For this problem, we are imagining a star (AY Sixteenus) that is located at RA = 18 hours and Declination = +32 degrees. We are asked here to determine the LST of this star on the meridian as viewed from Cambridge.
For this problem, it is important to consider what LST is really telling us. LST is the local sidereal time, which is defined by a far away star. Fortunately for us, AY Sixteenus is exactly that, a far off star. By definition, AY Sixteenus will always be present for an observer at the zenith at 18:00 LST, as long as they are in the northern hemisphere. While the solar time may very throughout the year, the LST will not, and the star will always be present at LST 18:00.
The second part of this problem deals with solar time, rather than strictly Local Sidereal Time, which makes things a bit more interesting. This asks on what date will the star be on the meridian at midnight. To solve this, we want to consider on what date will LST 18:00 be equal to midnight.
Let's begin with the knowledge that LST is equal to 0:00 at noon on March 20th. Furthermore, LST will be equal to ~12:00 at midnight on March 20th. Since we are interested in when AY Sixteenus will be present overhead at midnight, we need to gain ~6 hours in LST for this to occur.
Since LST gains 4 minutes each solar day, we can determine how many days it will take to gain 6 hours:
\[ 6\,hours * \frac{60\,min}{1\,hour}* \frac{1\,day}{4\,min} = 90\,days\]
Knowing that AY Sixteenus will be present overhead 90 days following the Vernal Equinox, we can simply count 90 days past March 20th and discover that this will occur on June 18th.
Collaborators on this problem included Willie Pirc and Johnathan Budd.
Good!
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