reason for this, but I won't go into it now.

Incidentally, the catalog positions are for Epoch 2000.0, so you'll have to precess the coordinates for whatever year your probe will be launched. In addition, at launch time, your position for the system will be four years out of date because of the light travel time to the system. You're not seeing it where it is now, but where it was four years ago. Also keep in mind, it will also have moved even further off position in the 40-odd years it will take your probe to get there. All this has to be taken into account or you will miss your destination. It is a moving target.

Once all these purely geometrical effects are corrected for, you still have to deal with the kinematics of the Alpha Centauri system. Proxima has a cataloged proper motion of 3853 milliarcseconds/yr in a Position Angle of 281.5d (measured clockwise from N). Since it is in orbit around the center of gravity of the A-B pair, the numbers for A and B are slightly different than those for Proxima (and keep in mind they are also orbiting around each other). A's proper motion is 3710 mas/yr, PA 277.5d. B's proper motion is 3724 mas/yr, PA 284.8d. The radial velocities (motion IN the line of sight) for Proxima, A and B are all AWAY from us, at 16, 26 and 18 km/sec, respectively.

So how do we approach a system like this? We want to get a good look a Proxima, because it has a planet, but we might also want to study the stellar A and B components in detail. It may not be possible to get as close as we want to both objectives because our approach velocity will be extremely fast (0.1c) and we may not have enough capability to deploy sufficient delta-v to do both. We will have to think long and hard on which target we intend to favor, and by how much, and it may be wise to delay that decision and make careful measurements on our final approach, allowing for time to radio those observations to mission planners on earth so that final maneuver instructions can be transmitted back.

And remember, at these speeds, and with our limited secondary propulsion system capability, the earlier you communicate maneuvering instructions to the spacecraft the better. If you get hailed by the local Centaurians as you fly through the system the message will never get relayed back to earth in time for you to do any braking or course changes. You won't hear about it until long after the encounter is over.