General Astronomy
Marking Time
What is Time?
Everyone understands Time.
Ask any fifth grader.
Are you sure?
"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
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?
Time
For 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'
Time
Since 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 Time
What 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 Wheel
The 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 Time
The first basis of measuring time is by
using Astronomical events
The 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 Time
This is the time 'marked' by the apparent
position of the Sun
When 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 Sundials
The Forbidden City,
Bejing,China
Front yard of house
at 605 Baron St,
Tom’s River, NJ
Milan, Italy
Zodiac sundial, 1768
Created 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 Time
The 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
Summer
Solstice
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
You may have noticed this shape
on a world globe – straddling the
international date line
Equinox
Winter
Solstice
Mean Solar Time
Our 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 degrees
Or one full turn every day.
Mean Solar Time
The 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 Time
There'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.
Time Zones
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
Greenwich Time (BST, British Standard Time)
– Romeo Eastern Standard Time (EST)
– Quebec Atlantic Standard Time (AST)
†
Where a zone boundary splits a country, all parts of the country are
placed in the same time zone.
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 Time
Recall 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 Time
1.
2.
3.
4.
Start on the previous day that sidereal time and solar time match up at
midnight (Sept. 21 or March 21)
Determine sidereal time at midnight on the day you want
Determine sidereal time for the clock time you want
Stars having an RA within about 6 h of that sidereal time will be visible
Date
Spring equinox
(March 21)
RA of Sun
LST at midnight
0h
12h
(BY DEFINITION)
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. 21
LST at midnight  8h 30m
8 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 Evolution
325AD 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 Evolution
1582AD 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 Calendar
A slight additional modification of the
Gregorian Calendar was done (Rule 3).
The calendar is now accurate to 1 day in
20,000 years
Here's the current rules
1. Every 4th year is a Leap Year
2. Only Century's divisible by 400 are Leap Years
1.
2.
1700, 1800,1900 are not leap years
1600 and 2000 are leap years
1.
4000, 8000 and 12000 are not leap years
3. Century's divisible by 4000 are Common 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
Mayan Calendar
•
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.
Or
December 21, 2012
Notice the calendar 'Rollover'
12.19.19.17.19
13.0.0.0.0
13.0.0.0.1
- December 22, 2012
- December 23, 2012
- December 24, 2012