Distances to Nearby Stars
Distances are particularly easy to calculate if we use the parsec as our distance
unit and we know the parallax shift of a star.
Distances from Parallax Angles
In that case, the distance of a star in parsecs is just,
D = 1/p,
where D
is the distance in parsecs and p is the parallax angle in seconds of arc.
For example, Sirius has a parallax angle of 0.38 seconds of arc and thus
its distance from the Earth is
D = 1 / 0.38 = 2.6 pc = 8.6 ly.
The nearest
star (other than the Sun) is Proxima Centauri, in the
alpha Centauri triple-star system. It has a parallax of
0.77 seconds of arc, corresponding to a distance of 1.30 pc = 4.2 ly. Therefore, all
stars have parallax angles of less than one second of arc.
Distances from Hipparcos
As noted earlier, the Hipparcos mission has permitted the parallax angles and thus the
distance of many nearby stars to be determined with unprecedented precision.
The table below gives parallax angles and distances for the five nearest stars in the
Hipparcos data base. Notice the remarkably small uncertainties (typically 0.2-0.3 percent)
for these measurements listed in the last column.
The right panel has a link to a longer
table of the nearest stars, all of which are close enough for reliable parallax
measurement.
|
Distance to the Five Nearest Stars Using Hipparcos Data
|
| Star |
Parallax
(arc sec) |
Parallax Error (arc sec) |
Distance
(pc) |
Distance
(ly)+ |
Distance
Error
|
| *Proxima Centauri |
0.77233 |
0.00242 |
1.2948 |
4.2231 |
0.31%
|
*Alpha-
Centauri A |
0.74212 |
0.00140 |
1.3475 |
4.3950 |
0.19%
|
*Alpha-
Centauri B |
0.74212 |
0.00140 |
1.3475 |
4.3950 |
0.19%
|
| Barnard's Star |
0.54901 |
0.00158 |
1.8215 |
5.9409 |
0.29%
|
| Lalande 21185 |
0.39240 |
0.00091 |
2.5484 |
8.3120 |
0.23%
|
|
|
|
+One light year = 3.261633 parsecs
*Members of the same triple star system
Wolf 359 (2.35 pc) is closer than Lalande 21185, but is not in the Hipparcos data base
|