If you want to reach somewhere, what is the most important thing that you must know? You need to know about the specific coordinates of that place, that is, the address of that place. To analyze any object, to focus our probe on that object, we need to have some information about it’s position. Position of a place on Earth is defined by the two geographic coordinates, the latitude and the longitude. Well, these coordinates specify the address of objects on Earth. But what about the address of distant objects in deep space? This is where celestial coordinate systems come into picture.
On Earth, we use latitudes and longitudes to find cities, towns, mountains etc. In the similar fashion, we use celestial coordinates to locate objects in the sky. The celestial coordinates have wide applications in astronomy and astrophysics. So, the fifth article of the Basics of Astrophysics series is dedicated to the study of different celestial coordinate systems.
What is a Celestial Sphere ?
To understand the concept of celestial coordinates, we must first learn about the celestial sphere. Whenever we look upwards, all the heavenly bodies appear to lie on the inner surface of a large imaginary sphere, with us being at centre of that imaginary sphere. They appear to lie in the same way as the artificial stars lie on the dome of a planetarium. This large imaginary sphere is known as the celestial sphere.
Now draw a straight line in the direction of gravity through the observer and extend it. It will meet the celestial sphere at two points. The vertical above point is known as the Zenith and the vertical below one is known as the Nadir. The plane through the observer perpendicular to the line joint Zenith and Nadir cuts the sphere in a great circle. This great circle is known as celestial horizon.
Now draw a line though the observer parallel to the Earth’s rotational axis. It will meet the celestial sphere in two points. The intersection point above the horizon is called North Celestial point and the one below is known as South Celestial point. The great circle having these two points as its poles is called the celestial equator. The plane of Earth’s equator and that of celestial equator is the same. The great circle passing through the Zenith, Nadir and the celestial poles is called Meridian.
The great circle describing the apparent path traced by sun over the course of one year is known as ecliptic. The ecliptic intersects the equator at two points called the equinoctial points. The point though which the sun crosses the equator from north to south is called the First Point of Aries. The other point of intersection is known as the First point of Libra.
The Three Celestial Coordinate Systems:
With the basic information about the celestial sphere in hand, we are now in a position to understand the three basic celestial coordinate systems. So, let’s proceed, beginning with the Horizontal system as follows:
1. The Horizontal Coordinate System (Altitude and Azimuth)
Let Z denote the Zenith and A denote the position of any star. If we draw a draw circle ZAX, then the position of star can be defined on the celestial sphere either by the arc NX, the arc AX or by the arc ZA and the angle NZA. The arc AX measured along the great circle ZAX represents the angular distance of the star from horizon. This is known as its Altitude. The complimentary arc ZA is called the Zenith distance of the star.
The arc NX of the horizon between the North point and the foot of great circle through the star, or the angle NZA between the meridian and great circle is called the azimuth of star. It is measured either eastwards or westwards, from the north point. In this way, the positions of stars are defined in the Horizontal celestial coordinate system.
2. The Equatorial Coordinate System (Right Ascension and Declination)
The second system is what we call the Equatorial System. If we draw a great circle PAM through the star, then the position of star may be defined by either the arc PA and angle QPA or by the arc QM or angle QPA. The arc PA is called the North polar distance of the star and the complementary arc AM giving the angular distance of the star from the equator is called the Declination of the star.
Declination is measured positive or negative depending upon the position of the star in north or south of the equator. The great circle PAM is called the is called the star’s declination circle. The right ascension(R.A) is the arc of the equator YM between the first point of Aries and the foot of declination circle. Since the first point of Aries shares common diurnal (during the day) motion as the stars, both R.A and the declination of star remains unchanged during the diurnal motion. ( Refer to the celestial sphere shown above for the notations used)
3. The Ecliptic Coordinate System (Celestial Latitude and Longitude)
The third one in the list is the Ecliptic System.If a great circle is drawn through the pole of the ecliptic and the star, the angular distance of the star from the ecliptic measured along this great circle is called the celestial latitude of the star. The arc of the ecliptic intercepted between the First point of Aries and the foot of above great circle measures the celestial longitude of the star.
During its diurnal motion, the celestial latitude and longitude of a star remain unchanged in the same way as the the right ascension and declination. While the latitude is measured positive or negative depending upon whether the star lies to the north or south of the ecliptic, the longitude is measured eastwards from 0 to 360 degrees.
The concept of celestial coordinate system is one of the most important ones in astronomy and astrophysics. I know, this concept appears to be quite complex and difficult to grasp in one go. However, another reading will make it easier. I tried to explain it in the simplest language possible and I hope that this article was successful in giving you at least a basic flavor of these crucial notions practiced widely in the field of astronomy and astrophysics. So far, whatever we covered was astronomy rather than astrophysics. But this was essential. From the next article, we will starting digging deeper into the core concepts of astrophysics. If you have any questions, feel free to contact me.