1. Times and Calendars Dr. Matt Wiesner Based on slides by Dr. Wei Cui
Lecture 3
Times and Calendars
Dr. Matt Wiesner
Based on slides by Dr. Wei Cui
Lecture 3
Purdue University, Astronomy 363

2. Purdue University, Astronomy 363
Review
What are zenith and nadir?
What are latitude and longitude?
What is a diurnal circle?
What are right ascension and declination?
What is retrograde motion?
What is an equinox?
What is a solstice?
What is the obliquity of the ecliptic?
Demo in Stellarium
Lecture 3
Purdue University, Astronomy 363

3. Purdue University, Astronomy 363
Timekeeping
Day 12 hours day, 12 hours night ( hours varied due to summer/winter until 1200s) (not quite equal to rotational period)
Minute 60 (after Middle Ages)
Second 17th century (60)
Month Moon
Year Orbit of Earth
Week 7 days, 7 classical planets
What is a planet (classically)?
What was the first planet “discovered”?
Lecture 3
Purdue University, Astronomy 363

4. Purdue University, Astronomy 363
Lecture 3
Purdue University, Astronomy 363

5. Purdue University, Astronomy 363
Sidereal and Solar Day
Sidereal Day: time between two upper transits of a star
Due to the Earth’s rotation, a celestial object transits the observer’s meridian twice a day, upper transit (crossing the zenith meridian) and lower transit (crossing the nadir meridian).
Solar Day: time between two upper transits of the Sun.
Due to the Earth’s motion, a solar day is longer than a sidereal day.
Lecture 3
Purdue University, Astronomy 363

6. Purdue University, Astronomy 363
360° days
1°  (1/ ) days
= 3.94 min
Explain difference
Taken from Stephen Tonkin’s Astronomical Unit
Lecture 3
Purdue University, Astronomy 363

7. Purdue University, Astronomy 363
More rigorously
Key assumptions: The axes of earth rotation and orbital motion are the same and angular speed is constant.
The effect of the offset is quite small.
They are offset by 23.5 deg! Angular speed varies.
Lecture 3
Purdue University, Astronomy 363

8. Purdue University, Astronomy 363
Mean Solar Time
Sun time:
When the Sun crosses the local meridian (reaches highest point), it is noon
Tomorrow when it does that again, it is noon again
But this day length varies (more than 24 h around Jan. 1, less than 24 h around Sept. 1)
Clock time
Every day is 24 hours
Problem arises because (a) Earth changes speed around Sun and (b) the length of circle covered by Sun varies due to obliquity of ecliptic
Lecture 3
Purdue University, Astronomy 363

9. Purdue University, Astronomy 363
Mean Solar Time
Apparent solar time (sun time) is based on the Sun’s position with respect to the local observer’s meridian.
It is measured by a sundial.
Mean solar time (clock time) is the solar time corresponding to a “mean Sun”.
The “mean Sun” moves along the celestial equator at a constant rate.
The mean solar day is the average length of an apparent solar day.
The mean solar time is the basis for the time kept by mechanical and electronic clocks.
Lecture 3
Purdue University, Astronomy 363

10. Purdue University, Astronomy 363
Equation of Time
The amount of time that needs to be added to the mean solar time to arrive at the apparent solar time. Equation of time= Apparent solar time -Mean solar time
Expand the discussion in different months.
Lecture 3
Purdue University, Astronomy 363

11. Purdue University, Astronomy 363
The Analemma
Lecture 3
Purdue University, Astronomy 363

12. Origins of the Analemma
Ellipticity of Earth’s orbital motion and tilt of Earth’s rotation axis
Lecture 3
Purdue University, Astronomy 363

13. Purdue University, Astronomy 363
Lecture 3
Purdue University, Astronomy 363

14. Purdue University, Astronomy 363
Time zones
For every degree of longitude you travel west, local noon occurs 4 minutes later (Rankin)
Telegraph and railway presented a problem
Time zones ~15° wide (time can vary a lot from mean solar time)
International Date Line ~ opposite Prime Meridian
Lecture 3
Purdue University, Astronomy 363

15. Purdue University, Astronomy 363
Effects on time
Moon slows Earth by about s/century.
Rotation rate varies due to oceanic and atmospheric temperatures
Earthquakes can change rotation rate
One second is 9,192,631,770 times the period of the radiation emitted by hyperfine transition of Cesium-133 atom at absolute zero
International atomic time (TAI)
The second is defined to be 1 mean solar second in AD 1900.
Lecture 3
Purdue University, Astronomy 363

16. Purdue University, Astronomy 363
Time Standards
Local mean solar time
GMT + local longitude
Civil time
GMT + Nzone x 1 hour (going east)
Coordinated universal time (UTC)
Synchronize to within 0.9 s of the mean solar time by using leap seconds.
Lecture 3
Purdue University, Astronomy 363

17. Purdue University, Astronomy 363
Local Sidereal Time
LST defined as hour angle of the vernal equinox
Hour angle is angular distance west of zenith meridian
LST=H+a
Measuring local sidereal time by observing a star with known RA.
HA: angle measured from the zenith meridian.
LST: HA of the vernal equinox.
Lecture 3
Purdue University, Astronomy 363

18. Purdue University, Astronomy 363
Calendars
Tropical year
Interval of time between successive passes of the Sun through the vernal equinox, mean solar days.
Sidereal year
Period of Earth’s orbital motion with respect to the celestial sphere, about 20 min longer than the tropical year, due to the precession of the equinoxes ( days)
Lecture 3
Purdue University, Astronomy 363

19. Julian and Gregorian calendars
Roman calendar: 12 months, 355 days (add extra month occasionally)
46 B.C.: Caesar added 3 months to get vernal equinox back to March (ultimus annus confusionis)
Julian calendar had days
One day every 128 years
Vernal equinox March 11 (Easter moving later)
Pope Gregory XIII, 1582
October 4 October 15
Leap days in century years only if divisible by 400
Lecture 3
Purdue University, Astronomy 363

20. Julian and Gregorian calendars
Bull Inter gravissimas (among the most serious duties…)
Britain and British territories 1752 (September 2September 14)
Benjamin Franklin, “It is pleasant for an old man to be able to go to bed on September 2, and not have to get up until September 14.”
Most commonly used calendar throughout the world
Lecture 3
Purdue University, Astronomy 363

21. Purdue University, Astronomy 363
Lecture 3
Purdue University, Astronomy 363

22. Purdue University, Astronomy 363
Question
A person came to my observatory and said he “bought” a star for his girlfriend. He wanted me to show her the star, located at coordinates (10h 45m 3.591s, -72° 41’ 4.26”). I was outside Chicago. Could I comply?
Lecture 3
Purdue University, Astronomy 363

23. Purdue University, Astronomy 363
Question
In the Old Man and the Sea, Hemingway described the old man lying in his boat off the coast of Cuba, looking up at the sky just after sunset: “It was dark now as it becomes dark quickly after the sun sets in September. He lay against the worn wood of the bow and rested all that he could. The first stars were out. He did not know the name of Rigel but he saw it and knew soon they would all be out and he would have all his distant friends.” Explain what is astronomically incorrect about this passage.
Lecture 3
Purdue University, Astronomy 363

24. Purdue University, Astronomy 363
The Sun is in Virgo (RA~13)
Near the autumnal equinox
Orion (RA~5)
Lecture 3
Purdue University, Astronomy 363

25. Purdue University, Astronomy 363
Question
How many degrees are on the complete celestial sphere?
Lecture 3
Purdue University, Astronomy 363

26. Purdue University, Astronomy 363
Circumference:
2pr=360°
r=57.3°
Surface area:
A=4pr2=4p(57.3°)2=41,253 deg2
Lecture 3
Purdue University, Astronomy 363

27. Purdue University, Astronomy 363
Reading Assignments
Chapter 2,
Lecture 3
Purdue University, Astronomy 363