With the equinox coming up on 23 September, this month we change gear from summer to autumn. As well as the weather experiencing a welcome cooling, the constellations on view are gradually shifting: the trio of bright stars marking the summer months – Vega, Deneb and Altair – are sinking towards the west, while the dim autumn constellations are rising in the east. It’s not easy to pick out the patterns that the ancient Greeks drew in this maze of obscure stars, but there’s one shape you can’t miss. Above the steadily glowing planet Saturn you’ll find four stars making a perfect geometrical figure: the “Square of Pegasus”.Traditionally, these stars mark out the body of the flying horse Pegasus, with his neck stretching out to the right. Pegasus was always depicted as flying upside-down, so his nose – marked by the star Enif – is an upward tick at the end of this line.Pegasus was created when drops of blood from the severed head of the Gorgon Medusa – whose face turned people to stone – fell into the ocean. Stretching his wings as he flew over central Greece, Pegasus saw a mountain that was inexorably growing higher as it responded to the singing of the Muses. Pegasus struck Mount Helicon with a hoof, arresting its development and gouging out the Hippocrene spring, whose gushing water is said to inspire sublime poetry. In his Ode to a Nightingale, John Keats calls for “a beaker full of the warm South/ Full of the true, the blushful Hippocrene.” If you’re in search of your poetic muse, you can still hike to the Hippocrene spring from the village of Elikonas in Boeotia.Pegasus then teamed up with the hero Bellerophon to destroy the monstrous Chimera – part lion, part goat and part snake. Eventually Bellerophon urged Pegasus to fly him up to join the gods on Mount Olympus. Incensed by Bellerophon’s hubris, Zeus sent a gadfly to sting the winged horse; in pain, Pegasus flung the hero off his back. But Zeus was glad to welcome Pegasus to Mount Olympus, where he carried the great god’s supply of thunderbolts.The lefthand star in the Square of Pegasus has an odd history. The ancient Greeks regarded Alpheratz both as the horse’s navel and as the head of the neighbouring constellation Andromeda. In the 1920s, the International Astronomical Union adjudicated in favour of the princess, and this star is no longer officially part of Pegasus.Algenib and Markab, marking the bottom and right corners of the Square, are heavier, brighter and hotter than our Sun, and shine blue-white. Even through binoculars, you can make out that Scheat – at the top – is a different beast. Its reddish hue reveals that this star has expanded in its old age to become a cool giant star.Enif, depicting Pegasus’s nose, is the most remarkable star in the constellation. This orange-coloured supergiant is some 183 times wider than our Sun, and shines 8,000 times more brightly – usually. But in 1972, a huge flare erupted on Enif’s surface, and for ten minutes this star appeared five times brighter in our skies, rivalling Altair in the nearby constellation Aquila.Point a small telescope towards Enif, and you can see why it’s been nicknamed “the pendulum star.” Next to Enif you’ll spot a fainter bluish star: it’s not actually a companion, but happens to lie almost behind it. Now tap your telescope lightly, so that Enif moves side to side – and you’ll see the fainter star swing round like a pendulum!This optical illusion is an example of the Pulfrich effect, first investigated by German physicist Carl Pulfrich in the 1920s. The light from the fainter star takes longer to register on your retina than the image of Enif, so when the stars are moving the dimmer one seems to lag behind the motion of Enif itself. Sweep the sky near Enif with a pair of binoculars and you’ll stumble over a fuzzy blob of light. M15 is a tight ball of half a million stars, lying 36.000 light years away from us. It’s one of the oldest star clusters in the Milky Way galaxy, dating back over 12 billion years.One of the constellation’s less conspicuous stars, Helvetios (51 Pegasi), has an even greater claim to fame. In 1995, it was the first sun-like star discovered to have an orbiting planet. This world is about 50 per cent as massive as Jupiter – hence its name Dimidium, meaning “half” – but it astounded astronomers because it whirled round its star much more closely than Mercury orbits the sun. It opened researchers’ eyes to a whole new kind of planet, unlike any in the solar system: huge worlds so near to their stars’ incandescent surface that they have been dubbed “hot jupiters.”What’s UpVenus has been a fixture of our dusk skies for most of this year: but by the end of September the Evening Star has dropped down towards the Sun and disappeared. Its curtain call is spectacular pas-de-deux with the crescent Moon on 14 September. The night sky at around 11pm this month (Nigel Henbest)Saturn is rising about 8 pm, and the Moon sails by the ringworld on 26 and 27 September. Pegasus (see main story) lies over in the east, above Saturn, and you can use it as a signpost to nearby constellations. Below Enif, lines of stars spilling down to the horizon mark out water flowing from a pitcher held by the water-carrier, Aquarius, to the southern fish, Piscis Austrinus. To the right, Capricornus (the sea-goat) appears as a boat-shape of stars. Underneath the Square of Pegasus, Saturn lies among the stars of Pisces (the fishes); while the sea-monster, Cetus, lurks down on the horizon.In the early morning skies, you’ll find Mars in Gemini, rivalling the constellation’s principal stars Castor and Pollux: the Moon is near the Red Planet on 7 September. Jupiter lies below Mars, shining over ten times brighter. The giant planet has encounters with the Moon on the mornings of 8 and 9 September.Finally, we may be treated to a shower of shooting stars on 9 September as the Earth slams into a stream of debris shed by comet 45P/Honda-Mrkos-Pajdušáková in 1927.Diary3 September: Moon near the Pleiades4 September, 8.51am: Last Quarter Moon7 September, early hours: Moon near Mars 8 September, early hours: Moon near Jupiter9 September, early hours: Moon near Jupiter; maximum of 45P-id meteor shower11 September, 4.27am: New Moon14 September: Moon near Venus17 September: Moon near Antares18 September, 9.44pm: First Quarter Moon23 September, 1.05am: Autumn equinox25 September: Neptune at opposition26 September, 5.49pm: Full Moon near Saturn27 September: Moon near Saturn30 September: Moon near the Pleiades