Arcminutes and arcseconds, the parsec, heliocentric parallax for measuring distances, and using Cepheid variables and other variable stars and their light curves.

What this dot point is asking

Edexcel statements 13.10 to 13.12 and 13.14 to 13.18 want you to understand arcminutes and arcseconds, the term parsec, how to find distances using heliocentric parallax, the light curves of variable stars (short and long period, eclipsing binary, Cepheid, novae and supernovae) and their causes, gravitationally bound stellar groupings, and how Cepheid variables are used to find distances.

Arcminutes, arcseconds and the parsec

These arc units are needed because parallax angles are tiny (well under one arcsecond even for nearby stars). The parsec is defined directly from parallax, which is why it is the astronomer's natural distance unit: a star at one parsec has a one-arcsecond parallax, a star at two parsecs has half an arcsecond, and so on. This connects to the units of Topic 7.

Heliocentric parallax

This is the key calculation: distance in parsecs equals one over the parallax angle in arcseconds. The nearer the star, the larger its parallax, so the method works best for nearby stars (large parallax) and fails for very distant ones (immeasurably small parallax). The Earth's orbit provides the baseline, which is why it is "heliocentric" (Sun-centred) parallax. The simple reciprocal relationship is exactly why the parsec was defined as it is.

Variable stars and their light curves

Light curves are graph-reading tasks: the shape reveals the cause. An eclipsing binary shows regular dips as each star blocks the other (statement 13.15); a Cepheid shows a smooth, repeating rise and fall; a supernova shows a sharp spike then a slow fade. Binary stars and clusters are gravitationally bound groupings (statement 13.17). Reading the period from a light curve is a common exam skill.

Cepheids as standard candles

This makes Cepheids standard candles: objects of known true brightness used to measure distance. The chain is period to absolute magnitude to distance, extending the distance ladder far beyond the reach of parallax, out to other galaxies. Cepheids were how the distances to other galaxies were first established, a direct foundation for Hubble's law (Topic 16).

How Edexcel examines this

This is telescopic Paper 2 content with calculation and explanation marks. The parallax calculation uses $d = 1/p$ (parsecs and arcseconds): find the distance from a parallax angle, and explain the shift as the apparent motion of a nearby star against distant stars due to the Earth's orbit. Arc units are tested by conversion ($1$ degree $= 60' = 3600''$) and the parsec by its parallax definition. Light curves are graph-reading: identify the variable type and read off the period (especially for eclipsing binaries and Cepheids). The Cepheid question rewards the period-luminosity relationship giving the absolute magnitude, then comparing with apparent magnitude for the distance, making Cepheids standard candles. Synoptic links run to the magnitude scale and distance modulus (Topic 13), the parsec (Topic 7) and Hubble's law (Topic 16). The commonest errors are mishandling the parallax reciprocal and the arc units, so secure $d = 1/p$ in parsecs and arcseconds.

Try this

Q1. State the formula linking a star's distance in parsecs to its parallax angle in arcseconds. [1 mark]

• Cue. $d = \dfrac{1}{p}$ (distance in parsecs equals one over the parallax in arcseconds).

Q2. State what property of a Cepheid variable is used to find its true brightness. [1 mark]

• Cue. Its period of pulsation (via the period-luminosity relationship).