The Celestial Sphere

Creating a map of the Heavens above!

Representational Image: An Armillary Sphere — The different rings show the positions and markings of various night sky objects. These rings include the Ecliptic (that includes the markings of the Zodiac) and the Celestial Equator among others. (“Armillery Sphere 1”, by Stew Dean, Licensed under CC BY-NC 2.0)

As our curiosity made us make different theories about the Universe, we needed physical markings and models to test these theories. Additions and changes to these models formed the basis of the evolution of our knowledge. With this, today we have an internationally accepted system of markings and positions to help us identify and name various objects in the Night Sky. The basis of this system is the Celestial Sphere.

Centralizing Coordinates

As the name suggests in itself, the Celestial Sphere refers to an extension of the Earth as a sphere into the Night Sky. All the terrestrial markings, including the Equator, latitudes, longitudes, and the Poles, immediately extend to the Night Sky to form the Celestial Equatorial Coordinate System:

Celestial Equator — The extension of the Earth’s Equator into the Universe is what is known as the Celestial Equator.

Celestial Poles — The extensions of the Geographic North and South Poles of the Earth onto the Celestial Sphere are known as the North and South Celestial Poles respectively.

Declination and Right Ascension— The extensions of the Earth’s latitudes are known as Declination Circles, while those of the Earth’s longitudes are known as Right Ascension Circles. In this way, the general coordinates of any object in the Night Sky are represented by a combination of these two measures — Right Ascension (commonly called RA), and Declination (commonly called DEC). This forms the Equatorial Coordinate System in Astronomy. The positions (coordinates) of stars are fixed on a particular RA and Declination and vary very little with time¹. (We’ll get back in a minute on how to use this system.)

Figure 1: The North Celestial Pole depicted directly above the Geographical North Pole — The bright spot towards the slight left of the image is the Sun, the concentric circles depict the Declination Circles, while the apparent straight lines appearing to radiate out from the center depict the Right Ascensions Circles. Note that in this image, the RA circles are appearing as straight lines due to the large field of view of 176°. Similarly, the South Celestial Pole is such that it appears at the top at the South Celestial Pole. Shown in red is the Ecliptic.

Ecliptic — The locus of the path traced by the Sun around the Earth around the year, traced on the Celestial Sphere is called the Ecliptic (shown in red in the image above). Alternatively, it can be said that the Sun completes one round about the Ecliptic in about 365.25 days (1 solar year). There are four main points of interest on the Ecliptic. The Northernmost point of the Ecliptic is known as the Summer Solstice, while the Southernmost is known as the Winter Solstice. The two points where the Ecliptic intersects with the Equatorial Plane are known as the Equinox (Vernal and Autumnal). They are named so as they correspond to the position of the Sun on these days. For example, on 21st June, the Sun will be at the Summer Solstice position, its highest position in the sky in the Northern Hemisphere, while the opposite holds for the Southern. The situation reverses on the day of the Winter Solstice when the Sun reaches its lowest point in the Northern Hemisphere, and correspondingly, its highest position in the Southern skies.

Figure 2: Ecliptic and the Celestial Equator. ♈︎(𝛾) represents the first point of Aries. The position of the Sun is below the Celestial Equator implying that it is higher in the sky for Southern latitudes than for Northern latitudes (Joshua Cesa, CC BY 3.0, via Wikimedia Commons, converted to JPG).

Now we get back to RA-Dec coordinate system. Declination (denoted by
δ) is taken to be 0° at the Celestial Equator and becomes positive Northwards to culminate at +90° at the North Pole. In the Southern Hemisphere, the declination is taken to be negative with the South Pole at –90°. Right Ascension (denoted by α) is taken to be 00ʰ at the Vernal Equinox (also called the ‘First Point of Aries’², denoted by ♈︎) and increases Eastward in the same unit of ‘hours’ (depicted as a subscripted ‘h’). Hence the Summer Solstice is located on the 06ʰ circle, Autumnal Equinox (also called the ‘First Point of Libra’², denoted by ♎︎) on the 12ʰ, and the Winter Solstice on the 18ʰ circle. The 00ʰ circle coincides with the 24ʰ circle, denoting the completion of the circle. For example, the coordinates of Sirius are about 6ʰ 45ᵐ RA and –16° 45'.

Figure 3: Measuring the coordinates of any point located on the Celestial Sphere using Right Ascension and Declination (from Wikimedia Commons).

You might wonder why the unit of Right Ascension is ‘hours’ and ‘minutes’. The reason is that the Equatorial System is defined such that the rate of change of the Right Ascension is 1ʰ (as a unit of RA, 15°=1ʰ) per hour (as a unit of time). So for example, if at noon, the 9hr circle is at the top at a particular place, it would be the 10hr circle at 1 PM there. Well, if you think about it, this seems to be more or less obvious since roughly the same stars are visible each night at the same spot for a couple of days¹, implying that they appear to move 360° in about 24 hours. And since the positions of stars are fixed on the Celestial Sphere, this also implies that the RA circles cover 360° in about 24 hours. This figure (23 hours 56 minutes 4 seconds, to be exact) is so accurate that it is used for Sidereal Timekeeping, and is the basis of a large number of calendars in the world.

Somewhere in astronomical literature, you might see the usage of the terms ‘Ecliptic Coordinates’ or ‘Galactic Coordinates’ or ‘Supergalactic Coordinates’. This just means that the 0° plane for measuring horizontal angle has been taken along the Ecliptic (inclined at ≈23.5° with the Celestial Equator), Galactic Plane (inclined at ≈63°), and the Supergalactic Plane respectively (inclined at 84.5° with the plane of the Milkyway).

Figure 4: The Equatorial (RA-Dec) Coordinate System at Port-de-Bouc, France. Note that this time, the North Celestial Pole is not right at the top and is inclined at some non-right angle to the Horizon. This is because the Equatorial system is not observer-based and is fixed to the Universe. So how it appears in the Night Sky keeps on changing from place to place. The degree measure of the NCP (North Celestial Pole) or the SCP (South Celestial Pole) gives us the Latitude of the place. As previously discussed, the RA circles too move from East to West during the Night Sky. This non-observer-oriented thingy prompts us to introduce another coordinate system fixed to the Observer — the Alt-Az Coordinate System.

Figure 5: Various astronomical coordinate grids — Equatorial Grid (depicted in Blue), Ecliptic Grid (in Pink), Galactic Grid (Green), and Supergalactic Grid (in Yellow).

Decentralizing Coordinates

A big disadvantage of the Equatorial System is that this system is not Observer-based, so it is quite impractical and difficult to use for a normal night sky enthusiast. To overcome this problem, we have devised another Coordinate System, known as the Altitude-Azimuthal Coordinate System (or Horizontal Coordinate System), which is completely observer-based and varies from one place to another.

Figure 6: The Alt-Az Coordinate System at Port-de-Bouc, France. Notice that in this image, the green circles (representing the Altitude and Azimuthal lines) are in contrast to Figure 4 showing the RA-Dec system at this place. The Altitude lines here, meet at the exact top and the concentric circles depicting growing Altitude too tend to coalesce there. Hence, this coordinate system is Observer-based, making it more convenient for amateur night sky observers.

This coordinate system consists of a hemisphere at the center of which stands the observer. A few elements used in this particular system are:

Altitude — The ‘height’ of an object in the night sky, measured as an angle formed by the line of sight of the observer when seeing the object with the 0° plane (Horizon).

Azimuthal — The horizontal angle of a point on the Celestial Sphere measured from the North in a clockwise manner. Hence, North is taken to be at 0°, East at 90°, South at 180°, and West at 270°.

Horizon — The lowest visible point to the observer, usually located right in front of the observer’s eyes. It may be characterized into two types — True Horizon (the actual theoretical line located directly in front of the Observer’s eyes) and Visible Horizon (the line depicting the minimum height in the sky visible to the observer unobscured by trees or buildings). The True Horizon is taken to be at 0° altitude.

Zenith — The topmost point in the Night Sky, i.e. the point directly above the Observer — present at exactly 90° altitude.

Nadir — The point directly opposite the Nadir on the Celestial Sphere. This means that Nadir is the Zenith for an observer located directly opposite our present observer on the Earth.

Meridian — The imaginary line passing through the Zenith, Nadir, and the 0° and 180° Azimuthal points, is known as the Meridian.

Figure 7: The Observer-based Alt-Az Coordinate System (CheCheDaWaff, CC BY-SA 4.0, via Wikimedia Commons)

Hour Angle — The azimuthal angle between any night sky object and the meridian is known as the Hour Angle.

Local Sidereal Time — The time elapsed since the point of Vernal Equinox (0hr RA) last passed the meridian is called the Local Sidereal Time. Equivalently, it can also be defined as the hour angle of the point of Vernal Equinox.

Figure 8: Polar points of different coordinate systems — Zenith (in Blue), North Ecliptic Pole (NEP, in Brown), North Celestial Pole (NCP, in Red), North Galactic Pole (NGP, in Green), North Supergalactic Pole (NSGP, in Yellow).

The Alt-Az Coordinate System forms the most convenient coordinate system for land-based observational astronomy and casual night sky observers, as it gives an accurate location onto where one can find a particular point from his specific location in terms of its height above the horizon and its angle.

Some Other Elements

The choice of the Coordinate system forms the most basic pre-requisite for astronomers and skywatchers. But a few other elements also need to be taken care of.

Figure 9: ¹This 4-minute difference between sidereal and solar day is responsible for the apparent movement of the stars along the Ecliptic which is what causes the change in Zodiacs. (Tauʻolunga, CC BY-SA 3.0, via Wikimedia Commons)

1. You might have observed a ¹ appearing earlier on in the text when I mentioned that the position of the stars remains fixed each night “for a couple of days”. Well, then what happens over a couple of weeks? The stars change their positions. And why is that? It's because of the 4-minute difference between the duration of a Sidereal Day and a Solar Day that causes this slow relative rotation of the Equatorial Coordinate System with respect to the day and night period on Earth. This gap between the ‘two types of days’ is almost compensated over a year after which, the same stars appear to be in the same spot as they were the last year…
2. …almost. Even the annual compensation fails to account for the Precessional changes of the Earth that change the orientation of the Equatorial grid over time, albeit very slowly. Yet this change is enough to cause deflections of about 1.38° per century. Hence, it becomes crucial for astronomers to ‘reposition’ the EQ system for consistency from time to time (about every 50 years or so). This repositioned system is then used as a reference for the next few years and is known as ‘Epoch’. The current epoch J2000 is fixed at the coordinates of the night sky objects as of 1 January 2000 at 12 Noon UTC of the Julian Calendar (that gives its ‘J’ and ‘2000’).
3. For the ease of nomenclature and classification of stars, the whole celestial sphere is divided into 88 fixed regions known as the Constellations. These Constellations, as an official astronomy term, are not groups of stars, but rather regions on the Celestial Sphere, named after their constituent groups of stars (the erstwhile ‘constellations’).
4. An important point to note is that the positions of all the heavenly bodies are not fixed on the Celestial Sphere. These include the Moon, the planets, and the Sun. These ‘wanderers’ (Planeta) are wayyyy closer than any other celestial body, so, are in constant motion with respect to the background stars. Hence, they cannot be designated with any particular coordinates on the Celestial Sphere.
5. Talking about the constellations, due to the effects of sidereal-vs-solar-day, the constellations along the Ecliptic appear to move eastwards with time and the Sun appears to ‘enter into a new constellation every month. This constellation is ‘obscured’ by the Sun and hence, the Sun is said to be in that particular ‘Zodiac’ during that time interval!
6. But even the Zodiacs have not been untouched by the phenomenon of Precession. Due to precession, our Zodiacs have changed quite a lot since they were first used. Vernal Equinox (though called the First Point of Aries) doesn’t happen in Aries anymore but in Pisces. Neither does Autumnal in Libra (it happens in Virgo). In fact, the dates of the zodiacs (the period when the Sun lies in the region spanned by that Constellation) themselves have shifted to about a month after where they were when they were set up, along with the descent of Scorpio (that now spans only about a week) and the ascent of a new constellation on the Ecliptic, Ophiuchus.

Figure 10: Constellation Names and boundaries visible from Port-de-Bouc, France.

So this was an overview of a few important concepts one needs to keep in mind before heading into astronomy. In the next couple of articles, we’ll continue from where we left off in Celestial Mechanics in the last article, and will also look at some concepts related specifically to observational astronomy and optical devices. So, pretty exciting stuff coming soon!

All graphics were made using Stellarium, an open-source software.