3.9.2.3
Astronomical Distances
Astrophysics | AQA A-Level Physics
Key Definitions
Astronomical unit (AU): the mean distance from the centre of the Earth to the centre of the Sun. 1 AU $= 1.50 \times 10^{11}$ m.
Light-year (ly): the distance travelled by light in one year. 1 ly $= 9.46 \times 10^{15}$ m.
Parsec (pc): the distance at which the radius of the Earth's orbit (1 AU) around the Sun subtends an angle of 1 arcsecond. 1 pc $= 3.08 \times 10^{16}$ m $= 3.26$ ly.
The astronomical unit
- The AU is based on the mean Earth-Sun distance because the Earth's orbit is slightly elliptical: closer in January ($1.471 \times 10^{11}$ m) and further in July ($1.521 \times 10^{11}$ m).
- The AU is useful for distances on the scale of the solar system.
The light-year
- Calculated as: distance $= c \times t = (3 \times 10^8) \times (3.15 \times 10^7) = 9.46 \times 10^{15}$ m.
- The light-year is useful for interstellar distances, such as the distance to nearby stars or neighbouring galaxies.
The parsec
- The parsec is defined using parallax anglesThe apparent shift in position of a nearby star against the background of distant stars, caused by the Earth's orbital motion around the Sun. Measured in arcseconds.. An arcsecond is $\frac{1}{3600}$ of a degree.
- Using trigonometry: $\tan\!\left(\frac{1}{3600}\right) = \frac{1 \text{ AU}}{1 \text{ pc}}$, which gives 1 pc $\approx 3.1 \times 10^{16}$ m.
- The parsec and light-year are much larger than the AU, making them useful for measuring distances on the scale of stars and galaxies.
Common Mistake
You do not need to memorise the conversion factors. They are given in the data booklet: 1 AU $= 1.50 \times 10^{11}$ m, 1 ly $= 9.46 \times 10^{15}$ m, 1 pc $= 2.06 \times 10^5$ AU $= 3.08 \times 10^{16}$ m $= 3.26$ ly. You just need to be able to use them.