Astronomy Beginner’s Guide: Part 3 Co-Ordinate Systems

By Duncan Lunan

The most obvious way to tell someone else where to look for something in the sky, would be to give its height above the horizon and bearing left or right from some landmark.   And if you don’t know what the landmarks are, the most obvious thing is to take a bearing from the north-south line, which passes directly overhead through the zenith.   This line is termed the Observer’s Meridian.

Fig 1. alt-azimuth coordinates

The height of an object above the horizon is called its altitude, and its bearing from the north point is the azimuth.  Azimuth can be measured east or west from the observer’s meridian in the north, or in the eastward direction on round to 360°.  The simplest type of telescope mounting is one which goes up and down, left and right, and this is termed an altazimuth mount.

However, the height and bearing of an object in the sky keeps changing as the Earth rotates.  The only apparent exception is the Pole Star, and even that makes a very small circle in the sky over 24 hours; but for general observing purposes it’s usually possible to treat the Pole Star as fixed on the observer’s meridian.  Its height above the horizon in degrees is equal to the latitude of the observing site  (Fig. 1).  At the north pole, of course, the Pole Star would be overhead and the celestial equator (the projection of the Earth’s equator on to the sky) would coincide with the horizon.

Anywhere else, the Equator crosses the sky in an arc which cuts the horizon at points due east and due west.  Any object distant from the Earth will cross the sky daily in a track parallel to the equator, and another co-ordinate system is needed for that. 

Fig. 2 Right Ascension and declination coordinates

The convention in positional astronomy is to regard the sky as a sphere of infinite extent, with the Earth at its centre.  Solid models of the celestial sphere have been made since ancient times: an ancient Greek poem describes one apparently made in Egypt, and copied from a still older one made further north about 2700 BC.  One of the intriguing features of a celestial sphere is that the constellations are inverted left-to-right, because in imagination we are looking at the Universe from ‘outside’.

The celestial equator and the celestial poles are simply the projections of the Earth’s equator and poles on to the celestial sphere  (Fig. 2).  The position of any star above or below the equator then corresponds to the latitude on Earth at which the star is overhead.  The parallels of latitude on Earth, projected on to the sky, are termed parallels of declination and declination is measured from the equator, north or south (positive or negative) in degrees.

The maps for my monthly column ‘The Sky above You’ were drawn by Jim Barker for a latitude of approximately 45 degrees north, so that they can be used by readers in Europe and North America.  (The column has appeared in magazines with overseas circulations, and may do so again.)   For UK readers a few stars are missing in the north:  our circle of circumpolar stars which never rise or set is larger than these maps would indicate.  Jim elongated some of the maps to show the stars of the Plough  (Ursa Major)  as circumpolar, but in central Scotland the circumpolar circle also takes in Deneb, Vega and Capella.

These factors also make the 9 p.m. Universal Time  (GMT)  a little inconvenient in midsummer, since in Scotland in June that’s only just after sunset!   But no-one has ever complained, so it can’t be too big a problem.  The other effect is that the map shows more stars in the south than we normally recognise.  Many Scottish observers paid little attention to Aquarius,  Capricornus and Sagittarius until we had to peer for them near the horizon to locate Halley’s Comet in late 1985.  I have seen Fomalhaut in the Southern Fish and Antares in Scorpius from Scotland, from up hills and right down on a sea horizon;  from Turkey they’re brilliant;  but Grus, the Crane, is a constellation I’ve seen only from the USA.

I was in Big Bear Lake, California  (which is a mountain community, 2500 feet higher than you can get in Britain without an aeroplane)  in the summer of 1984, to be the opening speaker at a spaceflight symposium, and stayed on in Los Angeles, the Bay Area and then Florida until October.  On the night before the symposium I was interviewed by the local radio station, and asked what differences struck me as a visitor from Britain.  My reply, as an astronomer, certainly made a change from the usual stuff about driving on the right and ice in the drinks!  On my first night I went out of doors as soon as it was dark, to renew my acquaintance with the American sky.  As it was my third visit to the USA the effect was less disconcerting than on my first trip, but even after more than two months, the sense of strangeness lingered.

What makes the difference is simply the change of latitude.  Even in the U.K., moving just a few degrees south, down to the south of England, has quite a marked effect on the appearance of the sky.  English readers wouldn’t notice anything very odd about the phrase “as soon as it was dark”, but in Scotland, even on the latitude of Glasgow, we’re far enough north and near enough to the Midnight Sun for twilight to last throughout the night from the end of May to the beginning of August.  Although California is well north of the Tropics, even there twilight is very brief by British standards.  From Big Bear the sunsets were spectacular, seen from above and through the smog of Los Angeles.

Wherever you are in the Earth’s northern hemisphere, the altitude of the Pole Star above the horizon is equal to your latitude.  In Big Bear and in Northridge the Pole Star is only 40 degrees above the horizon, which puts it very close to the mountains.  All the rest of the sky has rolled northwards accordingly, so that the planets Mars, Jupiter and Saturn, low in Britain’s southern sky throughout that summer, were seen riding high here in the darkness; and the surrounding constellations of Scorpius and Sagittarius stand out in full brilliance, where (in Scotland at least) one would be lucky to see even a bright star like Antares, right down on the horizon. 

The other strange effect of the change of latitude, which hit me as soon as I walked out of doors on that first night in California, is that the constellations can appear at angles we never see in Britain.  Facing the doorway, as my eyes began to adjust to the darkness, there was the constellation of Cygnus, the Swan – with Albireo, the head of the swan, higher in the sky than Deneb, which marks its tail.  At that angle the figure of a great bird is much more obvious, rather than the ‘Northern Cross’ which is what we sometimes call Cygnus in Britain.

Throughout the summer the Summer Triangle of Deneb, Vega and Altair was similarly affected, with Altair higher than Deneb so that the isosceles triangle pointed upwards, as it can never do in the UK.   In the Winter Triangle of Betelgeuse, Procyon and Sirius, in the morning, before sunrise, Sirius was out to the right of Orion, higher than Betelgeuse, while Procyon had not risen at all!  Orion himself lay on his side, with Rigel higher than Betelgeuse, whereas in Britain we always see him more or less upright, even when the Hunter is shouldering his way into the sky in early winter.  Still further south in Florida at the end of my trip, when we left at 6 a.m. for the Space Shuttle liftoff,  Orion was almost directly overhead, though still at that ‘extraordinary’ angle.

The Southern Sky

In the southern sky of course everything looks different:  most of the constellations are the same  (the Southern Cross was visible from Britain in megalithic times, and from Jerusalem during the Crusades), but the other way up;  and with north at the top of the map, east is now on the right, something the first navigators to sail down the coast of Africa couldn’t get anyone to believe  (there are major mistakes in both the first two Lord of the Rings movies because they were filmed in New Zealand).   In 2011 I was asked to contribute a regular monthly piece on astronomy for a new Falkland Islands television station.  I’ve never been south of the equator, or any further south than San Diego in California, so I’m aware that it would be very easy to get details wrong, since the whole sky is upside-down relative to our viewpoint in the northern hemisphere, and they’re at midwinter as we hit midsummer.   Mercury was visible after sunset in mid-July but lost in twilight here, for example.  For basic information I was relying on a book which I bought in my teens, An Easy Guide to Southern Stars, by M.A. Orr  (Gall and Inglis, Fourth Edition, undated).    I bought it at the London Planetarium when it was newly opened and the sales assistant was very concerned that I might not realise it was for the southern hemisphere.   It’s fine for a general guide to the constellations and seasons, but no help for detailed month by month forecasts.

In 2011 my first step was to buy a southern planisphere:  that’s a device with two superimposed circles and a mask let into the upper one.  You set the date and time you want by matching them up at the edges, and the area within the mask then gives you the stars which are in the sky at that time.  The first one I used was with the Marr College school telescope in 1957 – in those days they were made of cardboard, usually by Phillips.  I bought my first one at the London Planetarium in 1959 and it’s a collector’s item because the upper disc is in plastic – nowadays both are.  But I’m not going to name the manufacturer of the new southern one because there’s something odd about it.  In theory you use a planisphere by holding it over your head, lining up the northern edge with your northern horizon, but in practise it’s a lot easier to hold it in front of you and turn it around as you turn.  It doesn’t work with this one, though, because when you try it the constellation names are the wrong way up, as if they still had their northern hemisphere orientation!

There’s a website which gives you southern hemisphere skies month by month – for ten degrees further north than the Falkland Islands, which isn’t too bad.  Similar ones for the USA are usable here, except that they show some of the stars of the Plough dipping below the horizon late in the year – we can see them all year round.   But the real problem with the first website is that it doesn’t go into the future, even for next month, let alone two months ahead.  

Linda found a website which helps a lot,   The first thing to watch with it is that timings are in Universal Time  (Greenwich Mean Time as we used to call it), so you have to remember to subtract four hours, in summer, to get Falkland Island Summer Time.  The way I did it was to print maps for the middles of July and August, for an hour after sunset, near midnight and near sunrise, so that I could talk the viewers through each night.  The other thing to watch is that when you’re holding the map towards the camera, looking down on it, the constellations are the ‘right’ way up, the way we see them, not as seen down there.  I did my best to get it all right, but in spite of all my efforts, there was a verbal slip in each of the six pieces I recorded.  We offered free membership of Astronomers of the Future to anyone in the Falkland Islands who spotted them, but nobody took us up on it.

Mintaka, the right-hand star in Orion’s Belt, lies almost exactly on the Celestial Equator, which is the plane of the Earth’s equator projected on to the sky.  At the equator, Mintaka passes overhead every 24 hours.  So the arc from Polaris to Mintaka is of course 90 degrees;  it’s easy to imagine the Celestial Equator, at right-angles to that arc, running across the sky to cut the horizon due east and due west of the observer.  At the North Pole, Polaris would be overhead, Mintaka would be on the horizon, and every visible star would be circumpolar.   But for any other latitude, everything in the sky seems to be moving parallel to the Celestial Equator as the observer is carried around by the rotation of the Earth.  That’s why many astronomical telescopes have ‘equatorial mounts’, with a ‘polar axis’ pointing north at an angle equal to the observer’s latitude:  it means that once the telescope is locked on to a star it can be tracked in a single movement along the ‘equatorial axis’.  The Moon, stars and comets have their own small movements from hour to hour, but these are easy to correct for.

Longitude on Earth is measured from the Prime Meridian, which runs through the poles and through Greenwich, becoming the International Date Line on the other side of the world.   But as explained above, the Observer’s Meridian projected on to the sky belongs to the altazimuth co-ordinate system.  To find a fixed meridian on the celestial sphere, we turn to the Earth’s orbital motion.

The Ecliptic

The Earth’s orbital plane, projected on to the celestial sphere, is the Ecliptic – the path of the Sun among the stars through the year, furthest from the equator at the solstices and cutting it at the equinoxes.  The Ecliptic runs through the constellations of the Zodiac, and the Sun, Moon and planets all move within that band.   Right Ascension is measured along the equator from where the Sun crosses the Ecliptic at the Vernal Equinox, marked with the Greek letter gamma in Fig. 2.  (The Autumnal Equinox is marked with the letter omega.)   Right Ascension  (R.A.)  can be read off either in degrees or in hours and minutes.

As the clocks go back, the sky performs a trick we impose on it every autumn – seeming to jump more than a fortnight, so that: stars which rose at ‘10 p.m.’ the previous night now rise at their true time of nine.  Well – 8.56, if you want to be really precise.  That four minutes  (actually a little less, on average) corresponds to a movement of just under a degree by the Earth in its orbit.   365¼ of them bring us back to where we were.

The plane of the Earth’s orbit around the Sun is the Ecliptic, the center line of the Zodiac, and the Earth’s axis is inclined to it by 23.5 degrees;  as the Sun moves along the Ecliptic over the course of the year, its horizon position varies from its most southerly midwinter rise and set, when it’s overhead at the Tropic of Capricorn, to its most northerly midsummer rise and set, when it’s overhead at the Tropic of Cancer.   Those events are the  midwinter solstice and the midsummer solstice, respectively.

Those names only apply in the northern hemisphere, of course;  in the southern hemisphere the seasons are the other way round, and in June when the Midnight Sun never sets within the Arctic Circle, Antarctica is in darkness even at midday.   In December Antarctica has permanent daylight, as it had when humans first saw the full Earth on the Apollo 17 mission, and when Earth and Moon were photographed in the Galileo spacecraft flyby of 1992.

The Equinoxes

Midway between the solstices lie the equinoxes, on or around March 21st and September 21st, with slight variation year to year, for the same reason that we need an extra day in the calendar every four years.  At the spring equinox and again at the autumn equinox, the Sun is overhead at the equator and day and night have the same 12-hour length all over the world  (hence ‘equi-nox’).  The terminator, dividing day from night, passes through the north and south poles, and if the Earth were a prefect sphere with no atmosphere, the Sun would rise due east and due west everywhere.  (The Earth’s equatorial bulge, the local skyline and atmospheric refraction all affect what you actually see on those days.)

Another anomaly of modern times is that we’re now confused about the timing of the seasons:  we call the spring equinox ‘the first day of spring’ and the summer solstice ‘the first day of summer’ although it’s also still ‘midsummer’s day’.  The Celtic calendar and its Neolithic predecessor more sensibly marked the ‘cross-quarter days’ between solstices and equinoxes:  Imbolc  (now Candlemas)  at the beginning of February, Beltane  (now May Day), Lammas at the beginning of August, and Lughnasagh  (now Martinmas)  at the beginning of November.  In the Middle East the onset of the seasons used to be marked by the heliacal rising  (first-time visibility before sunrise)  of the four Royal Stars:  Aldebaran for spring, Regulus summer, Antares for Autumn and Fomalhaut for winter.   Now, due to Precession of the Equinoxes  (see below), they all appear earlier in the year.

In older observatories there are still ‘transit instruments’, beautiful telescopes made only for timekeeping, moving only in a very accurate north-south axis.  You also find two clocks, one showing Universal Time, the other Sidereal Time – time by the stars, measured from the Vernal Equinox.  If you know your Local Sidereal Time, and the Right Ascension of your target, you can point your telescope with great accuracy to any star in the catalogue before you open the dome.  Universal Time is the same as Greenwich Mean Time, which marks the average motion of the Earth around the Sun during the year – the slightly elliptical motion of the real Earth around the real Sun became too much of a nuisance long ago!

Nor is the Vernal Equinox a fixed point.   The pull of the Sun and the Moon on the Earth’s equatorial bulge produces a slow movement of the Earth’s axis termed Precession  (Fig. 3).   As the Pole moves due to Precession, the Equator moves with it, moving around the Zodiac with a period of 26,000 years, and a result the Vernal Equinox moves steadily along the Ecliptic from year to year.  When the Greek astronomers mapped the sky the Vernal Equinox was in Aries.  By convention it is still referred to as ‘The First Point of Aries’, although at present it is in Pisces.

Astrologers, however, cling even more firmly to the past.   The houses of the Zodiac listed in most horoscopes still assume that the Sun is in Aries in March.   Consequently if you think you are an ‘Aries’ you are in fact ‘Pisces’, and so on round.  The Sun has actually been in Pisces for the whole of the Christian era, which is why the Fish was an early Christian symbol.  Some astrologers divide the Zodiac into twelve arcs of equal size, irrespective of the size of the constellations:  this is the basis of claims that we are entering the new age of Aquarius, although the Vernal Equinox won’t actually get there for another 400 years.

Fig. 3 Ecliptic coordinates

For astronomers, one consequence of precession is that any accurate star chart or catalogue using right ascension and declination has to state the date for which it was compiled  (e.g. ‘Epoch 1950.00’), and correction tables have to be used to pinpoint celestial objects with precision.  The alternative system of Ecliptic latitude and Ecliptic longitude measured on the Ecliptic has the same problem in longitude, although ecliptic latitudes are constant.

To find reference points among the ‘fixed stars’ we have to detach ourselves from the planet Earth and its motions.   Then the most obvious marker is the centre line of the Milky Way, as we see it, though it doesn’t quite coincide with the disc plane of the spiral galaxy of which our Sun is a member.   Galactic latitude is measured in degrees north or south from the Galactic Equator, and for Galactic longitude, the Galactic Centre provides the zero point – but it’s not so easy to find.  Going by counts of stars visible to the telescope along the Milky Way, astronomers had determined that the most dense region was in Scorpius, and the Galactic Centre was marked as being there until 1959.  By then, however, radio astronomers had discovered that the true nucleus of the Galaxy was hidden from us behind clouds of dust in Sagittarius, so the galactic latitudes and longitudes on all the maps had to be changed.   When working with galactic co-ordinates, it’s always necessary to check the compilation date of the map.

Fig. 4 galactic coordinates

Even now, however, we don’t have a truly fixed co-ordinate system.   Our Sun lies two-thirds of the way out from the centre of the Galaxy, and orbits around it with a period of 200-250 million years.  The bearing to the Galactic Centre has changed by about 7 degrees since the first tool-using hominids appeared on Earth:  we have not found the ‘fixed stars’ yet.   That name for the basic framework of the Universe was coined before it was realised that the familiar stars do move – even if taking thousands of years to move perceptibly on the celestial sphere.  But over 200-230 million years, the ‘View from Earth’ of everything visible is altered  (including the Magellanic Clouds, satellites of our Galaxy, and its nearest neighbour M31 in Andromeda, the most distant object visible to the naked eye.)  In that time, our Sun orbits right round the Galaxy.

Beyond the Milky Way galaxy, we find a Local Group of three spirals, plus elliptical galaxies and irregulars.   Within that, our spiral has its own motion.   But beyond, we find other groups, clusters, super-clusters – groupings of the galaxies which we used to class as the biggest objects in the Universe, until we began to find structures in between them.  The expansion of the Universe, the physical growth of space-time itself, gives all the more distant assemblies of galaxies a radial motion away from us.  Surely, then, that defines the basic frame of reference – the ‘fixed stars’ to which a gyroscope points? 

However, in the early 60’s radio astronomers detected the 2.7 degree-background radiation which appears to be the last ringing of the Big Bang, filling the whole Universe.  All was well until the radiation turned out to be asymmetric:  we are not at rest with respect to it, but moving at 60 km. per second – we and the entire Local Group, because we are in a flyby around the Virgo Cluster, under the influence of still larger attractors beyond, on a timescale longer than the history of the Universe to date.  But there’s a more interesting consequence:  because of time dilation, which is experienced by every moving object according to relativity theory, time passes here a little more slowly than it would if we were at rest.  If the background radiation defines the truly fixed frame of the Universe, and we move with respect to it, then so must everything else – even Newtonian physics tells us that.  The search for the framework of space has revealed that we all have a slight advantage on the passing of time, and get to see just a little bit more of the total play.

See also:

Astronomy Beginner’s Guide: Part 2 Compass Points in the Sky

Amateur Involvement in Astronomy: Part 1 of Our Beginner’s Guide

The Sky Above You – April 2021

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