Astronomical units, light-years, and parsecs are all units of distance, but they are defined differently and are useful on different astronomical scales. This is SL and HL content within E.5 Fusion and stars, especially stellar parallax.
How the Units Differ
| Unit | Definition and typical use | Equivalent distance |
|---|---|---|
| Astronomical unit (AU) | Approximately the mean distance between Earth and the Sun. It is convenient for distances within planetary systems. | |
| Light-year (ly) | The distance travelled by light in a vacuum during one year. It is commonly used for distances between stars. | |
| Parsec (pc) | The distance at which 1 AU subtends an angle of one arcsecond. It is directly connected to stellar parallax measurements. |
These units describe the same physical quantity, so choosing one does not change the distance. The scale simply keeps numerical values manageable: Earth is about from the Sun, while the nearest stars are several light-years away. Because , AU is impractical for most stellar distances. Conversely, metres make astronomical numbers unnecessarily large.
The parsec comes from geometry. Observers measure the apparent shift of a nearby star against distant background stars from opposite sides of Earth’s orbit.
A light-year follows from distance equals speed multiplied by time:
A parsec is defined using stellar parallax. If a star has a parallax angle , measured in arcseconds, its distance is
For example, a star with arcseconds is at
This is equivalent to .
A common misconception is that a light-year measures time. It does not: the word “year” appears because time is used to define the distance travelled by light.
Exam Technique
For E.5 questions, identify the required unit before calculating. When using , the parallax angle must be in arcseconds and the resulting distance is in parsecs; convert only if the question requests metres or light-years.