Coordinate systems

Coordinate systems are methods used to define an object’s position in space with numbers. Astronomers use them to tell each other where objects in the sky are located. As with any coordinate system, however, both the geometry and the origin must be defined before we can make sense of any positions we are given. For instance, hanging a picture on the wall two feet to the left of the light, or two feet to the left of the door handle, would be two very different positions indeed!

The usual up-down, left-right manner of defining positions, like one would on a flat map, is unfortunately of no use to astronomers. The sky surrounds us completely and bodies move on the so-called celestial sphere, once thought to be a fixed sphere to which the stars were stuck whilst the planets travelled across. Now astronomers treat the celestial sphere as though objects were projected onto it. Given the curved surface of this sphere, it is far easier to use spherical coordinates (coordinates using angles) rather than the flat distances between points we are used to.

3b. Horizontal Coordinate System

The horizontal coordinate system uses the observer’s position on Earth as a reference point, and is useful for determining when an object will rise and set in the sky. It uses altitude (Alt.) or elevation (El.) and azimuth (Az.) as coordinates. Altitude or elevation is defined as the angle from the observer’s local horizon to the object, the same angle at which an observer’s head would be raised to look at the object. The angle is expressed as between 0.00 and 90.00 degrees. The azimuthal angle is the angle an observer must turn from North through East to point in the direction of the object, similar to a bearing, or telling a good friend to ‘watch out for that bludger at 3 o’clock.’ This angle is expressed as between 0.00 and 360.00 degrees. With these two angles, you can define any point on the sky above your head. You can also define a third coordinate, the distance from the observer to the object, but this is not necessary to locate objects on the celestial sphere.

3c. Equatorial Coordinate System

Professionally, however, astronomers must be able to record the positions of the stars and other heavenly bodies without reference to their current position and time. A standard was constructed that treated the now defunct celestial sphere as its reference frame instead, defining the origin not to be directly North of the observer, but at the apparent location of the centre of the Sun at the vernal (spring) equinox, in the constellation of Pisces. To avoid confusion, the equatorial coordinate system uses different names for its angles than the horizontal system, although they are similar in spirit. Altitude is replaced by declination (Dec), which is now the angle from the celestial equator (the same as the Earth’s equator) to the object in degrees running from -90.00 to 90.00 degrees. Compare declination in astronomy to terrestrial longitude. Right ascension (RA) replaces the azimuthal angle, and is the angle eastward of the vernal equinox – the celestial equivalent of terrestrial longitude. This angle can also be given in degrees, although it is most commonly given as hours, minutes, and seconds. It runs from 00:00:00.00 to 12:00:00.00

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For the astronomer looking up at the night sky, however, it is a lot easier to think in terms of horizontal coordinates, so a conversion is needed. There are ways to convert between horizontal and equatorial coordinates yourself, but this would involve some complicated and time-consuming mathematical calculations that are beyond the scope of this course. All you need for this course is an appreciation of what the coordinates refer to, and the differences between the two systems. You then can use a planisphere (an instrument used to compute star charts) or an astrolabe (a type of inclinometre used to predict the locations of celestial objects) to find objects in the night sky – a much simpler method than trigonometric equations, by far! Either of these tools would be a worthwhile purchase for any budding astronomer who does not wish to do excessive trigonometry.

3d. A Practical Way to Navigate the Sky

Even after converting into horizontal coordinates, you may find it difficult to navigate without a sextant (an instrument that measures the angle between two visible objects). One way to measure distances on the sky is to make use of the consistent ratio between the size of your hand and the length of your arm. Stand with your arm outstretched and your hand splayed. The distance across your hand is 10 degrees, the width of the finger is 1 degree, and the length of your knuckles from base to tip is approximately 6, 4 and 3 degrees respectively. To illustrate, the Moon is 0.5 degree and Venus is between 1/6 or 1/36 of a degree, depending on how close Venus is to us at that time. Our nearest spiral galaxy, Andromeda, is so large that on a dark night, with a good telescope, it appears 3 degrees long on the sky - six times larger than our Moon.

3e. Finding Planets

The planets move across the celestial sphere in haphazard ways, due to the relative motion of their orbits compared to Earth. As noted above, we recommend using a planisphere or an astrolabe to calculate where the planets will be at any given time in the sky.Mercury, Venus, Mars, Jupiter, and Saturn may be visible to the naked eye in clear skies, although in light-polluted Muggle cities, Mercury, especially, will be difficult to find. In clear skies, using binoculars, Mercury may be found close to the horizon after sunset or before sunrise. Venus is much the same, although it can be higher in the sky, but no higher than 47.8 degrees above the horizon when the Sun is not visible. The planets will not be too distinguishable from bright stars with the naked eye. However, as the planets are relatively close to us compared to the stars, their reflected light appears more like a tiny disk than a pin-prick of light, and the light will not undergo scintillation when passing through the atmosphere. In other words: stars twinkle; planets do not.

Due to the flat nature of the solar system, with the planets orbiting the Sun in the same plane, one can find the rough position of the planets tracing the same line as the Sun across the sky. This line is known as the ecliptic - the path the Sun follows over the course of one year, as traced on the celestial sphere. One can use this information to approximate where the dimmer planets Uranus and Neptune will be. You will need at least three objects - either three visible planets, or two planets and the Sun. Draw a line through all three objects, and then search for Uranus and Neptune near that line. Note: whilst the Moon’s orbit is close to the ecliptic, it can vary by several degrees – approximately 5 degrees at its worst. Due to the proximity of the Moon to the Earth, this deviation appears huge on the celestial sphere, so the Moon can appear far from the ecliptic. Therefore, using the Moon to find planets in this way should be a last resort.

3f. Constellations and Skies

Astronomers divide the skies into 88 sections, each named after one of the official 88 constellations. These are internationally recognised within the Muggle and wizard astronomical communities, as locations of objects sometimes are given by the constellation they are in or near. Many objects are recorded as Messier X or MX, after French Muggle Astronomer Charles Messier, who recorded a list of notable celestial objects in 1771. Officially, we keep the same names for objects and constellations as those they were given by Messier, although Muggles may have different, colloquial names for constellations and smaller subsections of them (asterisms). The stars in constellations are not necessarily near each other in space, but just appear close as they are projected onto the celestial sphere.

Due to the Earth’s axial tilt compared to the plane of the solar system, and depending on your latitude, objects in the southern and northern skies are not necessarily exclusive to their namesake hemispheres. However, there may be objects that are not visible from your location, whatever the time of the year.

3g. Signs of the Zodiac

The constellations of the zodiac are special because they lie on the ecliptic. Everyone can see at least some of the signs of the zodiac throughout the year. These are, from east through south, Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpius, Ophiuchus, Sagittarius, Capricornus, Aquarius, and Pisces. To remember this order, we suggest the mnemonic ‘all trustworthy griffins cull loathsome vampires lying strictly on socks containing acrobatic puffskeins,’ though you may have your own. To know what zodiacal constellations are in the night sky tonight, find the astrological star sign of someone born today, and then find the opposite sign in the zodiac. We use the opposite sign, as star signs are assigned by what constellation the Sun is in on the day of one’s birth, so those in the night sky will be opposite in the zodiac. For example, if someone is born in mid-March, their star sign is Pisces, so the constellation visible in the night sky would be Virgo. More information on the zodiac is given in the chapter ‘The Sun.’

3h. Northern Skies

The celestial North Pole can be found by locating the very bright star, Polaris. Polaris is currently 0.7o away from the celestial North Pole (although this changes with precession of the Earth’s axis), and is, in reality, one main star with two much smaller companions. Polaris is also at one end of the constellation Ursa Minor (Little Bear), also known as the Little Cart, after the invention of the Goncol cart by a revered Hungarian wizard. The constellation of Draco the Dragon surrounds Ursa Minor, leading to the tale of the impatient Hungarian Horntail that upturned a cart whilst fleeing the farm it had ravaged for dinner one night.

Highest in the sky in April, Ursa Major (Great Bear) is very well known by the pattern of stars contained within it, called the Big Cart or the Plough. The last two stars in the Big Cart, Dubhe and Merak, point in the direction of Polaris. Crossing the cart diagonally through the other stars in Ursa Major will lead you to two galaxies: M81 (Bodes Galaxy, a spiral galaxy), and M82 (the Cigar Galaxy). Both of these galaxies will require a telescope to see. Visualizing a line through the last star in the handle of the Big Cart (Alkaid) through Polaris and on for 30 degrees will bring you to Cassiopeia, the big ‘W’ in the sky.

To find the Andromeda Galaxy, located approximately 2.6 million light years away and visible with the naked eye in good skies, first locate three constellations: Pegasus, Cassiopeia, and Andromeda. The end star of the constellation Andromeda is the upper left star of the Great Square of Pegasus, an easy-to-spot rectangle of stars that is one of the largest geometrical shapes in the night sky. Cassiopeia also is easy to spot due to its ‘W’ or ‘M’ shape. Draw a line from the star Ruchbah, in Cassiopeia, to the star Sirrah (also called Alpheratz), the closest star in the square of Pegasus to Cassiopeia. Intersect that with a line between two stars in the legs of Pegasus - mu Andromedae and Mirach. Halfway between mu Andromedae and this intersection lies the Andromeda Galaxy.

3i. Southern Skies

The southern skies are considered the more impressive of the two skies by many astronomers due to the wide variety of celestial objects visible in them. There is no conveniently bright star available to find the southern celestial pole. However, one can find the approximate centre by locating Crux, the Southern Cross. Draw a line along the longest axis of the cross towards the narrow end of the Cross points, down four-and-a-half times longer than the Cross itself. This point is 5 or 6 degrees from the south celestial pole. Or, make an equilateral triangle with the Small and Large Magellanic Clouds, those bright starry smudges in the night sky that are actually older, satellite dwarf galaxies of our own galaxy. The constellation Centaurus is standing directly over Crux, or, as the story goes, lying slain with a sword in his belly. This is a fairly recent story brought into existence, it is believed, by anti-centaur factions in an effort to legitimise their beliefs. Instead, Crux used to be considered an extension of Centaurus, depicting the legs of the Centaur.

The bright band of stars one can see across fairly dark skies is called the Milky Way, which is made up of billions of stars from our own disk-shaped galaxy, also called the Milky Way. The centre of our galaxy can be found at the intersection of the ecliptic and this bright band of stars. The dark bands permeating the Milky Way are actually dust clouds, shielding the light from background stars and harbouring newly-formed stars. Notable amongst them is the Coalsack Dark Nebula, overlapping the western part of Centaurus and the northern part of Musca. It is only 10% as bright as the surrounding Milky Way. You also may be able to make out the shape of an Emu along the length of the Milky Way, using the Coalsack Dark Nebula as the head.Another stunning, bright nebula that is visible to the naked eye is M42, or the Orion Nebula, located in the constellation of Orion, the dual-wand-wielding wizard. The nebula can be found as the middle star on the sheath of Orion’s belt, where he keeps his wands. You may need a small telescope to see this nebula. The darker the skies, the vaster and brighter the nebula appears.