**Conversion between Celestial Co-ordinates and Horizontal Co-ordinates**

To reach this point has been the goal of the whole course so far. We now show how to calculate the position of any celestial object in the night sky. What we are really after is to be able to calculate the solar time an object is at a certain altitude and azimuth. Of course, if we know the right ascension and

**hour angle**of an object, we can work out the local sideral time, and from that the solar time and UT. Therefore, we will start by calculating the altitude and hour angle of a celestial object with right ascension

**α**and declination

**δ**.

We said earlier that the difficulty is knowing which spherical triangle to draw. In the figure below I have solved that problem for you. See if you can work out what the angles and arc lengths labelled with question marks should be, then hover your mouse over the image to see if you're right.