Local Sidereal Time

Local Sidereal Time was explained in this problem as the right ascension at the local meridian at that moment.  At noon on the vernal equinox, when the Earth is pointing directly at the sun, the right ascension is 0.00 hours.  Every month, the right ascension increases by two hours, a result of the difference between a 24-hour solar day and a slightly longer stellar day.  We then drew the following picture to help us understand right ascension.

The first part of the problem asked what the LST would be at midnight on the vernal equinox.  My initial thought was that it would be 12:00, but then I realized that I had failed to take into account the four-minute difference between a solar day and a stellar day.  Since midnight is half a day after noon, it would be twelve hours and 2 minutes after 0:00, making it 12:02.  

The second part asked what the LST would be 24 hours after the time from part (a).  Following the same thought pattern as in the first part of the problem, I found that it would be 24 hours and the additional four minutes after 12:02 hours.  The LST would be 12:06. 

In the third part of the problem, we were asked to find the LST at that moment.  When we solved the problem, it was around 3:00 pm on February 5.  That date is about a month and a half before the vernal equinox, meaning The RA is 21 hours after 0:00.  We figured that, if noon on that date is 21:00, then 3 hours after noon is 0:00.  The next part of the problem asked us to find the LST at midnight on that same date.  To find this, I just added nine because midnight is nine hours after 3:00, making the LST 9:00.  

The final problem asked me to find the LST at sunset on my birthday.  My birthday is in the beginning of January, and because I've always lived in the northern hemisphere where days are shorter in the winter, sunset is usually around 6.  The beginning of January is about two and a half months before the vernal equinox, meaning the LST at noon is about 19 hours after 0:00.  Six hours after 19:00 would be 25:00, but since LST resets at 0:00, the LST at sunset on my birthday is 1:00.