AstorPearls - Astronomy Software
 The Equatorial Coordinate System

Coordinate Systems in General

To get a feeling of this important concept, let’s be a little abstract for the moment and define a coordinate system in general. A Coordinate System is a geometric construct that enables us to locate Objects in a Space. A space could be anything: a long rope, a sheet of paper, the space of a living room, or a surface of a sphere. The last example is more relevant to our discussions, but it is still enlightening to talk about the other examples. Before we do, let’s say that object location will be represented simply by a bunch of numbers.

Origin and Dimension

A long rope is an example of what is called a one dimension space. An object in this space could be just a knot somewhere on the rope. It has a single dimension because all what we need to locate the knot is a single number, how far it is from a known location called the origin. The origin could be the point where the rope is attached to a wall or even the point where you hold it with your hand! We have complete freedom to pick the origin. Once we do, all locations can be determined relative to it. However, for some coordinate systems, a good choice of the origin makes our life easier when describing object locations.

Figure 1
                                                Figure 1

How about a sheet of paper? I hope we can already see the difference. If our object is a small point on the paper, a single number is not enough to locate this point. Let’s pick the point on the top-left corner of the sheet to be our origin. Obviously we need to know two numbers to locate the point: how far from the left and how far from the top. A sheet of paper is a two dimensional space - we need two numbers (or two coordinates).

Figure 2
                                                Figure 2

The space of your living room is an example of three dimensional space. You need the distance from three walls to fully define the location of a point in this space - think about it carefully. Are there spaces with more dimensions? Indeed! But we won’t be able to visualize or imagine these higher dimension spaces; our brain is a 3D creature!

Figure 3
                                                Figure 3

Great Circles of a Sphere

Since we’ll be talking about circles on a spherical surface all the time, we need to understand the concept of a great circle. It is simply a circle with its center coincides with the center of the sphere and its radius equal to the radius of the sphere. Figure 4 shows an example of a great circle (red) and another circle that is on the sphere still, but not a great circle (blue).

Figure 4
                                                Figure 4

Important Examples of Great Circles

The celestial sphere contains an important set of great circles that we need to fully understand:

  • Your Horizon: A great circle that contains your North-South and East-West directions. It is the circle result when your horizon extends in all direction and intersects the celestial sphere. Think of cutting an orange two halves with a large knife!
  • The Celestial Equator: is the great circle result from extending Earth equator until it cuts the celestial sphere.
  • Your Meridian: is the great circle passing through NCP and your Zenith.
  • A star’s vertical circle: A great circle passing through the star and your zenith.
  • A star’s hour circle: a great circles passing through the star, NCP and SCP. It is perpendicular to the celestial equator. It also rotates with the stars due to the earth rotation around its axis.

The Space of the Celestial Sphere

The surface of the celestial sphere is two dimensional. It is like a sheet of paper, but it is a curved space not a flat one. So we need two numbers to locate any point on this surface. This point could represent a star, planet, or any other object. In the sheet of paper example mentioned earlier, we used to edges of the paper and defined the location of a point relative to these edges. In a similar fashion, we need two great circles on the sphere. Instead of distance, angle will be the natural choice for this system. Figure 5 shows two great circles, and two angles representing the coordinates of a star on this spherical surface.

Figure 5
                                                Figure 5

Equatorial Coordinate System

Equatorial Coordinate System is no difference from the example of figure 5. What makes it special is the choice of the two reference circles. As the name indicates, one of these circles is the celestial equator. The other circle could be any great circle perpendicular to the celestial equator. The choice was in favor for a circle that passes through the so called vernal equinox - it is the point at which the Sun crosses the equator from south to north (means spring) on its apparent yearly journey around earth.

Now describing the location of a star is simple:

  • Measured, in the celestial equator, the angle between the hour circle of the vernal equinox and the hour circle of the star is the first coordinate called the Right Ascension (&alpha). It is measured in hours, minutes, and seconds from the vernal equinox going east. Since Earth performs a complete rotation once every day, 24hrs represent 360 degrees. It is more convenient to use hours/minutes/seconds here.
  • Measured in the star’s hour circle, the angle of declination of the star from the equator called - naturally - the Declination (δ). It is measures in angles from 0 to 90 degrees north and from 0 to -90 degrees south. Figure 6 shows a star in the northern hemisphere with its right ascension and declination angles.

Figure 6
                                                Figure 6

Now we hope you are not scared anymore when hearing terms like Right Ascension and Declination!!!