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Activity 9 – Roller Coaster Stars


Once you are familiar with some of the most impressive binocular targets, it is time to explore variable stars – stars that grow brighter and fainter over time. Three of the easiest variable stars to observe are featured in this activity. The three are all of a type known as Cepheid variable stars.

Specific Learning Outcomes

You will locate and observe a Cepheid variable star, recording your observations as a light curve showing the variations in brightness over several weeks.

Planning and Preparation

Observing the light curve of a variable star usually requires a series of observations spread over several weeks.

Northern Hemisphere observers are recommended to observe delta Cephei. Southern Hemisphere observers are recommended to observe l Carinae. Both of these stars are circumpolar at most latitudes so they can be observed all year round. However, in the equatorial zone you might find that both of these stars are too low in the sky. In that case choose eta Aquilae, which will be best observed in the months of June to September. (Use your Star Wheel to find out more about when and where these stars will appear at your latitude.)

Next print the finder chart and comparison chart for the appropriate star (download here).

These stars are visible to the naked eye under dark conditions, but binoculars are essential if there is some light pollution at your observing site. For most city observing sites you will need binoculars.

What You Need

Science Background Knowledge

Vocabulary checkpoint

Magnitude: A measure of the brightness of a star. The Ancient Greek astronomers divided the stars into six magnitudes. First-magnitude stars were the brightest, and sixth-magnitude stars were the faintest. This system has been kept in modern times, although magnitudes are now measured more accurately, and it has been extended to cover stars fainter than the eye can see unaided. This table shows how the modern numbers match up with the ancient magnitudes:

Ancient Greek magnitude

Modern magnitude


Numbers lower than 1.5


1.5 to 2.5


2.5 to 3.5


3.5 to 4.5


4.5 to 5.5


5.5 to 6.5

Too faint to see unaided

Numbers higher than 6.5

The three Cepheid variable stars that feature in this activity are all 4th magnitude stars, never brighter than 3.3 or dimmer than 4.4.

Period: When something repeats in a regular pattern, its period is the amount of time for one complete cycle. For a variable star this is the time between it reaching a peak of brightness, and reaching its next peak of brightness.

Light curve: A light curve is a graph showing the showing the variations in brightness of a variable star over time. For a Cepheid variable star the light curve usually covers several days or weeks. There is an example below.

Variable Stars

Variable stars are stars that vary in brightness. Some of them vary in an irregular way, due to flares, fades, or cataclysmic outbursts. Others vary in a regular way. The regular variable stars include:
  • stars that vary because one part of the surface is brighter than the rest and they are rotating,
  • stars that vary because there are two stars orbiting each other and the fainter star regularly passes in front of the brighter star causing it to dim, and
  • stars that vary because the star itself is pulsating (pulsating variable stars).


Cepheids are a particular type of pulsating variable star. They are named Cepheids after the star delta Cephei which is a prime example of the type.

Cepheids have a special part to play in astronomy. The period of a Cepheid can be used to determine how much light it is giving out, and this information can be used to work out how far away it is. Cepheids are used to find out how far away distant galaxies are.

Cepheids are stars at a particular stage in their life cycles. Typically a star is stable for most of its lifetime while it gets energy from turning hydrogen into helium. The energy rushing out from the centre of the star balances the pressure of gravity pushing in, and the star settles into a stable state. This is called the main sequence stage. In the case of our sun we believe that it has been in its main sequence stage for 5 billion years, and it will last another 5 billion years before the hydrogen is all gone.

When the hydrogen is gone from the core, the star uses up the hydrogen from around the core and it swells up to become a red giant. When the last of the hydrogen has gone the force of gravity overwhelms it, and the star collapses. But not for long. The increased pressure brought about by this collapse is enough for the helium to start turning into carbon, and this marks the beginning of a new stage in the star’s life; helium burning.

A star does not settle into a steady state so easily in the helium burning stage. Large stars, between three and nine times as massive as our sun, usually go through lengthy periods during which the star expands and contracts on a regular basis; something like a cross between a jelly wobbling and a ball bouncing, but much bigger and slower and much more regular. During these parts of its helium burning stage, the star is known as a Cepheid variable star.

Cepheids typically change brightness by between half and two magnitudes, and have periods of between 1 and 50 days. The three Cepheids that feature in this activity vary in brightness by about one magnitude. They are among the brightest Cepheids in the night sky.

The five brightest Cepheids



Magnitude when brightest

Magnitude when dimmest

Change in magnitude



Ursa Minor




4.0 days

l Carinae





35.5 days

Beta Doradus

Dorado *




9.8 days

eta Aquilae





7.2 days

delta Cephei





5.4 days

source: General Catalogue of Variable Stars
* Dorado is between Hydrus and Carina.

Here is a typical Cepheid light curve:

This light curve was drawn with data taken from: http://brahms.phy.vanderbilt.edu/~rknop/classes/a250/esmark/.

The light curve goes up and down like a roller coaster. The star goes from dimmest to brightest quite quickly, and then grows dimmer more slowly. This is typical of Cepheids. As the star grows dimmer, there are one or two little bumps in the light curve. These bumps are also typical of Cepheid stars. They appear in different parts of the curve for different stars. (You are not expected to be able to detect these bumps in this activity, because the method used is not precise enough to show them.)


Begin with the finder chart and find the variable star you are observing. You will probably need to spend an hour or so becoming familiar with the stars on the chart before you try to make any observations.

Use the comparison chart (example on right) to estimate the magnitude of the variable star. Compare the variable star with other stars in the area. If you find a nearby star that looks to be the same brightness, then the magnitude of the other star tell you the magnitude of the variable star. If you cannot find a suitable match, then you can still estimate the magnitude by finding a brighter neighbour and a fainter neighbour. The magnitude of the variable star will be between the magnitudes of the two neighbours.

The comparison chart shows stars to magnitude 8. The number of stars that you can see depends on how dark your night sky is. With binoculars, even in a city, you may be able to see to magnitude 8 or 9.

The comparison chart shows the magnitudes of stars to one decimal place, but the decimal point is omitted. This means that 40 on the chart is magnitude 4.0, 35 is magnitude 3.5 etc. Variable stars are labelled “V” with their magnitude range. Stars fainter than magnitude 6.5 do not have their magnitudes shown.

Before you begin, study the comparison chart so you know which stars are going to be useful. Useful stars will be from about magnitude 3.2 to 4.5. Brighter or fainter stars are not useful as comparison stars for the three Cepheids in this activity. The illustration on the right shows part of the delta Cephei comparison chart, with useful stars highlighted.

Keep an observing log. Record the date and time of every observation, as well as the viewing conditions. Also be sure to record the comparison stars that you used for each magnitude estimate. This is all vital information if you need to come back to your log to check your data.

You will need to observe often enough and for long enough to build up a complete picture of at least one period of the Cepheid you are observing.

For delta Cephei and eta Aquilae this means trying to observe every night for a couple of weeks. If weather interrupts your observations you might need to keep trying for three or four weeks. You will then have a patchy light curve covering several periods. From this you should be able to piece together quite a good picture of what a single period looks like. (If you are able to do both evening and pre-dawn observations then you should be able to build an excellent picture of the light curve in a single week of clear skies.)

For l Carinae this means trying to get two or three observations per week for at least one month, preferably two. This is sufficient to build a picture of the light curve.

Draw a light curve using the data in your observing log. Draw a graph showing time along the bottom and magnitude up the side. The above example can be used as a guide. Be sure to adjust the scale if you need to so that the light curve is not squashed flat.

Estimate the period of the variable star. Look at your light curve and pick out a complete cycle. The length of this cycle is your estimate of the period of the star. Does your figure agree with the published figure?

Follow Up and Extension

There are many more variable stars that can be observed with binoculars and the Cepheids are only a small portion of them. Visit the AAVSO website for more details on variable stars including online tutorials and charts.

Downloadable Resources

delta Cephei finder chart  (87 KB)

delta Cephei comparison chart  (124 KB)

eta Aquilae finder chart  (76 KB)

eta Aquilae comparison chart  (95 KB)

l Carinae finder chart  (137 KB)

l Carinae comparison chart  (113 KB)

Help with printing and downloading

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URL http://www.AstronomyInYourHands.com/activities/rollercoaster.html   Publication date 30 June 2003
Copyright © C J Hilder, 2003. All rights reserved.