THE CELESTIAL SPHERE

The stars are at a very large distance from us. So the relative movement between them is of no consequence to day-to-day observations. We therefore imagine the stars to remain fixed on a sphere of very large radius with the earth at its centre. We call this sphere the celestial sphere.

At any point of time we can only see the upper half of the celestial sphere. The point on this dome right above our head is known as zenith. The lower boundary of this dome is the horizon. As the surface is 2-dimensional, to specify the position of any star on this dome we need two coordinates. We usually use a spherical polar coordinate system and ignore ‘r’. One system is the alt-azimuth system. The shortest line (great circle) is drawn from the zenith joining the star right down to the horizon. The angle the star makes above the horizon measured along this line is known as altitude. The position of this line with respect to some fixed reference is known as azimuth. Usually the meridian line (the line joining the zenith and the pole star) is taken as the reference and angle of meridian is measured westward from it.

Due to rotation of the earth, the entire celestial sphere appears to rotate around the earth, once in about 24 hours. There are two points on the sphere, which do not move – they are the celestial north and south poles. If we extend the axis of the earth to meet the celestial sphere, it would cut the latter at these two points. Very close to the celestial North Pole (for all practical purposes, right at the celestial north pole) lies the famous Pole star or North Star (systematic name: α-Ursae Minoris.). This star remains fixed in its position. At any latitude λ in the northern hemisphere, the altitude of the pole star is λ above the horizon. All the other stars seem to rotate around the North Star in circles in the anticlockwise sense (think why?). The further the (angular) distance of the star from the pole star, the greater its radius of the traced circle.

When the angular distance increases to 90º, the traced circle becomes a great circle – the celestial equator. If we extend the plane containing the equator in space, the circle formed by its intersection with the celestial sphere is known as the celestial equator. As the angular distance exceeds 90º, the circles traced become smaller and smaller.

At any latitude in the Northern Hemisphere there will some stars that are always above the horizon (in fact all stars less than λ from the pole). If we draw a line from the North Star through where we are standing to intersect the celestial sphere in the south at λ below the horizon, we will get the celestial South Pole. There will be some stars around the South Pole that will always be below the horizon. The rotation in 24 hrs is 360º. Simple calculation shows that in 1 hr it is 15º and it is 1º in 4 minutes.

The sun moves along with the celestial sphere but together with that it shifts every day a bit to the east with respect to the celestial sphere. This is due to the westward revolution of the earth. As the period is 365 days, the sun moves 360º/365 = 1º (approx) in one day. Now, the time we follow is based in the rising and setting of the sun (solar time). Any star moves 1º to the west with respect to the sun in one day and hence rises 4 minutes earlier. After 1 month it rises 2 hours earlier. So we see different stars during different seasons. The path taken by the sun the celestial sphere is known as the line of ecliptic to which we will come later.

Contributed by Archisman Ghosh