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
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
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
Purdue University, Astronomy 363 Lecture 3 Purdue University, Astronomy 363
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
Purdue University, Astronomy 363 360° 365.2422 days 1° (1/365.2422) days = 3.94 min Explain difference Taken from Stephen Tonkin’s Astronomical Unit Lecture 3 Purdue University, Astronomy 363
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
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
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
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
Purdue University, Astronomy 363 The Analemma Lecture 3 Purdue University, Astronomy 363
Origins of the Analemma Ellipticity of Earth’s orbital motion and tilt of Earth’s rotation axis Lecture 3 Purdue University, Astronomy 363
Purdue University, Astronomy 363 Lecture 3 Purdue University, Astronomy 363
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
Purdue University, Astronomy 363 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. Lecture 3 Purdue University, Astronomy 363
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
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
Purdue University, Astronomy 363 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) Lecture 3 Purdue University, Astronomy 363
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 Lecture 3 Purdue University, Astronomy 363
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 Lecture 3 Purdue University, Astronomy 363
Purdue University, Astronomy 363 Lecture 3 Purdue University, Astronomy 363
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
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
Purdue University, Astronomy 363 The Sun is in Virgo (RA~13) Near the autumnal equinox Orion (RA~5) Lecture 3 Purdue University, Astronomy 363
Purdue University, Astronomy 363 Question How many degrees are on the complete celestial sphere? Lecture 3 Purdue University, Astronomy 363
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
Purdue University, Astronomy 363 Reading Assignments Chapter 2, 2.1-2.3 Lecture 3 Purdue University, Astronomy 363