TimeTime

“Does anybody really know what time it is?Does anybody really care?” – Chicago

The Sky’s Natural CyclesThe Sky’s Natural Cycles

Early cultures noticed 3 obvious periodic intervals:Early cultures noticed 3 obvious periodic intervals:– day:day: 86400 seconds on average between each noon 86400 seconds on average between each noon – month:month: 29.53 days between each full moon 29.53 days between each full moon– tropical year: tropical year: 365.24 days between June solstices365.24 days between June solstices

Problem: None of these numbers divide evenly Problem: None of these numbers divide evenly into one another.into one another.– How to construct a calendar?How to construct a calendar?

…with great difficulty

Stonehenge

A modern solution to our A modern solution to our complicated calendar?complicated calendar?

Alliance, Nebraska

Stonehenge: 3100 BC – 1600 BC

Timekeeping DevicesTimekeeping Devices

1657-1940s: Pendulum clock1657-1940s: Pendulum clock

C. Huygens presenting pendulum clock to Louis XIV

Accuracy: ~ 10 sec/day

Timekeeping DevicesTimekeeping Devices

1940s: quartz oscillator1940s: quartz oscillator– use piezoelectric effect to drive vibrations in a use piezoelectric effect to drive vibrations in a

quartz crystal using electric current from an quartz crystal using electric current from an oscillator circuitoscillator circuit

Quartz “tuning fork” with oscillation freq = 32768 Hz

Accuracy: < 1 sec/day

Timekeeping DevicesTimekeeping Devices

1950s: atomic clocks:1950s: atomic clocks:– fill a microwave cavity with a fill a microwave cavity with a

pure gas (cesium, rubidium, pure gas (cesium, rubidium, hydrogen) that has a hyperfine hydrogen) that has a hyperfine energy level structureenergy level structure

– gas emits hyperfine transition gas emits hyperfine transition microwaves, cavity is tuned for microwaves, cavity is tuned for resonance by being connected resonance by being connected to an electronic oscillator to an electronic oscillator feedback circuitfeedback circuit

Modern chip-scale atomic

clocksAccuracy: < 10-9 sec/day

Local Apparent Solar TimeLocal Apparent Solar Time

Equal to the hour angle of the Sun + 12 hEqual to the hour angle of the Sun + 12 h

Why are sundials generally lousy timekeepers?Why are sundials generally lousy timekeepers?

Mean TimeMean Time

Introduce a ‘mean’ Sun that moves along the Introduce a ‘mean’ Sun that moves along the celestial equator celestial equator (not the ecliptic) at a (not the ecliptic) at a fixed ratefixed rate..

Determine this rate by using the ICRS as a Determine this rate by using the ICRS as a reference frame.reference frame.

Call the local mean time at 0° longitude Call the local mean time at 0° longitude (Greenwich) ‘Universal Time’ (UT1)(Greenwich) ‘Universal Time’ (UT1)– UT1 is the preferred time system for astronomersUT1 is the preferred time system for astronomers

Modern (SI) Definition of TimeModern (SI) Definition of Time

In pendulum clock era, 1 second was 1/86400 of In pendulum clock era, 1 second was 1/86400 of the mean solar day, as measured by transit the mean solar day, as measured by transit instrumentsinstruments– but the mean solar day is constantly changing, due to but the mean solar day is constantly changing, due to

variations in Earth’s spin and its orbit around the Sunvariations in Earth’s spin and its orbit around the Sun

1967: by definition, one second is the duration of 1967: by definition, one second is the duration of 9 9 192 631 770 periods of the radiation periods of the radiation corresponding to the transition between the two corresponding to the transition between the two hyperfine levels of the ground state of a cesium hyperfine levels of the ground state of a cesium 133 atom at rest at absolute zero.133 atom at rest at absolute zero.

Time for Some ComplicationsTime for Some Complications

The SI second (based on physics) is totally independent The SI second (based on physics) is totally independent of the second that is 1/86400 of a mean solar day (based of the second that is 1/86400 of a mean solar day (based on astronomy)on astronomy)

The world requires a uniform, unchanging time standard, The world requires a uniform, unchanging time standard, but also needs it to be roughly in sync with day/nightbut also needs it to be roughly in sync with day/night

Astronomers need to be able to point telescopes and Astronomers need to be able to point telescopes and accurately time extraterrestrial eventsaccurately time extraterrestrial events

TAI = international atomic time (physics, SI seconds)TAI = international atomic time (physics, SI seconds)

UT1 = Universal time (astronomy, non-SI seconds)UT1 = Universal time (astronomy, non-SI seconds)

UTC = Coordinated Universal TimeUTC = Coordinated Universal Time

What your watch/GPS usesWhat your watch/GPS uses

Administered by international standards Administered by international standards organizationsorganizations

Runs in step with TAI (uses SI seconds), but Runs in step with TAI (uses SI seconds), but with a prescribed offset to keep it within one with a prescribed offset to keep it within one second of UT1second of UT1

The offset is periodically changed by introducing The offset is periodically changed by introducing ‘leap seconds’ (which may be abolished in the ‘leap seconds’ (which may be abolished in the near future)near future)

Standard (Zone) TimeStandard (Zone) Time

Invention of railways and the telegraph led to the Invention of railways and the telegraph led to the adoption of standard time in 1884:adoption of standard time in 1884:– world is divided into 24 major time zonesworld is divided into 24 major time zones– standard time (offset from UTC) is the same standard time (offset from UTC) is the same

everywhere within a time zone everywhere within a time zone

ConsequenceConsequence: the Sun is : the Sun is notnot usually due South usually due South when your watch reads noon.when your watch reads noon.

exact time of solar transit depends on your longitude, exact time of solar transit depends on your longitude, time zone, day of year, and small variations in the time zone, day of year, and small variations in the Earth’s rotationEarth’s rotation

Each time zone spans roughly 15Each time zone spans roughly 15ºº of longitude of longitude

ComplicationsComplications

Not all countries like the Not all countries like the time zone scheme (China).time zone scheme (China).

Some use daylight saving time:Some use daylight saving time:– move clocks back 1 hr in late Fallmove clocks back 1 hr in late Fall– start/end dates of DST different in start/end dates of DST different in

Europe and N. AmericaEurope and N. America

Lafayette uses Eastern Daylight Lafayette uses Eastern Daylight Time from spring through fall.Time from spring through fall.

International Date LineInternational Date LineWhere the calendar day begins. Where the calendar day begins.

what is the date and time in Japan right what is the date and time in Japan right now?now?

14 hours ahead of

EST

http://time.is/UTC

Our CalendarOur Calendar

The YearThe Year

Solar year: Solar year: length of time for the Sun to length of time for the Sun to return to the same equinox.return to the same equinox.

Tropical year: Tropical year: length of time for the mean length of time for the mean Sun to travel exactly 360° along the Sun to travel exactly 360° along the eclipticecliptic

Sidereal year: Sidereal year: length of time for Earth to length of time for Earth to return to same spot in its orbit w.r.t. ICRS return to same spot in its orbit w.r.t. ICRS (20 min longer than tropical year)(20 min longer than tropical year)

Where our calendar comes fromWhere our calendar comes from

Julian calendar developed circa 200 AD, RomeJulian calendar developed circa 200 AD, Rome– each year had 365 days and 12 monthseach year had 365 days and 12 months– every fourth “leap” year had 366 daysevery fourth “leap” year had 366 days

Julian year (365.25 days) slightly longer than Julian year (365.25 days) slightly longer than tropical year (365.2422 days) tropical year (365.2422 days) – equinoxes and solstice dates migrated over time.equinoxes and solstice dates migrated over time.– by the 16th century, March equinox had slipped back by the 16th century, March equinox had slipped back

to Mar. 11to Mar. 11

The Gregorian CalendarThe Gregorian Calendar

1582: Pope Gregory XIII institutes major reform:1582: Pope Gregory XIII institutes major reform:– ten days were dropped: Oct 5, 1582 became Oct 15.ten days were dropped: Oct 5, 1582 became Oct 15.

– a century year was only a leap year if divisible by 400.a century year was only a leap year if divisible by 400.

The year 2000 was a leap year, but 1900 was not.The year 2000 was a leap year, but 1900 was not.– part of the infamous ‘Y2K’ problempart of the infamous ‘Y2K’ problem

– cost the world ~$400 billion to change software codecost the world ~$400 billion to change software code

– on Jan 1, 2000, the U.S. Naval Observatory master clock on Jan 1, 2000, the U.S. Naval Observatory master clock website read 1 Jan 19100.website read 1 Jan 19100.

Worldwide standard is now Gregorian Calendar.Worldwide standard is now Gregorian Calendar.

Dates in the Modern EraDates in the Modern Era

Modern dates contain A.D. (Anno Domini)Modern dates contain A.D. (Anno Domini)– Also used: C.E. (Common Era)Also used: C.E. (Common Era)

System invented by D. Exiguus in 547 A.D.System invented by D. Exiguus in 547 A.D.– reckonedreckoned Jesus Christ was born 754 years after Jesus Christ was born 754 years after

Rome was foundedRome was founded

Dates before 1 A.D. are B.C. (Before Christ) Dates before 1 A.D. are B.C. (Before Christ)

There was no year zero.There was no year zero.

Julian DatesJulian Dates

Many areas in astronomy require specification of a specific Many areas in astronomy require specification of a specific datedate– e.g. variable stars, planetary orbitse.g. variable stars, planetary orbits

Calendar dates are a problem because of leap years, non-Calendar dates are a problem because of leap years, non-uniform historical international adoption of Gregorian uniform historical international adoption of Gregorian calendar (some as late as 1922: USSR, 1923: Greece)calendar (some as late as 1922: USSR, 1923: Greece)

The The Julian date Julian date is the integer number of days since Jan 1, is the integer number of days since Jan 1, 4713 B.C. according to Julian calendar.4713 B.C. according to Julian calendar.

‘‘modified’ Julian dates often used: MJD = JD - 2400000.5 modified’ Julian dates often used: MJD = JD - 2400000.5 (MJD begins at midnight UT, JD begins at noon UT)(MJD begins at midnight UT, JD begins at noon UT)– 0h0m on Sept 9, 2015 = JD 2457274.5 = MJD 57274.00h0m on Sept 9, 2015 = JD 2457274.5 = MJD 57274.0– plan your big astronomy bashplan your big astronomy bash: Feb 24, 2023 (MJD 60000.0 !!): Feb 24, 2023 (MJD 60000.0 !!)

Coordinate EpochsCoordinate Epochs

Because of precession of the celestial equator on the sky, Because of precession of the celestial equator on the sky, astronomical coordinates are always accompanied by an astronomical coordinates are always accompanied by an epoch.epoch.

B1950: Coordinates on Jan 1, 1950, based on Besselian B1950: Coordinates on Jan 1, 1950, based on Besselian (tropical) year of 365.242… days(tropical) year of 365.242… days

J2000: Coordinates on Jan 1, 2000, based on Julian year J2000: Coordinates on Jan 1, 2000, based on Julian year (exactly 365.25 days)(exactly 365.25 days)

To calculate coordinates on a given date, must apply a To calculate coordinates on a given date, must apply a spherical transformation based on Earth’s axial precession spherical transformation based on Earth’s axial precession parameters. parameters. http://ned.ipac.caltech.edu/forms/calculator.html