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Lecture 3
Times and Calendars
Dr. Matt Wiesner
Based on slides by Dr. Wei Cui
Lecture 3
Purdue University, Astronomy 363
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Review
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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
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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”?
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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.
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360° 365.2422 days
1°  (1/365.2422) days
= 3.94 min
Taken from Stephen Tonkin’s Astronomical Unit
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More rigorously
Key assumptions: The axes of earth rotation and orbital
motion are the same and angular speed is constant.
They are offset by 23.5 deg!
Angular speed varies.
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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
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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.
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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
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The Analemma
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Origins of the Analemma
Ellipticity of Earth’s orbital motion and tilt of Earth’s
rotation axis
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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
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Effects on time
• Moon slows Earth by about 0.0016 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.
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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.
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Local Sidereal Time
• LST defined as
hour angle of the
vernal equinox
• Hour angle is
angular distance
west of zenith
meridian
• LST=H+a
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Calendars
• Tropical year
– Interval of time between successive passes of the Sun
through the vernal equinox, 365.24219 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
(365.25636 days)
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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 365.25 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
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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
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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?
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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.
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• The Sun is in Virgo (RA~13)
• Near the autumnal equinox
• Orion (RA~5)
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Question
• How many degrees are on the complete celestial
sphere?
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• Circumference:
– 2pr=360°
r=57.3°
• Surface area:
– A=4pr2=4p(57.3°)2=41,253 deg2
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Reading Assignments
• Chapter 2, 2.1-2.3
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