Measurement of Distance to Stars

The Sun is the star closest to Earth; the next-closest star is roughly $4.29$ light years away. At such enormous distances, even the parallax measured using the widest baseline available on the Earth's surface (roughly the Earth's diameter) is far too small to detect. So for stars, astronomers instead use the diameter of the Earth's own orbit around the Sun as the baseline — observing the same star from two points on the Earth's orbit that are as far apart as possible, i.e. two positions six months apart, separated by $2\ \text{AU}$ (see Example 1.2).

For measuring these very large distances, astronomers use three special units, all built from the metre:

• 1 astronomical unit (AU) $= 1.496 \times 10^{11}\ \text{m}$ — the mean distance between the centre of the Earth and the centre of the Sun.
• 1 light year $= 9.467 \times 10^{15}\ \text{m}$ — the distance travelled by light, in vacuum, in one full year.
• 1 parsec (pc) $= 3.08 \times 10^{16}\ \text{m} \approx 3.26$ light years — defined as the distance from which a baseline of exactly 1 AU subtends a parallax angle of exactly 1 arcsecond ($1''$). …