Lecture 3

Times and Calendars

Dr. Matt Wiesner

Based on slides by Dr. Wei Cui

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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

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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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Lecture 3 Purdue University, Astronomy 363 4

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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Lecture 3 Purdue University, Astronomy 363 6

Taken from Stephen Tonkin’s Astronomical Unit

360° 365.2422 days

1° (1/365.2422) days

= 3.94 min

More rigorously

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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.

Mean Solar Time

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• 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

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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Lecture 3 Purdue University, Astronomy 363 13

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

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• LST defined as hour angle of the vernal equinox

• Hour angle is angular distance west of zenith meridian

• LST=H+

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

2September 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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Lecture 3 Purdue University, Astronomy 363 21

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:– 2r=360°

r=57.3°

• Surface area:– A=4r2=4(57.3°)2=41,253 deg2

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Reading Assignments

• Chapter 2, 2.1-2.3

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