AY Sixteenus

In this problem, we were told that there was a star, AY Sixteenus, located at a R.A. of 18 hours and a declination of +32$^{\circ}$.  We were asked to draw a graph of elevation vs. time of the star as seen from the meridian at the Mt. Hopkins observatory in Arizona.

The first step in solving this problem was to figure out if, and if so how, the elevation would change throughout the year.  Intuition told us* it would change because as we observe throughout the night, the star appears to rise and fall in the sky.  Further thought, however, reminded us that we were only graphing the view of the star as seen through the meridian.  When the star passes over the meridian every night, it's at the same elevation, which makes sense because a star's declination remains constant throughout the year.

The next obstacle was trying to find a constant value for the the star's elevation.  Originally, we thought it should be equal to the star's declination.  But declination is the angle from the equator to the star and elevation is the angle of the star above the observatory's horizon.  The Mt. Hopkins observatory is approximately 32$^{\circ}$ above the equator.  Using the information that the star is infinitely far away, we determined that the angle of view from Mt. Hopkins was basically the same as that from the equator.

When viewed from the ground through the meridian, the star is at zenith, meaning it's directly overhead.  That led us to the conclusion that AY Sixteenus, when viewed through the meridian, is at a constant elevation of 90$^{\circ}$.     

*By us, I mean our group made up of Dennis Lee, Delfina Martinez-Pandiani, and me.