Marking Time

General Astronomy

What is Time?

"What then is time? If no one asks me, I know: if I wish to explain it to one that asketh, I know not."

-- St. Augustine

Everyone understands Time. Ask any fifth grader.

Are you sure?

What is Time?When most people think about time, they are

thinking about the MEASUREMENT of time, not time itself.

Philosophers have been debating the nature of time since the ancient Greeks– Is time linear or cyclic?– Is time continuous or discrete?

• What would be the smallest unit of time?– Does time 'flow' or is it a container?

• Does time 'flow' only in one direction?– What the heck do we mean by 'direction'?

– Is is a dimension like height, width and length?

TimeFor Sir Issac Newton, time is an absolute entity,

independent of everything else:"Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly and by another name is called duration. Relative, apparent, and common time is any sensible and external measure (precise or imprecise) of duration by means of motion; such a measure—for example, an hour, a day, a month, a year—is commonly used instead of true time."

-- Principia

Thus it is a linear "stream" flowing only in one direction.This is a view largely created by St. Augustine in forming the foundations of the Judeo-Christian philosophy.In Ancient Greek and in Dharmic religious philosophies, time is more cyclic: Ages repeat endlessly according to a 'Wheel of Time'

TimeSince we don't have much chance of

solving the problem here and now, we will limit ourselves to something we can handle:

The Measurement of Time

We can view events as happening separated by a time duration and deal with devising a consistant framework to compare and order these events.

Measuring TimeWhat is the smallest unit of time?

Planck Time

Is is approximately 5.4 x 10-44 seconds

At smaller times than this, reality can no longer be described by classical Physics.

The Time WheelThe Timewheel (Időkerék) is the world's largest hourglass, situated in Budapest, Hungary. It is made of granite, steel, and glass, and weighs 60 tons. The "sand" (actually glass granules) flows from the upper to the lower glass chamber for one year. The last few grains of sand flow through at exactly midnight on New Year's Eve and the Timewheel is then turned 180 degrees so the flow of the sand can resume for the next year. The turning is done by manual power using steel cables and it takes roughly 45 minutes for 4 people to complete the half turn. --Wikipedea

Measuring TimeThe first basis of measuring time is by

using Astronomical eventsThe periodic motion of the heavenly bodies lends itself to this.

Rising at dawn, taking shelter at dusk; Few things are more natural in the

primitive world.

Local Apparent TimeThis is the time 'marked' by the apparent

position of the SunWhen the Sun is due South (in the

Northern hemisphere); or the highest point in the sky, then it is NOON

This is the time measured by sundials.The gnomen is oriented along the north-south plane and has the same angle as the latitude where it stands.

Other types of SundialsThe Forbidden City, Bejing,China

Front yard of house at 605 Baron St,Tom’s River, NJ

Milan, ItalyZodiac sundial, 1768Created by the Accademia di Brera Summer solstice - the rays strike the bronze on the floor Winter solstice - it stretches to the meridian. (Duomo di Milano - Used prior to Greenwich)

Local Apparent TimeThe problem is that the Sun's position appears to be different at noon at different times of the year.

For example, it takes a lot longer in June for the Sun to get to it's highest point than it does in December (Northern hemisphere again)

Apparent Solar Time

In this image, the photo was taken every week for a year at the same time, local noon.

Note that the images of the Sun are in different positions and that the spacing between images changes.

This is the Analemma

Equinox

Summer Solstice

Winter Solstice

You may have noticed this shape on a world globe – straddling the international date line

Mean Solar TimeOur first correction is to pretend that there is

an 'average' (rather fictitious) Sun which would appear to move across the sky at the mean yearly rate.

The mean Sun marks time steadily, day after day, month after month at a rate of 15 degrees per hour.

Yep, 15 degrees/hour X 24 hours = 360 degreesOr one full turn every day.

Mean Solar TimeThe Equation of Time

The difference in time between the mean sun and the apparent sun

Differs less than 1 minute on any given day, but is cumulative so that at most there is a 16m difference.

Notice where the curve crosses the zero minutes point: The solstices and the equinoxes.Also see the how the graph looks like the photos of the Sun's position on a previous slide.

Mean Solar Time

– Local Mean Time (LMT)• This is the time marked off by the

apparent position of our fictitious 'mean' Sun.

• Noon is when the mean Sun crosses our meridian

– Greenwich Mean Time (GMT)• Noon is when the mean Sun crosses the

Prime meridian.

Local Mean TimeThere's still a problem. LMT is dependent on the longitude

(After all, that's why it is 'Local').For example, the longitude of Pomona, NJ is 074 º 35'; for

Philadelphia, PA it is 75º 07'

This is about a 0.53º difference. At 15º per hour, this is about 2 minutes of time.

So, every time you want to go to Philly, you will have to reset your watch by 2 minutes back; when you return to Pomona, you have to set your watch forward by 2 minutes.

A bit inconvenient.

So, How do we adjust and avoid this problem? We all agree that for everyone in a 15º zone, noon will occur at the same time (ignoring where the mean and the true Sun is positioned).

We section off the longitudes in areas, or zones, roughly centered† on the 15º increments. We then use "Zone Time"

– Zulu– Romeo– Quebec

† Where a zone boundary splits a country, all parts of the country are placed in the same time zone.

Time Zones

Greenwich Time (BST, British Standard Time)Eastern Standard Time (EST)Atlantic Standard Time (AST)

The World's Time Zones

Time Zones• Daylight Saving Time

– For those regions which use Daylight Savings Time, it effectively moves their timezone one zone to the east.

– EST (Romeo) EDT (Quebec)• Instead of the 5 hour time correction from EST

to Zulu it becomes a 4 hour correction.– Not all areas use DST; Hawaii, for

example

Time• Zulu = Universal Time

– Astronomical• Universal Coordinated Time (UTC)

– Atomic Clock• Kept in synchronization using 'leap

seconds'; one every 1 – 2 years

Sidereal TimeRecall the Sidereal Day?This was the rotation of the earth

with respect to the ‘fixed stars’Sidereal Time is therefore ‘Star

Time’ as measured by the stars instead of the sun.

Sidereal Time = RA on your meridian right now

Calculating Sidereal Time1. Start on the previous day that sidereal time and solar time match up

at midnight (Sept. 21 or March 21)2. Determine sidereal time at midnight on the day you want3. Determine sidereal time for the clock time you want4. Stars having an RA within about 6 h of that sidereal time will be

visibleDate RA of Sun LST at midnight

Spring equinox (March 21) 0h (BY DEFINITION) 12h

Summer solstice (June 21) 6h 18h

Fall equinox (Sept. 21) 12h 0h

Winter solstice (Dec. 21) 18h 6h

For example, what is the local sidereal time on January 28th at 8pm?LST = 0h at midnight on fall equinox (Sept. 21)LST at midnight advances 2 h every month (and about 0.5 h every week)Jan. 28 is 4 months and 1 week after Sept. 21LST at midnight 8h 30m8 pm is 4 h earlier, so LST 4h 30m = RA of your meridian

Calendars

• Early Calendars were Lunar in nature– Early Roman, Modern Hebrew and

Chinese• Others are Solar in nature• Some points in the year were

marked by the appearance in the sky of certain stars or patterns such as Sirius or Orion

Egyptian Calendar• The civil calendar that was introduced in Egypt between

c.2937 and c.2821 BCE had 12 months of 30 days each. • Five epagomenal days, "days out of time," were placed

between the 30th of the last month and the first day of the new year to bring the total to 365 (1st day of new year corresponds to Aug 29)

• Although the rising of Sirius (Sothis) originally marked the new year (Thoth 1), the missing quarter day in the civil calendar caused a "wandering year" as the rising of Sirius cycled through the days of the year

• The Decree of Canopus is an on an ancient Egyptian memorial stone stele, the Stone of Canopus, it is a decree by the Pharaoh Ptolemy III in 239 BC declaring a calendar reform (amongst other things):– According to the reform every fourth year, the 5–day "Opening of the

Year" ceremonies would include an additional, 6th–day. The reason given was that the rise of Sothis advances to another day in every 4 years, synchronizing the beginning of the year with the heliacal rising of the star Sirius, rather than following the seasons.

Calendar Evolution• Roman Republican Calendar

– Lunar• 12 Lunar months (starting at the New

Moon)– 355 days per year– Every 3 years it slips 1 month

• Corrected by using Empty and Full years– Empty years were 12 months– Full years had 13 months

– Circa 70 BC, the calendar was controlled by the priesthood and was used for political football • when friends were in office (or perhaps

some bribes were used) , the year was Full

Calendar Evolution

• Circa 46BC, Julius Caesar proclaimed a calendar reform after consulting with an astronomer, Sosigenes of Alexandria– By 46BC, a Roman traveling from town to town could find

himself going from year to year– Solar Calendar of 12 Months; 365.25 days

– Three years would be Common Years with 365 days– The 4th year add a day to February giving a Leap Year

– Made the seasons and holidays realign by forcing the vernal equinox back to the traditional March 25th by adding 3 extra months to 46BC making it a year of 445 days (Known as the 'year of confusion')

Calendar Evolution325AD The Council of Nicea fixed religious dates (Christian)

For example, Easter is defined as the 1st Sunday after the 14th day of the newly full moon which falls after the 21st of March

Intentionally designed to avoid Easter falling on Passover

By this time (from 46BC to 325AD), the error of 11m 14s excess per year has accumulated to 3 days.

Calendar Evolution1582AD Pope Gregory reformed the calendar again.

– In the 1500-odd years of using 365 days per year the seasons had slipped again with the 1st day of Spring occurring on March 11th instead of March 21st

– Solar with 365.2425 days • Implemented using Leap Years

– March 25 start of year was moved to January 1st.

– October 4, 1582 was followed by October 15th (by Proclamation)

– Non-Catholic countries resisted the Pope's decree. It wasn't until the mid-1700s that England and the Colonies changed to the Gregorian Calendar.• Causing riots, due to 'loss' of 12 days ("of

life") 9/2/1752 9/14/1752

The Gregorian CalendarA slight additional modification of the

Gregorian Calendar was done (Rule 3).The calendar is now accurate to 1 day in

20,000 yearsHere's the current rules1. Every 4th year is a Leap Year 2. Only Century's divisible by 400 are Leap Years

1. 1700, 1800,1900 are not leap years2. 1600 and 2000 are leap years

3. Century's divisible by 4000 are Common Years1. 4000, 8000 and 12000 are not leap years

The Julian Day

• This is simply a "day counter" which identifies each day by numbering it from an arbitrary date far in the past

• Computes day as the number of days elapsed since January 1, 4712 BCE

• A day begins at Noon Universal Time

• October 3, 2004 is JD 2452916.0

The Mayan Calendar• More sophisticated and complicated than Julian or Gregorian

calendars• Really a day counter useful for computing astronomical events

such as the helical rising of Venus• Composed of three separate devices: Loosely corresponding to

our week, year and Julian Day schemes• The first is the sacred almanac, the Tzolkin. This follows the

week scheme of having a number of perpetually reoccurring names for days (Monday, Tuesday,…, Monday).– In the Tzolkin there are 20 names for the days (kin) instead of 7– In addition each day is accompanied by a number from 1 to 13

which were then also repeated• The 1st day was therefore "1 imix", followed by "2 ik", up to the 13th day

which was "13 Ben". The next day, "ix" was accompanied by 1 as "1 ix" up to the 20th day or "7 Ahad". At this point the day names started up again with "imix", but with the number 8 ; that is, "8 imix"

• This gives 13 x 20 = 260 individual names for the days before "1 imix" repeats.

– No attempt was made to match certain days with given times of the year or any given events

Mayan Calendar• The second device was a 365 day period (Tun) equivalent to our year

– No leap year schemes since the Maya didn’t attempt to fix the starting point to any given season, etcetera.

– The 365 days were divided into 18 winals of 20 days each, with 5 "unlucky" days tacked on as a 19th winal.

– Each day was numbered (0 thru 19) according to its position in the winal, thus the Maya would speak of 17 Yaxkin similar to our use of November 20

– Thus a given day might be 7 ik 15 Yaxkin (we might say something like Wednesday, 23 December)

– In our calendar, we can have January 11th fall on a Tuesday every few years, but the Mayan scheme would have a given day (like 7 ik 15 Yaxkin ) occur only once every 52 years

• The third scheme was the "Long Count" – A perpetual tally of days starting on 3114 BC– Analogous to our Julian Day scheme– The Long Count employed a vigesimal numbering system (i.e.

base 20) which incorporated the idea of a zero and a place holder– The Maya also counted 400-year periods called Baktuns.– Also 20 year k'atuns– Today a typical long count date is written thus: 12.19.19.17.18– This represents 12 baktuns, 19 k'atuns, 19 tuns, 17 uinals and 18

k'ins.

Mayan Calendar

Notice the calendar 'Rollover'

12.19.19.17.19 - December 22, 201213.0.0.0.0 - December 23, 201213.0.0.0.1 - December 24, 2012

Or December 21, 2012