For anyone only occasionally glancing at the night sky, the stars seem to be randomly scattered around the sky. However, the more experienced observer realizes that the stars remain in fixed positions to each other, forming patterns known as constellations. This allows us to make maps of the sky. But how exactly can we define the position of a celestial object? How do celestial coordinates fit into a star map? We'll discover it here.

The Sky is a Sphere

Do Stellar Distances Matter?

The stars and other celestial objects (such as nebulae, galaxies and clusters) aren't all at the same distance from the Earth. However, we can’t determine this with the naked eye. Since we are gifted with two eyes, we can get a sense of depth and determine if an object is close to us or not. When we look at something, both our eyes don't see the same image. Because of the distance of about 7cm between our eyes we notice that closer objects 'move' relatively to the background if we alternately watch through each of our eyes.

This is known as parallax, and the distance between the two points of observation (in this case our eyes) is called the base. The farther an object is from us, the smaller a parallax it has. The stars however are located at such a great distance that a base of a mere 7cm isn't sufficient to notice any differences in stellar distance.

Now what would happen if we were to enlarge the base, if we could take a look at an object from two different places with a considerable distance between them? Well, even if we move to the opposite side of the Earth, increasing the distance between 'our eyes' (the base) to approximately 12,700 km, we still won't be able to see a stellar parallax *.

The importance of this is that at a given moment, the sky looks the same at every place on Earth. The relative positions of celestial objects are the same everywhere. This enables us to produce star maps that are accurate all over the world at a given time.

No They Don’t!

So now that we know that there's actually a point in developing star maps - and consequently coordinate systems, how is it done? The first basic principle of every star map is that, since we can't 'see' celestial distances anyway, all stars and other celestial objects are placed at the same distance from the Earth. In doing so we place all those objects on an imaginary sphere or globe surrounding the Earth. That's exactly how the sky is pictured in a star map.

Of course, one person can never see the celestial sphere completely. The stars located right under your feet aren't visible because the planet you're standing on is blocking the view. In fact, we always see only half of the celestial sphere, namely the part of it that is above the local horizon. The point located right above your head, the highest point in the sky, is called the zenith. The point opposite to the zenith, under your feet and of course invisible, is called the nadir.

The Motion of Stars and Planets on the Celestial Sphere

The Daily Movement of the Stars

If you’d be watching a certain star for an hour or so, you’d notice that it doesn't just hang there motionless in the sky. In fact, stars and celestial objects rise and set just like the Sun does. This is caused by the rotation of the Earth. Since the Earth rotates around its axis from west to east, the Sun and stars move across the sky in a daily rotation, rising in the east and setting in the west.

In doing so, they all rotate around a certain point in the sky, one of the two celestial poles. These poles are exactly the points where the extension of the Earth’s axis intersects with the celestial sphere. An observer on the Earth’s northern hemisphere would only see the north celestial pole and an observer on the southern would only see the south celestial pole. Right in between the two celestial poles we can plot a line onto the celestial sphere, which is the imaginary extension of the Earth’s equator and is therefore called the celestial equator.

The altitude above the horizon at which you’ll find the celestial pole depends on your latitude. An observer at a latitude of 50°N would find the northern celestial pole at 50° above the horizon. To a person observing from the Earth’s north pole, the north celestial pole would be right above his head, in the zenith. The farther a celestial object is from one of the poles, the larger the circle is that it draws around that pole in its daily rotation. Because of this some stars never set and are always visible. These stars, which are close to the pole of your hemisphere, are called circumpolar stars*. In exactly the same way, some stars, depending on your geographical location, are too close to the invisible celestial pole and never rise above the horizon. The stars located between the circumpolar and invisible stars, rise and set just like the Sun and Moon.

The Movement of Stars in Space

Stars also move around the celestial sphere in another way. They are not fixed in space but instead they move at high speeds in different directions. This motion, which is called the proper motion of stars, is actually noticeable in the course of centuries. The constellations didn’t look the way they do now millions of years ago. That’s why every star map always specifically states for which year it is accurate. This is called the epoch of a star map and is usually the year 2000, although older maps may have 1950 as an epoch. Of course, the proper motion of stars over a period of just fifty years only becomes apparent in large telescopes.

The Movement of Planets

Planets, of course, require an entirely different approach. Being part of the solar system, their movement is much more apparent to us*. Because of that, it is obviously impossible to include them in a stellar map, since their positions change in the course of years, months or even days in the case of the inner planets.

In a certain way they are however included in a star map. All the planets more or less move in the same plane around the Sun. This plane is called the ecliptic, defined as the plane in which the Earth rotates around the Sun. The orbits of the other planets only deviate slightly from the ecliptic. The ecliptic can also be plotted onto the celestial sphere. By definition, this plotted ecliptic is exactly the path the Sun follows through the constellations in the course of one year*. On the celestial sphere, the planets will always be found near the ecliptic.

Two (or more) Possible Coordinate Systems

Two Spherical Coordinates

Back to our starting point: the sky is a sphere with poles and an equator. In fact, for every spherical coordinate system you need a reference circle like the equator. Accordingly, the two poles are defined as being opposite each other and each at an angle of 90° to the reference circle. Lines connecting the two poles and intersecting the reference line at a right angle are called meridians. Circles parallel to the reference circle are not surprisingly called parallels.

Now we can begin constructing a spherical coordinate system. One of the two coordinates is called the latitudinal coordinate. It indicates an angle above or below the reference circle and has a value between 0° and 90° or 0° and –90°. The other coordinate is called the longitudinal coordinate. Defining this coordinate is somewhat more complicated. First you need to establish a reference meridian on the reference circle. Every other meridian on the reference circle can then be defined as an angle on a circle (ranging from 0° to 359°). To define the longitude of a point on the sphere, we then simply determine what the angular distance is of the local meridian (the meridian going through that point) to the reference meridian.

Consider the Earth’s coordinate system for instance. The reference circle is of course the equator, and the reference meridian is the meridian of Greenwich. The latitude of a location on Earth is an angle between 0° and 90° north or south of the equator. The longitude of a location on Earth does not range from 0° to 359° but is rather defined as a value between 0° and 180° east or west of Greenwich*.

Celestial Coordinates

Now that we mastered the basics we can go on to the celestial coordinate systems. It all really comes down to choosing an appropriate reference circle.
A first possible reference circle is simply the horizon. The zenith and the nadir thus become the two poles of the coordinate system. In this system the latitudinal coordinate is simply called altitude (above horizon) and the longitudinal coordinate is known as the azimuth. The reference meridian is the one connecting the true north with the true south, with an azimuth of 0° being north, 90° being east and so on.

This system, known as the horizon grid, describes the position of an object at a certain location and a certain time. Consequently, the horizon coordinates of a celestial object change continuously, making this system not at all useful for mapping. It is however widely used to describe apparent trajectories of satellites and spacecrafts in visibility predictions, for example.

It is clear however that a fixed set of coordinates is needed to unambiguously define the position of a celestial object. This is achieved by choosing the celestial equator as a reference circle. In doing so, the north and south celestial poles become the poles of the coordinate grid. This system is the most common celestial coordinate system and is known as the equatorial grid. The latitudinal coordinate is called declination, while the celestial longitude of an object is called right ascension*.

Declination ranges from –90° to +90° (the ‘+’ is always included) but right ascension isn’t even measured in degrees, but in hours, minutes and seconds. Instead of 360 degrees, the equator is divided in 24 hours, each enclosing 15 degrees. Every hour is then subdivided in 60 minutes and every minute in 60 seconds. The reference meridian of 0 h is defined as the one on which the vernal equinox is located. This is the intersection of the ecliptic with the equator that is reached by the Sun at the beginning of spring. Using this system, every position in the sky can be determined, regardless of the observer’s location and observation time.

Other fixed grids are equally possible, such as the ecliptical and galactic grid, starting with the ecliptic and the galactic equator as a reference circle respectively. These, however, are only used for specific mapping purposes. The ecliptic grid would be appropriate for mapping objects in our solar system, and the galactic grid could be used for mapping objects in respect to our galaxy.