Last update: 31 May 2013

What we see in the Sky: Stars

How the stars appear to rise, set, and move throughout the night and the year; an explanation of celestial coordinates; a list and explanation of astronomical terms; and a longer than expected diversion on latitude and longitude (and mapping)

Quick note on the questioner: their identity is not revealed but think of him/her as a friendly alien, who may or may not be more intelligent than us. Or possibly a pet.

So what do we see in the sky?

Stars, sun, moon and planets - we can see the planets out to Saturn without a telescope (Mercury, Venus, Mars, Jupiter, Saturn). There are some other things, especially once you start using telescopes. For now, though, we're concentrating on using the movement that we see in the stars, sun, moon and planets to understand what's happening in the solar system. We'll start with the stars.

Does it matter where we're looking from?

Yes. You'll see different behaviour at different latitudes; and also longitudes in terms of the time at which things happen, but the longitude doesn't affect the general behaviour. When we want a specific example we'll take Winchester, UK - approximate latitude 51°N, approximate longitude 1.3degW (or 51.06 and 1.32 to be more accurate). You can also see more with clear air and low light pollution which is why the best observatories are on top of remote mountains. Now if you go out into space then it's even clearer and you don't have the atmosphere and the Earth isn't in the way of half the sky ... but leave that for now, we're talking about what people have seen for thousands of years.

Since you mention them, can you explain latitude and longitude please?

Sure. Greek philosophers seem to have believed from two and a half thousand years ago that the Earth is spherical, and it was as long ago as the first century that Ptolemy published an atlas with places located by latitude and longitude co-ordinates. There is a myth that Columbus 'proved' the world was round by his four voyages between 1492 and 1503. He was attempting to reach the East Indies (SE Asia, east of India) by sailing west from Spain to save going round Africa on the eastward route. He actually found the Americas (which he insisted was the East Indies). The first circumnavigation of the world was led by Magellan from 1519 to 1522, although he died on the way; of the five ships that set out only the Victoria made it all the way - the voyage is a fascinating tale of politics, mutiny, battles, shipwrecks and pursuits. However, the sphericity of the earth was widely accepted by scientists well before this - for example deduced by the way ships slowly disappear over the horizon or by the circular shadow of the Earth on the moon during a lunar eclipse (we'll discuss that when we talk about the moon).

Latitude lines are parallel to each other and range in value from 90°N at the North Pole to 0° at the equator to 90°S at the South Pole, the angles being measured from the centre of the Earth to the N or S of the equator. The 90° latitude (at either pole) is a single point, the length of the 0° latitude line (the equator) is about 40,000 km (25,000 miles), and the other latitudes have lengths somewhere inbetween. As we'll find out the Earth rotates about an axis through the earth between the N and S Poles, and the Equator is the line of latitude half way between the two poles. Now even without knowing this, there are good astronomical reasons to draw latitudes as they are - for example, on any day the length of day or the highest altitude of the sun is the same for all places with the same latitude. The equator has all days of length 12 hours (they're a few minutes longer actually due to various physical effects), whereas everywhere else has longer days in summer and shorter days in winter; it also experiences the quickest sunrise and sunset because the sun rises and sets more or less vertically. There are four other special lines of latitude - the Arctic Circle, the Tropic of Cancer, the Tropic of Capricorn, and the Antarctic Circle (approximately 66.5°N, 23.5°N, 23.5°S and 66.5°S respectively). Anyway, more on the significance of specific latitudes later when we talk about the sun.

Lines of longitude (or meridians) run from N Pole to S Pole perpendicular to the lines of latitude, and define the east-west position. Longitudes range between 180°E and 180°W, with the central 0° longitude line placed near the Royal Observatory, Greenwich, London (this is an arbitrary point, chosen through history - there is nothing special about 0° longitude). The angles are from the centre of the Earth to E or W of the Greenwich meridian. Each line of longitude has the same local time - that is, the instant that the sun reaches its highest altitude (which is the definition of local noon) is the same for all places on that longitude. As you travel each 15° of longitude east, the local time will be one hour later. Hourly time zones are thus defined in 15° longitude blocks...although it doesn't work out exactly like that. The time zone boundaries are adjusted by countries to ensure the time is the same in a country or a region; in addition some countries define daylight savings by advancing clocks an hour in spring and then back in autumn - this ensures more daylight in the evening and less in the morning. Now if you go 360° right round the globe back to where you are standing the time will be 360/15 = 24 hours later - which of course doesn't make sense and this is why there is an International Date Line at 180° of longitude. Similar to time zones, the International Date Line weaves it way between countries rather than being exactly on 180°. Crossing to the east means a day is subtracted, whereas a day is added crossing to the west. In the UK the time zone is Greenwich Mean Time (GMT), with British Summer Time (BST) an hour ahead between 1:00 AM the last Sunday of March and 1:00 AM the last Sunday of October. GMT provides the 'mean solar time' at Greenwich: that is, on average noon will be when the sun is at its highest at Greenwich in this time zone. It is only an average because various effects like the variable speed of the Earth (we'll discuss that later) mean the time of the sun's highest altitude at Greenwich has to vary slightly from noon on a day to day basis or else some days would be longer than others. GMT is also very close to Coordinated Universal Time (UCT) which is defined as a standard time for Earth (regardless of time zone) and is calculated using atomic clocks.

Now for accurate mapping it's more complicated than that, because the Earth is not a perfect sphere; in fact it's not even a perfect ellipsoid. To measure real latitude and longitude on the Earth a geodetic datum is defined. A datum is a set of values used to define a coordinate system. For instance WGS84 is used by GPS and is the most widely used global datum: it is defined by a reference ellipsoid (precise parameters of the ellipsoid are defined to best fit the Earth's shape); reference positions on the Earth defined with specific latitude and longitude values to 'anchor' the ellipsoid to the Earth; and a reference surface to model sea level (so that a third coordinate of height above sea level can be defined to measure depths or altitudes). Different datums will have slightly different coordinates for the same place - software exists to convert coordinates between datums (you can find programs online). Local datums can offer a better fit to the Earth than a global datum because they just have to be accurate over a smaller area. For instance Ordnance Survey maps used in the UK use the OSGB36 datum. The same coordinates in WGS84 and OSGB36 will be different places - up to about 100m apart.

Right I'm getting a bit carried away now, but these diversions allow us to explore side issues that catch our interest before I get back to finding the secret of the universe. Let me finish with a mention of mapping, and northings and eastings. Positions on the curved surface of the Earth can't be exactly drawn onto a flat two dimensional map. A mathematical projection is defined and this will distort the picture - either shapes will be inaccurate (for example, of a country) or the scale will be inaccurate (for distance and area - it will be different at different parts of the map) or directions (the bearing or angle) between points will be inaccurate; or possibly all three. As an example, this is why Greenland looks massive on a world map. However, you can be quite accurate if you restrict your map to a reasonably narrow area - so an accurate projection is defined in one area, and a different projection in a neighbouring area. The most standard way of doing this is to use a Universal Transverse Mercator (UTM) projection. This is a series of 60 projections each with a 6° wide longitude band; between them they cover the Earth (except for high latitudes near the Poles). The central meridian of each projection defines the projection and is the central longitude line of the area covered, for instance at 9°W, 3°W, 3°E, 9°E, etc. Maps are then drawn for a particular area, using the relevant projection, e.g. UTM with central meridian 3°W (the origin of the mathematical projection is then 3°W, at the equator). The maps are drawn with gridlines to pinpoint positions - to locate a position eastings (a value in metres east of the origin) and northings (the value north of the origin) are used, the eastings being given first. The origin is the central meridian (which is given a value of 500,000 eastings - so you don't get negative numbers as you go to the west) and the equator (given a value of 0 for points in the northern hemisphere; and 10,000,000 in the southern hemisphere - again so you don't get negative numbers in the south). UTM projections preserve shape and direction fairly closely but distort distance and area; they are more accurate near the central meridian; and are not applicable near the Poles (the UTM is valid from 80°S to 84°N - a different type of projection is generally used for mapping polar regions).

Grid north is the (up) direction of the northing grid lines on the map and this will vary slightly from true north (which points at the N Pole) except at the central meridian where they are equal. The difference is called grid convergence (or just convergence) which is defined as the bearing from true north to grid north - this will vary from point to point. This is measured as a bearing (or angle) which is positive to the east (or clockwise). For the UTM projection convergence is positive to the east of the central meridian and negative to the west; this means true north is to the west (or left) of grid north on the eastern side of the central meridian and to the east (or right) on the western side. A grid bearing is a bearing measured clockwise from the northing grid lines on a map with 0° being in the direction of grid north; for instance a direction of SW on the map is equivalent to a grid bearing of 135°. Since true north deviates from grid north by the convergence, then the true bearing at a point will deviate by the same amount from the grid bearing and they will be related by the formula true bearing = grid bearing + convergence (e.g. the true bearing is SW or 135°, convergence is +2° and therefore the grid bearing as measured on the map is 137° - slightly south of SW).

In addition to the variance between grid north and true north, if you are trying to navigate using a compass there is a different and third north - magnetic north, which is the direction a compass points. There is a Magnetic North Pole - somewhere in the Canadian Arctic at the moment - and a Magnetic South Pole, but a compass needle doesn't point exactly to the Magnetic North Pole; it varies according to the local magnetic field. Both the Magnetic North Pole and the local direction of a compass needle change over time. We are not going to get into the details of the Earth's magnetic field now! Suffice to say that at any point and date there is a magnetic declination (or magnetic variation) which is the bearing from true north to magnetic north, positive to the east (or clockwise). You can look this up on various websites - for instance, the Mag Dec Calculator at the US National Geophysical Data Center tells us that the magnetic declination for Winchester on 4 Mar 2013 is 1.62°W changing by 0.15°E per year. Now if you are trying to navigate accurately by map and compass, you don't need the difference between magnetic north and true north, you need the difference between magnetic north and grid north - which you can work out by the formula magnetic grid variation (also called grid magnetic angle) = magnetic declination - convergence - this gives you the bearing from grid north to magnetic north. As ever with bearings this is positive to the east (or clockwise). I'm going to reiterate the ins and outs of this formula because it's easy to mix the signs up: magnetic grid variation and magnetic declination and convergence are all bearings (which means they are positive to the east and negative to the west); magnetic declination is from true north to magnetic north, convergence is from true north to grid north and magnetic grid variation is from grid north to magnetic north. You have to get the signs right in the formula! Maps will usually tell you the magnetic grid variation for the year the map is published and the rate of change (the rate of change will be the same as for magnetic declination), so you don't need to worry about working it out from the magnetic declination and convergence. Quite often you don't need to worry about the difference between grid and compass (or magnetic) bearings because the difference may only be a few degrees, but sometimes this will be which case, here's how you swap between magnetic bearings and grid bearings when you are trying to navigate by map and compass: 1. If you have taken a grid bearing from A to B on the map and need to travel on a compass bearing from A to B, then compass bearing = grid bearing - magnetic grid variation. 2. If you've taken a compass bearing from A (where you are) to B (something you can see) and need to work out where you are on the map (the assumption is you can identify or guess what B is on the map), then the grid bearing between the two points A and B is given by manipulating the formula to grid bearing = compass bearing + magnetic grid variation. [And then your position A on the map is somewhere on a line from B drawn at the calculated grid bearing; if you can measure the bearing to another point C then you can triangulate your position - that is, you are at the intersection of the two bearing lines from B and C] Again, it's important to get the sign of the magnetic grid variation correct: note that the map may tell you that magnetic grid variation is e.g. 3°W - remember that the 'W' means it is -3, whereas an east magnetic grid variation would be positive.

Finally a brief word about the UK and the Ordnance Survey which uses the National Grid to cover the whole of Great Britain with its maps. The Ordance Survey uses a Transverse Mercator projection for its maps, but it is not a UTM projection because its central meridian is non-standard at 2°W and the latitude of the origin is 49°N. To avoid negative numbers a 'false origin' is defined 400km to the east of 2°W and 100km to the north of 49°N - that is, somewhere to the SW of the Scilly Isles. All of Great Britain and its islands (not Ireland though) are covered by the Ordnance Survey maps which extend 700km to the east and 1300km to the north of the false origin. As an example, Winchester Cathedral has grid reference approximately 448500 129500. Now that's to the nearest metre, so unless you were being very accurate you might truncate this to 44850 12950 (which defines a square with 10mx10m square) or 4485 1295 (which defines a 100m square) - using less than six digits tells you how accurate you are being (you have to use the same number of digits for the easting as the northing). The Ordnance Survey allow a further abbreviation by defining 'lettered' 100km squares which are specified on maps - e.g. the square with bottom left corner at 400000 100000 is SU, so the 4 and 1 can be left off the grid reference and Winchester Cathedral becomes SU485295 (to the nearest 100m) - note you typically don't put a space between the easting and northing values. The grid convergence for Winchester is approximately 0.5°, so true north is very slightly west of the north grid lines. You will see this grid convergence value stated on the Winchester Ordnance Survey map. As above we saw the magnetic declination for Winchester is 1.62°W (in 2013), so the magnetic grid variation will be -1.62 - 0.5 = -2.12, or 2.12°W (moving east by 0.15° per year). And indeed this is what is says on the map - well actually it was published in 2006 and it says 'magnetic north is 3.15°W of grid north moving 0.15°E per year', which works out more or less the same. So if you walk directly north according to your compass, you will be walking approximately 2° to the west on the map; and if you try and walk exactly along a north grid line, you will need to set your compass to 2°E. Try not to get lost.

As a summary, you're likely to use latitude and longitude for global activities such as global navigation or relating your position to the stars you are likely to see; and northings and eastings for local activities such as travel within a country or finding your way on a mountain. You may also need to take into account the variations between magnetic, grid and true north for accurate navigation. Now the technicalities and mathematics of goedetic datums, map projections, coordinate transformations, accurate mapping, GPS positioning, the Earth's magnetic field and general manipulation and storage of geographic data is a large subject and many companies work in these areas; for instance in GIS (Geographic Information Systems) software, mapping, surveying or GPS applications. So we'll leave it right there and get back to the main subject!

Zzzzz. Only kidding - shall we get back to the stars then? What do we see and how do they move?

To start with the obvious the stars appear at night (or during a solar eclipse - they are always there and we see them anytime the sun doesn't drown their light); and of course only when they're not obscured by clouds. Actually we can see the brighter stars and some of the planets during daylight, but generally only with an optical aid such as a telescope; this is more likely at times close to sunrise or sunset and it also helps to know exactly where to look. As the night goes on you see new stars appearing (rising) in the east and existing stars disappearing (setting) in the west. They travel across the sky in circles from east to west: which is anticlockwise if you're facing north and clockwise if you're facing south. Some stars don't rise or set but travel in permanent circles in the sky (and do so during daylight, but of course you can't see them then) - these are called circumpolar stars. The circles are around two fixed points - the North Celestial Pole (NCP) in the northern hemisphere and the South Celestial Pole (SCP) in the southern hemisphere (see the section on NCP and SCP below for a clarification on this). The north celestial pole is close to a star called Polaris or the Pole Star; however there is no easily visible star at the southern celestial pole - a constellation called the Southern Cross (used on several national flags, including Australia) - is used to point to it. Polaris hardly moves and always points north (to within a degree). The positions of the stars are always fixed in relation to each other. It's as if all the stars are on the inside of a giant celestial sphere (extending far out from the Earth) which rotates around us. The next night we will see the same - the stars have come back to their positions of the previous night - except they are there about 4 minutes earlier (3min 55.91s to be more accurate). After one year from any particular day, the stars will be back in the same position at the same time. [The maths does add up if you assume there are 365.24 days in the year, although there are two minor subtleties when presented like this: 1. 3min 55.91s * 366.25 gives 86,400s (24 hours) - you multiply the 'lag' by 366.25 and then you see the stars were in the same place 24 hours ago, that is after 365.24 days or one year! 2. Since 365.24 is not a whole number of days an averaging effect is in place here - after 365 days the stars are in the same place about one minute later than the original time (or 23 hours, 59 minutes earlier) and after 366 days the stars are there about three minutes earlier.]

Ok, a question: the stars rise in the east and set in the west - is that exactly east and west?

No. To answer this best I'm going to introduce celestial coordinates, the coordinate system we use for stars. Stars are considered as being on the underside of the fictitious celestial sphere I just mentioned; that is they are on the interior of a sphere that is centred on the Earth and has enormous (or infinite) radius. Note that this implies all the stars are the same distance from us, which is not true; however they are so far away we don't have any depth perception to tell which are closer or further from us - we'll get to how to estimate star distances later. We define a star's location by two celestial coordinates: 1. The declination (dec). This is the angle of the star (from the centre of the Earth) north of the celestial equator, where the celestial equator is the projection of the Earth's equator on the celestial sphere. So if the star is on the celestial equator the declination is 0, if it is directly above the N Pole it is +90 and if it is directly above the S Pole it is -90. 2. The right ascension (RA) is the angle eastwards from the vernal equinox, although it is usually measured in time units - from 0 hours to 24 hours (equivalent to 0° to 360°, so 1h is 15° and for example, an RA of 6h 30m is the same as 15 * 6.5 = 97.5°.). We'll get to what the vernal equinox is later - it is only the declination that is important to answer the question. Celestial coordinates are analogous to latitude and longitude on the Earth. For any visible star you can look it up in a star catalogue - e.g. the Bright Star Catalogue - and you'll find its RA and declination.

Whoa there! How do I find a star with, say, declination 25° and RA 11h? How do I locate the celestial equator and the vernal equinox (whatever it is), and then find the star?

Let's give some terms and definitions (and consequences and analysis) first, in a sensible order, then get back to your question (and the previous one). I'll repeat a couple we've already mentioned to put these all in one place. This actually ends up considerably longer than I intended, but it gives a lot of background for our subsequent discussions on observational astronomy and will keep those shorter (in theory). And it's mostly fascinating!

Fantastic. I can see you've set the scene to answer my question about how to locate a star. Can you go for it?

Ok. Let's take your example of a star with dec = 25° and RA = 11h, and assume we're in Winchester (51°N, 1.3°W) on 13 April. All new results here not fully explained are from spherical astronomy (and assume a spherical Earth and no refraction or other 'subtleties')! We'll do this step by step:

Right, I see you managed to slip in details of my previous question about which directions the stars rise and set. Are we done here?

More or less. I want to finish with a few notes on star rising and setting, focussing on what happens at the equator, the poles and intermediate latitudes. So ... here you go (with the usual caveat that results are approximate, assuming a spherical Earth, etc.):

And to finally finish this chapter, here's a list of the websites we've referenced:

Thank you.

No problem. Right, I'm going to move on now. There is of course vastly more to cover about the stars - for instance aberration of starlight, motions of individual stars and galaxies, star catalogues, orbital influences on star positions (like the precession of the equinoxes, nutation), the whole field of spectroscopy (analyzing starlight), etc.. But we'll cover that in future sections. It's the Sun next. However ... I need to take a hiatus, as my next story Culture Man needs to be written before the summer's out. Can you give me a hand with that?

Sure. Do you have any ice cream?

Next: What we see in the Sky: The Sun
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