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 March 20th, for 2013 and 2014).
a) What is the LST at midnight on the Vernal Equinox?
b) What is the LST 24 hours later (after midnight in part ’a’)?
c) What is the LST right now (to the nearest hour)?
d) What will the LST be tonight at midnight (to the nearest hour)?
e) What LST will it be at Sunset on your birthday?
First let's discuss the difference between LST and normal time. LST takes into account the revolution of the Earth around the sun, and has only 23h 56 min per day. Thus, the current LST is the current time, plus 4 minutes per solar day since the vernal equinox. I will use military time to avoid having to specify AM/PM.
a) What is the LST at midnight on the Vernal Equinox?
This is fairly easy. Midnight on the vernal equinox is exactly 12 hours of solar time after the noon of the equinox. Thus:
\[LST=\text{solar time} - 12h + (\text{Days since Vernal equinox} \times 4\text{ minutes/day})\]
\[LST=\text{24:00} -12h + (0.5days \times 4\text{ minutes/day})=\boxed{12:02}\]
b) What is the LST 24 hours later (after midnight in part 'a’)?
This is also straightforward. Intuitively, another day has passed, so LST is ahead another 4 minutes.
\[LST=\text{solar time} - 12h + (\text{Days since Vernal equinox} \times 4\text{ minutes/day})\]
a) What is the LST at midnight on the Vernal Equinox?
b) What is the LST 24 hours later (after midnight in part ’a’)?
c) What is the LST right now (to the nearest hour)?
d) What will the LST be tonight at midnight (to the nearest hour)?
e) What LST will it be at Sunset on your birthday?
First let's discuss the difference between LST and normal time. LST takes into account the revolution of the Earth around the sun, and has only 23h 56 min per day. Thus, the current LST is the current time, plus 4 minutes per solar day since the vernal equinox. I will use military time to avoid having to specify AM/PM.
a) What is the LST at midnight on the Vernal Equinox?
This is fairly easy. Midnight on the vernal equinox is exactly 12 hours of solar time after the noon of the equinox. Thus:
\[LST=\text{solar time} - 12h + (\text{Days since Vernal equinox} \times 4\text{ minutes/day})\]
\[LST=\text{24:00} -12h + (0.5days \times 4\text{ minutes/day})=\boxed{12:02}\]
b) What is the LST 24 hours later (after midnight in part 'a’)?
This is also straightforward. Intuitively, another day has passed, so LST is ahead another 4 minutes.
\[LST=\text{solar time} - 12h + (\text{Days since Vernal equinox} \times 4\text{ minutes/day})\]
\[LST=\text{24:00} -12h +(1.5days \times 4\text{ minutes/day})=\boxed{12:06}\]
c) What is the LST right now (to the nearest hour)?
Here is where it gets a bit more complicated because we need to work to find the number of days that have transpired since the equinox. It's not overly difficult, just time consuming. Conveniently, the current time is 12:00 on February 9th 2015 in Cambridge, MA, so we don't need to account for fractions of days. According to Internet sources, it has been 326 days since the vernal equinox.
d) What will the LST be tonight at midnight (to the nearest hour)?
This is easy. We already know the time at noon, so we just need to add another two minute offset like in problem a).
\[LST=\text{solar time} - 12h + (\text{Days since Vernal equinox} \times 4\text{ minutes/day})\]
c) What is the LST right now (to the nearest hour)?
Here is where it gets a bit more complicated because we need to work to find the number of days that have transpired since the equinox. It's not overly difficult, just time consuming. Conveniently, the current time is 12:00 on February 9th 2015 in Cambridge, MA, so we don't need to account for fractions of days. According to Internet sources, it has been 326 days since the vernal equinox.
\[LST=\text{solar time} - 12h + (\text{Days since Vernal equinox} \times 4\text{ minutes/day})\]
\[LST=\text{12:00} -12h + (326days \times 4\text{ minutes/day})\approx \boxed{22:00}\]d) What will the LST be tonight at midnight (to the nearest hour)?
This is easy. We already know the time at noon, so we just need to add another two minute offset like in problem a).
\[LST=\text{solar time} - 12h + (\text{Days since Vernal equinox} \times 4\text{ minutes/day})\]
\[LST=\text{24:00} -12h + (326.5days \times 4\text{ minutes/day})\approx \boxed{10:00}\]
e) What LST will it be at Sunset on your birthday?
e) What LST will it be at Sunset on your birthday?
My birthday is July 3rd. Internet sources claim that the next vernal equinox is on Friday, March 20th. My birthday is 105 days after the equinox. Sunset on my birthday will be at 19:25 in Cambridge (ignoring Daylight Savings Time which is only an annoyance on stellar scales).
\[LST=\text{solar time} - 12h + (\text{Days since Vernal equinox} \times 4\text{ minutes/day})\]
\[LST=\text{19:25} -12h + (105.3days \times 4\text{ minutes/day})= \boxed{14:25}\]
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