Declination Measurement
We need the declination of an object in the sky, in order that we could use the diurnal rotation of the Earth and consequent drift of a celestial object in the sky, to estimate its angular radius.
First, for definitions. Declination is One of the coordinates used to define position on the celestial sphere in the equatorial co-ordinate system. Declination is the equivalent of lattitude on the Earth. It is the angular distance, measured in degrees, north or south of the celestial equator. Celestial equator being the projection of Earth's equator on to the celestial sphere. Northerly declinations are positive and southerly ones negative.
Declination d is is the sum of the solar altitude a at noon and one's latitude f , with 90° subtracted from it, as can be deduced from the Figure below.
Here, Z is the zenith, P the north celestial pole, E the equator, and N,S are the north and south points.
We need to know our latitude - one of the exercises to be undertaken towards determining our Geography - needed for the submission of our timing data and determining the Astronomical Unit.
We will also need to measure the Solar altitude a at the local solar noon time of the day of our observation. The section on Earth Radius measurements discusses some of the concepts involved here - the definition of the local solar noon, the equipment that we need - a gnomon - to determine the Solar altitude at the local solar noon.
Once we are armed with our gnomon - fashioned out of a cricket stump, kho-kho pole or any other simple method - ensuring that we have a strictly perpendicular gnomon on a level ground - we are set to make the solar altitude measurements - which are more or less the same as the measurements that we needed to do for the Earth Radius determination.
We need to mark the shadow center at fixed, small intervals of the time - starting well before noon and going to an hour or two, after that. We need to measure the shadow lengths at each of these intervals and determine the shortest shadow. The Solar altitude is then given from a measurement of the the stick length and the shadow length -
using which we can obtain the declination of the Sun, on the day of our observations.