1. Astronomical time
SSP 2017

2. Astronomy = “naming of the sky”
One of the oldest human attempts to understand nature – early civilizations used it for timekeeping, principally.
diurnal = day/night cycle
lunar = moon cycle (month)
annual = sun cycle

3. A couple of ways to measure a day
Two ways to define the diurnal cycle:
• solar time, which is based on the Sun overhead (noon)
• sidereal (= star) time, which is based on stars overhead (transit)
Both are “correct”; however, the solar day dominated time measurement in nearly all civilizations. The solar day is defined as exactly 24 hours, and is slightly longer than the sidereal day (23h 56m s). Or, 1 mean solar day = sidereal days.

4. Advances in timekeeping
Various calendar reforms kept the year from getting out of sync with various annual cycles – the latest was the Gregorian calendar reform (1582) that “fixed” the leap year rule so that years evenly divisible by 400 were not leap years.
However, all these reforms make it hard to keep track, literally, of the days.

5. The Julian Date (JD)
Joseph Scaliger, a French classical scholar, was famed for his writings on Greek history. He found problematic the chronology of historical events, and proposed the Julian period of 7980 years as a standard block of time, regardless of calendar reform.
More importantly, he set 4713 BCE as the starting year, since that year preceded any known historical event. Astronomers in the 19th century, notably John Herschel, adopted this method of counting days.

6. The Julian Date (JD)
Herschel defined the start of the Julian Date calendar as noon (12h UT) on January 1, 4713 BCE. This start time, combined with the notion of “decimal days” (Laplace, 1799), gives us the modern Julian Date.
So January 1, 2017, 0h UT has the Julian date: JD
Clearly, you can figure out today’s Julian date by adding the number of days since January 1, then adding the fractional part of the day we are in (and adjusting for UT). Or use the Julian date calculator at

7. Advances in timekeeping technology
As a by-product of (nearly) winning the Royal Naval Board prize for the determination of longitude in 1773, John Harrison invented a much more accurate chronometer (clock).
A clock is set to noon in Greenwich, UK, when the sun is overhead there, and then the clock is transported to Boston, and now it reads 5 p.m., then it is inferred that the clock has move 5/24 of the way around the globe, or roughly 75 degrees of longitude.

8. Further advances in timekeeping tech
The 1884 International Meridian Conference establishes Greenwich Mean Time (GMT). GMT is also known as “Zulu Time” (military and aviation).
GMT was synchronized with Universal Temps Coordonné (UTC or, just UT) by the 1960 International Radio Consultative Committee.
Finally, in 1967, the SI unit of the second is redefined according to the frequency of a cesium atomic clock.

9. And, so, for SSP at CUB:
The time in Boulder (Mountain Daylight Time, MDT) is GMT – 6:00 h; it is GMT – 7:00 h for Mountain Standard Time.
Or, to rearrange this: MDT (Boulder) + 6 h = UT

10. And sidereal time?
Oh, it is still used by astronomers! Recall that “LST” stands for Local Sidereal Time.
Greenwich sidereal time (GST) = LST at Greenwich
So GST at any given time = GST at 0 h UT + sidereal time (in hours) since 0 h UT
= GST at 0 h UT * UT (h)
So LST at any given place on Earth
– W longitude (in hours)

11. Boulder Local Sidereal Time
Boulder is at 105° 15’ 45” W = ° = h
LST (Boulder) = GST at 0 h UT * UT (h)
– h

12. Recall that the hour angle (HA) of any object was the angle from the local meridian to the object’s position along the celestial equator.
If HA < 0 h then the star is rising; if HA > 0 h then the star is setting; and if HA = 0 h then the star is transiting.
Local sidereal time is therefore the hour angle of the vernal equinox (as shown).

13. Try this:
If Sirius has an RA = 6h 43m and a dec = –16° 39’, what is the LST when Sirius has an HA = 2h 17m?
Where in the sky would you look for the vernal equinox?

14. Try this:
If Sirius has an RA = 6h 43m and a dec = –16° 39’, what is the LST when Sirius has an HA = 2h 17m?
Where in the sky would you look for the vernal equinox?
Start with LST = HA + RA = 2h 17m + 6h 43m = 9h 00m
Since LST = HA of ϒ, so the vernal equinox is below the western horizon (LST is positive).

15. How about another?
You will observe your asteroid on September 13 at 12:00:00 a.m. (midnight) MDT. The ephemeris says that it has an RA = 23h 36.94m and a dec = –1° 58.3’. The GST for Sept. 13 (0h) is 23h 27m 08s.
What is the UT date/time of your observation?
What will the LST of the observation be?
What is the HA of the asteroid, and is it rising, setting or transiting?

16. UT calculation: Sept. 13 12:00:00 am + 6h
= Sept. 13 6:00:00 UT
LST (Boulder) = GST at 0 h UT * UT (h)
– h
= 23h 27m 08s * 6 h 0m 0s UT
– 7h 1m 3s
= 23h 27m 08s + 6h 0m 59s – 7h 1m 3s
= 22h 27m 04s
HA = LST – RA = 22h 27m 04s – 23h 36m 56s
= –1h 9m 52s (negative HA means “rising”)

17. Using the star chart to determine LST
The LST is 0 h by definition when the vernal equinox is on the local meridian (recall the LST is the hour angle of the vernal equinox)
Thus, it follows that if the vernal equinox is on the western horizon, the LST is 6 h; similarly, if the ϒ is on the eastern horizon, the LST is 18 h.