Blog #3 - Local Sidereal Time

Local Sidereal Time 

The Local Sidereal Time (LST) is the right ascension that is at the meridian right now. LST = 0:00 is at noon on the Vernal Equinox (the time when the Sun is on the meridian is March 20th, 2017).

a) What is the LST at midnight after the Vernal Equinox?

In class we solved that there is a 1° change in earth's meridian every day due to its rotation around the sun and its own rotation period. Thus there is roughly a 4 minute difference between Universal Time (UT) and LST. Considering midnight is half a day past noon and the LST is 0:00 at noon on the Vernal Equinox, we know that midnight must actually occur at 12:02. the extra two minutes occur from half of the 4 minute LST difference.

b) What is the LST 24 hours later (after midnight of part a)?

Following the same logic as part 'a', 24 hours later would produce the expected 4 minute difference between UT and LST giving us an LST of 12:06 at midnight the next day.

c) What is the LST right now (to the nearest hour)?

At the time the worksheet was completed, the time was 3 o'clock on January 30th. This produces a 48 difference from the metric of March 20th for the Vernal Equinox. \(48 days = 192 minutes = 3 hours 12 minutes\) and we must move back in time from the future Vernal Equinox. Thus we move back 3 hours and 12 minutes to get a time of roughly 20:48. However this would be the LST for noon on January 30th. We want 3 o'clock and thus add 3 hours (and technically 30 seconds to correct for the 4 minute/day difference). This brings the LST to 23:48:30, which rounds up to 0:00 at the nearest hour.

d) What will the LST be tonight at midnight (to the nearest hour)?

Following the same process as part 'c' we know that at 3pm on January 30th the LST was 23:48:30 which rounded up to 0:00. Moving forward 9 hours to get to midnight and adjusting for the 1.5 minutes to correct for LST we get 8:50 which rounded to the nearest hour gives us 9:00.

e) What LST will it be at the Sunset on your birthday?

My birthday is November 18th which is 243 days after the Vernal Equinox on March 20th. 243 days converts to 16 hours and 12 minutes of LST variation from the UT given the 4 min/day rate found earlier. Moving up from the 0:00 noon time on March 20th, noon on November 18th would occur at 16:12 instead. If we assume the sun sets around 6pm we add 6 more hours to this time and the appropriate 1 minute for LST adjustment and end up with 22:13 for sunset on my birthday.