There comes a time in every star's life . . .: The variable brightness of stars helps us to work out how far away and how old they are. Heather Couper and Nigel Henbest explain

Overhead in November - next to the constellation of Cassiopeia - is a straggly line of brightish stars, in which our ancestors saw the shape of one of their great heroes, Perseus. Among his best-known legendary exploits was beheading the snake- haired Gorgon Medusa, whose glance turned any onlooker to stone. In the constellation the position of Medusa's head is marked by a very unusual star called Algol - a star that winks.

Even Algol's name is old. Roughly translated from the Arabic, al Ghul means 'the demon' or 'the mischief-maker'. Some astronomers believe it was given this name because observers centuries ago knew about the star's variability. And if you look at Algol on the nights listed in the diary below, you, too, will see it looking fainter than usual. Approximately every three days Algol's brightness falls more than threefold for a period of 10 hours, before slowly climbing back to normal.

But Algol itself does not change in brightness. The explanation for its winking was worked out more than 200 years ago by a remarkable young English astronomer - who happened to be deaf and dumb - called John Goodricke. He realised that Algol consists of two stars very close together, orbiting so that they pass exactly behind and in front of each other, as seen from Earth. In an 'eclipsing binary' such as Algol, the brightness of the whole system drops when the dimmer star blocks off the light of the bright star.

Two years later, Goodricke noticed that the star delta in the neighbouring constellation of Cepheus was also inconstant. About every 5 1/2 days Delta Cephei fades to half its normal brightness and then recovers. Astronomers after Goodricke were able to show that Delta Cephei is truly variable: it swells and shrinks, becoming hotter and cooler as it does so. We now know that 'Cepheids' such as Delta Cephei are brilliant, giant stars becoming unstable as they approach the ends of their lives.

But they are not dying in vain. In 1912, Henrietta Leavitt at the Harvard Observatory in the US realised that brighter Cepheids - which are intrinsically bigger - took much longer to pulsate than fainter, smaller ones. Her colleagues followed up her work by showing that all Cepheids of a given size (and intrinsic brightness) will take the same time to brighten and fade.

Thus Cepheids can be used as 'standard candles' to measure distances in the universe. An astronomer picking out a Cepheid in a distant galaxy will know its real brightness from its variation time. By comparing this with the brightness the star appears to be, he or she can calculate the distance to the galaxy.

Variability is a phase that nearly all stars go through during some part of their lives. Very young stars change in brightness as curtains of natal material swirl in front of them. Middle-aged stars such as our Sun are largely stable, but elderly stars are again prone to variability. There comes a stage, late in every star's life, when it runs out of nuclear fuel. The hydrogen in its core that it fuses into helium (the reaction that keeps a star shining) gets used up, and with no energy flowing out, the core collapses and heats up. The star's outer layers billow out a hundred-fold, and the star becomes a 'red giant'.

The fate of our Sun is to become a red giant one day, although not until 5,000 million years in the future. Even if it doesn't swallow up the Earth when it swells, there is no way that life could survive close to the inflated surface of a red giant star. But better this than to be a planet around the ultimate variable star: a supermassive star that can suddenly 'go supernova' and blow up completely without warning.

The planets

Venus - setting two hours after sunset by mid-month - is putting in early practice as the Christmas Star, and starting to dominate the dark autumn evenings. But we have still not lost Saturn. Setting soon after 10pm, it is the only bright 'star' visible low in the south-west after darkness has fallen and Venus has set. With its glorious rings, it still makes a prettier telescopic picture than Venus, which looks like a three-quarters- full moon.

The other planet you can't ignore in the evening skies is blood- red Mars. This month it is positioned against the stars of Gemini, in line with Castor and Pollux, the heads of the twins. Even though it is so bright, it still hasn't drawn close enough to Earth to show anything more than a small disc through an average telescope.

Comets and shooting stars

The Earth runs through the path of two old comets this month, treating us to an extra scattering of shooting stars around 3 and 17 November. These meteors consist of cometary debris burning up in the Earth's atmosphere.

Astronomers are also looking forward to observing a recently rediscovered comet, which causes the year's best shower of shooting stars each August. Comet Swift- Tuttle was first found in 1862, and astronomers expected it to return in the early Eighties. When it did not show, Brian Marsden of the Harvard College Observatory recalculated the orbit and suggested it would return in late 1992. And at the end of September, Japanese astronomers picked up the returning comet very near to Marsden's predicted position.

The comet won't be a brilliant sight, but you may pick it out in the north-west towards the end of November, by 'sweeping' around the sky with binoculars.

The stars

Now is the best time of year to gaze beyond our own star city into the depths of space. On a moonless night, find the constellation of Andromeda: a line of stars emerging from the top left-hand corner of the barren Square of Pegasus. Look just above the middle of the line and, if your skies are dark enough, you see the misty oval that is the Andromeda galaxy.

This insignificant-looking patch, about the width of a couple of full moons, is in reality a galaxy of stars completely separate from and bigger than the Milky Way. But because it lies 2 1/4 million light years away, it is only just visible to the unaided eye. Large telescopes reveal its beautiful spiral shape and 400,000 million stars.

If you have truly transparent skies, try looking at the mirror-image position of the Andromeda galaxy on the other side of the constellation. You may just be able to work out the very dim shape of a smaller spiral galaxy, M33, in Triangulum. Slightly further away than the Andromeda galaxy, this is the most remote object visible to an extremely keen naked eye. And it is a sobering thought to consider that these galaxies are but two in an estimated 100,000 million in the universe, spread out over distances of up to 13,000 million light years.

Diary

2 9.11am Moon at first quarter

3 7.54pm Algol at minimum

10 9.20am Full Moon

17 11.39am Moon at last quarter

18 3.54am Algol at minimum

21 Mercury at inferior conjunction, 00.42am Algol at minimum

23 9.36pm Algol at minimum

24 9.11am New Moon

26 6.24pm Algol at minimum