I'll give some size estimates.
- Aberration, radial velocity: (v/c) for velocity v
- Parallax: (b/d) for baseline b and distance d
- Time delay: b/c for baseline b
For pulsars, time delay outside of cislunar space is IMO too large to make them very useful, because of aliasing -- which pulse is one observing? Navigation satellites include timestamp data in their pulses, so these satellites get around that problem.
I'll use Alpha Centauri as a reference, since it is the nearest star outside the Solar System, at 1.3 parsecs. From List of brightest stars, many of them are about 100 or so times farther, though some are not much farther, like Sirius at 2.6 pc, Procyon at 3.4 pc, Altair at 5.2 pc, and Fomalhaut and Vega at 7.7 pc. Some of them are 500 or more times farther, like Deneb.
Anything outside our Solar System is referred to Solar-System barycentric coordinates, where the origin is at the Solar System's barycenter, and the directions are from the Earth's averaged-out orbit and spin orientations at some time epoch, like J2000 (January 2000).
For Earthbound observations, it is routine to correct for the Earth's position and velocity, so let us see what the numbers look like.
Earth's center relative to SS barycenter: A-Cen's parallax is 0.77 as (770 mas) and aberration is 20.5 as.
Earth observer relative to its center: position ~ 6371 km from its barycenter, velocity at most 460 m/s. A-Cen's parallax is 33 mcas, and aberration is 0.32 as.
For low Earth orbit, I will use the ISS's altitude of 400 km. The ISS's orbital velocity is 7.7 km/s. A-Cen's parallax is 35 mcas and aberration is 5.3 as.
For geosynchronous orbit, the altitude is 36,000 km (total distance 42,000 km) and the orbital velocity 3.1 km/s. A-Cen's parallax is 220 mcas and aberration is 2.1 as.
For the Moon's orbit, the total distance is 384400 km and the orbital velocity 1.0 km/s. A-Cen's parallax is 2.0 mas and aberration is 0.7 as (700 mas)
For the nearby Earth-Sun Lagrange points (L1, L2), the total distance is 1.5 million km and the orbital velocity is 0.3 km/s. A-Cen's parallax is 7.7 mas and aberration is 0.2 as (200 mas)
So using parallax and aberration inside of the Earth's sphere of gravitational influence is not very feasible. That sphere is the Hill sphere, and it extends out to L1 and L2.
I'll now consider the Solar System outside of the Earth's Hill sphere. For the inner Solar System, we have numbers similar to those for the Earth, A-Cen's parallax is 0.77 as (770 mas) and aberration is 20.5 as.
One could find velocities with aberration if one wanted to, but one would need very precise measurements, and the results would not be very precise.
For the outer Solar System, I'll take Neptune, the farthest-known full planet, at 30.07 AU and 5.43 km/s. That gives A-Cen parallax = 23 as and aberration = 3.7 as.
So I turn to the nearby stars. They have a lot of velocity scatter, and the Sun has a velocity relative to those velocities' average, the Local Standard of Rest.
A rough summary: lecture11.pdf
Some recent work: [1501.07095] Determination of the Local Standard of Rest using the LSS-GAC DR1
Relative to the LSR, the Sun's velocity is 7.0 km/s inward, 10.1 km/s forward in orbit, and 5.0 km/s northward out of the Galactic plane. That's a total of 13.3 km/s.
From Allen's Astrophysical Quantities, I estimate the velocity dispersions of Sunlike and less massive stars as (inward-outward) 31 km/s, (forward-backward) 19 km/s, (northward-southward) 16 km/s, or a total of 40 km/s.
So to avoid being very restricted in what stars one can go to, one must depart from the Solar System at 100 km/s or more.
The star's position: xs = d*{1,0} + t*{vr,vt}
The spaceship's position: xt = v*t*{cos(a),sin(a)}
For them to meet, xs = xt, and I find
sin(a) = vt/v
t = d/(sqrt(v^2-vt^2) - vr)
List of artificial objects leaving the Solar System
The spacecraft: Voyager 1 17.0 km/s, Voyager 2 15.4 km/s, New Horizons 13.9 km/s, Pioneer 10 & Pioneer 11 11.9 km/s.
I thin that one will need at least 50 km/s departure speed, or likely 100 km/s, to avoid being very restricted.
Since 1 km/s ~ 1 parsec / million years, that means 1 pc / 10^4 years
That means an aberration of 1 minute of arc.
It would take 13,0000 years to make it to A-Cen.
Once there, stars like Sirius and Vega would be displaced by several degrees, most of the brighter ones would be displaced a lot less, like half a degree, and Deneb around 1/10 of a degree.
The best case for nuclear-energy propulsion I estimate at 0.1 c, giving an aberration of about 6 degrees and a radial-velocity shift of about 0.1.
Going much faster with onboard fuel will require antimatter, and that's full of problems. Though antimatter provides the highest-efficiency energy release, it is very hard to make and very hard to store.
I've tried to find the efficiency of making antimatter, and numbers are hard to find. But I once found 10^(-3) for positrons and 10^(-8) for antiprotons.
Antimatter's properties are easy to predict, since antimatter is not some sort of bizarro matter but just like ordinary matter with some properties mirror-imaged, like electric charges. Masses are not mirror-imaged, however. This mirror imaging cancels out of most familiar macroscopic properties, and one can use that to estimate how easily one can store antimatter.
Storing it is a HUGE problem, since antimatter tends to prematurely react with the ordinary matter around it, destroying itself and that matter in the process.
At first thought, it seems easy. Make lots of positrons. But they are just like electrons, and they electrically repel each other. To stabilize them, one must make antinuclei, and the easiest ones to make are antiprotons. That makes antihydrogen, and it boils at the same temperature as ordinary hydrogen: 20 K. Keeping it frozen will be a challenge.
One can make antimatter substances that boil at higher temperatures, but one has big problems. One can add antineutrons, but there are no stable nuclei at 5 and 8 nucleons. So getting past those gaps is challenging.
One problem with speed is reaction forces when changing couse and velocity. The change in inertia has to show up somewhere.
STNG had 'structural integrity fields' that kept the structure from tearing itself apart.
It would get worse if you had a rotating drum for artificial gravity.
[If this tangent is too distracting, please ask the Mods to delete this post, or hide it with Hide tags.]
Perverse perfectionism ranks somewhere on my List of 30 Biggest Faults. I am unable to proceed without posting a flaws-corrected version of the Nine Views of Orion. Again the eight views other than the central view from Earth are taken every 45 degrees along a circle of radius 20 ly centered at earth and perpendicular to the Earth-Orion line.
Many more stars are shown than in the previous effort (263 stars over the nine pictures). Abugfeature is that faint stars are colored black or dark grey; they are visible in the image if magnified.
Here is a list of the 16 stars brighter than 2.4 which occur in these images. These include the 7 brightest stars in Orion, 7 stars shown with labels, the second brightest star of Castor (a sextuple-star system), and the second brightest star of Capella (a quadruple-star system). Amusingly(?) Capella's companion was BARELY in a viewing frame of my earlier effort, while Capella itself was NOT -- I didn't note the connection then and labeled this companion as "unnamed star."
The first number in the entries following shows how many of the 9 views contain the star; the second number is the star's relative magnitude.
CAP : 1 Capella [-0.6] alpha Aurigae
--- : 9 Rigel [0.2] beta Orionis
--- : 1 Capella companion [0.3]
--- : 9 Betelgeuse [0.4] alpha Orionis
POL : 1 Pollux [0.5] beta Geminorum
ALD : 2 Aldebaran [0.7] alpha Tauri
CAS : 1 Castor [1.1] alpha Geminorum
aln : 1 Alnath [1.5] beta Tauri
--- : 9 Bellatrix [1.6] gamma Orionis
--- : 9 Alnitak [1.7] zeta Orionis
--- : 9 Alnilam [1.7] epsilon Orionis
alh : 4 Alhena [1.9] gamma Geminorum
mir : 7 Mirzam [2.0] beta Canis Majoris
--- : 9 Saiph [2.1] kappa Orionis
--- : 9 Mintaka [2.3] delta Orionis
--- : 1 Castor-companion [2.4]
Ultimately, the problems of antimatter production go away at around the time we have the technology to produce large quantities of anti-matter, which would require something around the sun, absorbing gargantuan amounts of energy. In order to have level of tech, we'd presumably have the tech to use magnetic fields to isolate antimater particles. The trouble becomes, you'd still need a large amount of anti-matter (100+ tons) to go any decent percentage of c. Anti-matter takes you farther at lower speeds, but then you aren't getting anywhere.
I ponder if anti-mass (not anti-matter) propulsion is possible. Even if it is, we continue to run into the problem that is the universe... it is too big. It might simply be an issue of being stuck in space, much like we can't just swim to bottom of the Pacific.