## Celestial longitudes and latitudes:

How to locate an object in the night sky? An object in the surface of spherical object like earth can be located by specifying latitudes and longitudes. Similarly for locating an object in the celestial sphere, we make use of celestial latitudes and celestial longitudes. We saw that measurements have to be made with respect to a standard. So to determine the position of celestial objects, a reference latitude and a reference longitude have to be chosen just like their geographic counterparts (i.e., the equator and the longitude through Greenwich). Now, these standards must be fixed with respect to the earth. So the possible choices for celestial latitudes are
- the ecliptic
- the celestial equator.

But even the celestial equator will change when the axis of earth's rotation changes. So we take the ecliptic as the reference.

. In the above figure, the point 'r' is the reference point in the ecliptic, corresponding to 0o longitude. The latitude of the point 'x' in the surface of the sphere is given by the angular measure of the arc 'xy' and the longitude is given by the angular measure of the arc 'ry'. Note that any point along the great circle passing through the points 'y', 'x' and 'k' have the same longitude.

Now we've to fix the starting point of celestial longitude. For fixing the reference for celestial longitude any arbitrary point can be chosen. Two most popular choices are the beginning point of the Mesha rashi and the Vernal equinox. The systems of measurement resulting from these two choices are the Nirayana and Sayana systems. Nirayana comes from Nir(without) and ayana(motion) and Sayana means 'with motion'. Due to precession of equinoxes, the position of vernal equinox changes. Hence in the Sayana system, the starting point of celestial longitude changes. Hence the name Sayana. Now why did they choose the Vernal equinox in Sayana system when it is not a fixed point? This maybe because the Vernal equinox corresponds to a point where the celestial equator intersects the ecliptic. Similarly Nirayana is so named because the beginning point of Mesha rashi is a fixed point in the ecliptic.

The longitudes measured in the Nirayana and Sayana systems are called Nirayana longitude and Sayana longitude respectively. The Sayana longitude leads the Nirayana longitude by a factor of Ayanamasa.

Sayana longitude = Nirayana longitude + Ayanamasa

Now lets take a look at the notation of the longitudes. It is specified in terms of rasis, degrees and minutes. A value of 8s 16o 04' will mean that the Sun has moved over 8 rasis and is in the 9th rasi at a displacement of 16o 04'.

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