**INTRODUCTION TO THE STARRY SPHERE**

The twinkling stars in the night sky lie on a giant sphere that even encloses us. This is how our brain perceives when we look up the night sky as if we are the center and under a dome-like structure. In astronomy, this will help us to define the directions of stars, which is convenient when we think of it as points on a sphere. This sphere is called the *celestial sphere*, whose radius is entirely arbitrary. The celestial sphere is the one that makes observations in astronomy easier for us. In this article, we will be looking into this *starry sphere *and how the objects in the sky are observed. Get aboard for the joy ride.

**GREAT CIRCLES**

Great circles are part of any sphere, including earth. A great circle is formed when an imaginary plane intersects the sphere and passes through the center. There are also small circles, which are formed by a plane but without passing through the center. You can think of these circles as slicing an orange with a knife. Not really slicing, but just imagine what would happen when you so so. It would actually trace a circle around the circle. This circle, when having the diameter of the sphere, will become the great circle and when not, will become the small circle. In other words, a great circle is the one that divides the sphere into two equal parts.

The celestial sphere can be visualized when star trails are traced in the sky using cameras. It is a practical tool of immense importance in astronomy and navigation, allowing us to plot positions of objects in the sky when their distances are unknown, where all the objects in the sky can be thought of as projected upon the inside surface of the sphere. For example, the rising and setting points of the sun, moon, planets, etc, are determined by their positions on this imaginary sphere.

**THE COORDINATE SYSTEM OF THE COSMOS**

Remember we are in the center of the celestial sphere. What comes to our mind when we think about the geometrical features of the earth? We tend to think about the equator, latitude, longitude, and things like that. Similarly, there are coordinate properties of the celestial sphere which makes it easier to plot objects on the sky. The main features of reference are-

- The north celestial pole and south celestial pole: This is the same as our north and south poles, but extended into space.

- Horizon: The horizon is our viewing plane and it changes with our position on earth.

- The celestial Equator: It is like a stretched out earth’s equator, infinitely into space.

- Zenith: As the name suggests, this is the point that is directly over our heads. ‘

- Meridian: Just like on earth, this is the line that extends from the north point on the horizon upwards through the zenith and then down to the south point.

- The ecliptic: It is the plane of the earth’s orbit around the sun.

Any star on the sky can be located using the celestial coordinates *Right Ascension(RA) *and* Declination(DEC).* These measures make up the * equatorial coordinate system*. This can be thought of as numbers on the x and y-axis, which when intersected at a point will give us the position of the point. The intersection of the RA and DEC gives us the position of an object in the sky. Stars and galaxies have almost fixed positions in Right Ascension and Declination. On the other hand, the Sun and planets, move among the stars, and hence their coordinates change throughout the year.

**Right Ascension: **RA is identical to the longitude of Earth. It is the angular distance of an object that is measured eastwards from the vernal equinox, along the celestial equator. The vernal equinox point is one of the two where theecliptic intersects the celestial equator. In simple terms, this is the spot that the Sun arrives on the first day of spring. It is usually measured insidereal hours, minutes, and seconds instead of degrees, with 24 hours being a full circle, i.e, 24 hours = 360 degrees.

**Declination: **DEC is identical to latitude and is the angular distance of an object North or South of the celestial equator. It is measured in degrees from -90° to +90°, where the celestial equator has a measure of 0 degrees declination. Polaris, the North Star, is close to Declination = +90 degrees. If you were standing on the Earth’s the North Pole, we would see it directly overhead.

Just to get an idea, let’s have a look at the below picture. This a slice of the sky, where the objects are labeled with the RA on top and the DEC on the left.

*The alt-azimuth coordinate system:*

There is another coordinate system to map objects in the sky, which is solely based on the observer’s position on earth, unlike the other system which is based on fixed features of the celestial sphere. Let us have a brief look at it. Here, an object’s position is measured in terms of its *altitude *and *azimuth. *Also remember, any point in the sky has one and only one altitude and azimuth. Small telescopes used by amateur astronomers tend to have altazimuth mounts since they are comparatively cheap.

**Altitude:** Altitude is the angular distance above the horizon; where straight up or overhead is 90o. The altitude of an object is important from a practical point of view since any object which has an altitude less than zero is below the horizon, and hence inaccessible. Also, the fainter the object is, it has traveled a larger airmass and more light is scattered or absorbed by the atmosphere

**Azimuth: **Azimuth is also an angular distance, measured clockwise from north (so east is measured as 90o). It is the horizontal direction of an object in the sky, from the observer.

**SOME SIMPLE MATHEMATICS**

Now let’s do some maths, especially spherical trigonometry. Trigonometry, as we know, deals with triangles on a plane. But what happens when we draw triangles on a sphere? This is where *spherical trigonometry *makes its way.

On a plane, two points can be represented by (x1, y1) and (x2, y2), As we have seen previously, on the celestial sphere, a point (position of an object) can be represented with its RA and DEC. So let’s take two points on the sphere and measure the distance between them. RA is also denoted by α and DEC is also denoted by δ.

Let the two points be A1(α1, δ1) and A2(α2, δ2). The angular distance(ᵞ) between the points is calculated by the *Law of Cosines, *according to which,

cos(ᵞ) = cos(90°-δ1)cos(90°-δ2) + sin(90°-δ1)sin(90°-δ2)cos(α1-α2)

Try to do a small activity to apply this formula. The question is “What is the angular separation between these two locations, in degrees?”

RA Dec

——————————-

A 2 hours 0 degrees

B 5 hours 0 degrees

This will only take a few seconds. Do try it out and let me know in the comments.

**CONCLUSION**

The celestial sphere is an interesting way to imagine our place in the vast universe and helps us to understand the cosmos in a better way through reference positions. Let’s wrap up with this and have a great time under the fascinating sky.

References: NASA, Sky & Telescope, Wikipedia