# Which Celestial Coordinate System?

Let’s see if I can teach you how to navigate the night sky.

In astronomy, a celestial coordinate system is used for specifying the positions of celestial objects: stars, planets, satellites and galaxies, and so on…

Coordinate systems specify a position in 3-dimensional space, or merely the direction of the object on the celestial coordinate sphere, if its distance is not known or not important.

Each celestial coordinate system is named after its choice of fundamental plane.

The coordinate systems are implemented in either spherical or rectangular coordinates.  These differ in their choice of fundamental plane, which divides the celestial sphere into two equal hemispheres along a great circle.  In applied mechanics, the three common coordinate systems are rectangular (or Cartesian), cylindrical, and spherical.

#### Rectangular Coordinates

In geometry, a rectangular or Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which indicate the distances to the point from two fixed perpendicular oriented lines, called the axes of the system.

The point where the two (or three) axes meet is called the origin and has (0, 0) (or 0, 0, 0) as coordinates.

Rectangular coordinates, in appropriate units, are simply the Cartesian equivalent of the spherical coordinates, with the same fundamental xy– plane and primary (x-axis) direction.

#### Spherical Coordinates

Spherical coordinates, projected on the celestial sphere, are analogous to the geographical coordinate system used at the surface of the Earth.

The animation shows a star’s galactic (yellow), ecliptic (red) and equatorial (blue) coordinates, as projected on the celestial sphere.  Ecliptic and equatorial coordinates share the vernal equinox (magenta) as the primary direction, and galactic coordinates are referred to the Galactic centre (yellow).

## The Horizon Celestial Coordinate System

In astronomy, we use the plane of the horizon.

A number of terms are used to describe the location or behavior of objects in the sky.

• The Zenith is the point on the celestial sphere that is directly overhead.

• The Nadir is the point of the celestial sphere directly beneath the observer.
• The North point is the point on the horizon in the direction of geographical north.
• The South point, as you would naturally expect, is the point on the horizon in the direction of geographical south.
• A vertical circle is really just what it says, i.e. any imaginary great circle which passes through the zenith.
• A meridian is a vertical circle which passes through the north and south points.
• The altitude – The angular distance from horizon to object, measured along a vertical circle.
• The azimuth is the angular distance along horizon from N (S) eastwards to vertical circle through the object (for Northern (Southern) hemisphere).

## The Equatorial Coordinate System

Celestial coordinates are key to the observation of the night sky.

The equatorial coordinate system is the normal coordinate system used by most professional and amateur astronomers using an equatorial mount that follows the movement of the stars in the sky throughout the night.

The equatorial coordinate system is centred at the Earth’s centre, but fixed relative to distant stars and galaxies.

The equatorial describes the sky as seen from the solar system, and modern star maps almost exclusively use equatorial coordinates.

#### Right Ascension and Declination

The coordinates are based on the location of stars relative to Earth’s equator if it were projected out to an infinite distance.  Celestial objects are found by adjusting the telescope’s or other instrument’s scales so that they match the equatorial coordinates of the selected object to observe.

The positions of celestial objects are then specified in terms of:

• ##### right ascension α (RA)
• comparable to terrestrial longitude,
• gives the angular distance of an object eastward along the celestial equator from the vernal equinox to the hour circle passing through the object,
• increases to the East from 0 h through to 12 h before coming back full circle to 24 h – the zero hour line,
• measured in sidereal hours, minutes and seconds – a result of the method of measuring right ascensions by timing the passage of objects across the meridian, as the Earth rotates.
• ##### declination δ (dec)
• analogous to terrestrial latitude,
• provides the angular distance of an object perpendicular to the celestial equator,
• positive to the north, negative to the south – e.g. the north celestial pole has a declination of +90° – the origin is the celestial equator, which is the projection of the Earth’s equator onto the celestial sphere,
• measured in degrees, arc minutes and arc seconds.

## East is West, West is East

A map showing parts of the sky has a grid of celestial coordinates superimposed on it.  As we look at a location near to the north celestial pole, we can notice how lines of constant right ascension converge towards the north.

With North at the top (increasing declination upwards), East is to the left (increasing right ascension leftwards).  This is the opposite of terrestrial maps, where east would be to the right and longitude increases rightwards.

The fact that East and West are reversed on sky maps is a consequence of the fact that celestial maps are looking ‘outwards’  (away from the Earth) whereas terrestrial maps are looking ‘inwards’ (towards the Earth).

## Navigating with the Stars

Finding a direction using the stars can be much quicker and easier than using a compass, and a lot more fun.

To navigate the stars all we need is a clear night sky and to locate a star directly above the place we want to get to.  It will point exactly the right direction for us, from a quarter of the globe away.

Distances between stars and other deep-sky objects, as they appear to an Earth observer, can be a matter for confusion to the untrained eye.

We quantify them in terms of their angular separation, which are measured in degrees or subdivisions of degrees.

A constellation may extend over many tens of degrees over the sky.  But what does it mean in practice?

For example, the full Moon or the Sun each subtends an angle of about half a degree, or 30 arc minutes (30′), as seen from the Earth.

And by the way, this is the reason why total eclipses do occur

The smallest angular size discernible to the naked eye is about 1 arc minute (1′) and the best angular resolution obtained with Earth-bound optical telescopes is less than 1 arc second (1″).

A good “Rule of Thumb” to remember.  Mine anyway…

# Converting Angles from Degrees, Minutes and Seconds of Arc to Decimal Degrees

Subdivisions in right ascension are measured in minutes and seconds where

• 1 hour (1 h) = 60 minutes, and
• 1 minute (1 min) = 60 seconds (60 s).

## And Back Again!

An angular distance of 1 h on the equator corresponds to 15° (since 360°/24 h = 15 degrees per hour).

An angle of 0.395 radians can be converted into degrees as follows. Since π radians is equal to 180°, the angle in question is (0.395

One of the other internal angles is a right angle (90°), so since the internal angles of a triangle add up to 180°, the third angle is

180°− 90°− 22.6° = 67.4°.

Whilst the separation of objects on the sky are often described in terms of the angle between them, areas of the sky are often described in terms of square degrees, square arc minutes or square arc seconds.

## Never Mind The Celestial Coordinates

Finally, look up at the sky!

Forget anything I have just said about the Maths, about the map and those boring celestial coordinates for a moment.

Because sometimes you just want to enjoy looking at the stars, and not tie yourself in knots about celestial coordinates.

So, just look right up above your head.  What can you see?

A few constellations are always visible above the horizon.

Look for patterns…

### Ursa Major

The keystone of the Eath’s star-studded vault is the “Big Dipper” – also known as the Plough or the Saptarishi.

The familiar saucepan-shaped asterism is easy to recognise at a glance to the zenith of the night sky.  Its component stars are the seven brightest of the formal constellation Ursa Major.

One of the brightest stars close to the celestial pole, Polaris has been used for navigation since late antiquity.  The reason it is so important for natural navigation is that it is always visible and sits directly over the North Pole.

### Polaris, The North Star

Polaris, the current northern pole star on Earth, can be located by imagining a line from Merak (β) to Dubhe (α) at the right edge of the Big Dipper.  We then extend this straight line 6 times to find Polaris in the “Little Dipper” – the tip of the tail of constellation Ursa Minor.

As Polaris lies nearly in a direct line with the Earth’s rotational axis “above” the North Pole, i.e. the north celestial pole, it stands almost motionless with all the stars of the northern sky appearing to rotate around it.

Therefore, it makes an excellent fixed point from which to draw measurements for celestial navigation and astrometry.

The elevation of the star above the horizon gives the approximate latitude of the observer.

### The Big W

Look around a bit.  On the other side…  Can you spot the weirdly-shaped W?  That’s Cassiopeia.

So get to know those stars above your head really well.  You can use them as reference points.

##### Those stars will guide you to the rest of the sky.

You’ll soon get the hang of it.  Extending an imaginary line again x amount of times from those stars to discover the other constellations depending on the astronomical season of the year…