Transcript Single-Trial Characterization of Evoked Responses

Physics 112
Star Systems
Lecture 2
Motions of the Heavens
Kevin H. Knuth
University at Albany
Fall 2013
"Who laid the foundations of the earth,
that it should not be removed for ever.“
- Psalms 104:5
What day is it today?
Calendars
Calendars are
how to know WHEN.
Calendars
There are three basic
components:
Year
Month
Day
The year is divided into
12 months.
Each month has 28, 29,
30, or 31 days.
There are 365 days per
year.
Why is it based on a YEAR?
Why are our calendars based on a year?
Why don’t they just count the number of days since some
starting point?
Why is it based on a YEAR?
Why are our calendars based on a year?
Why don’t they just count the number of days since some
starting point?
The annual cycle is important.
We need to know when to plant our crops.
When to hold certain festivals.
When other important events have been arranged
Mayan Calendar
Mayan Long Count
counts the number of
days since creation:
Aug 12, 3113 B.C.
Batkun Count
12. 18. 17. 16. 6.
Batkun Count
Batkun Katun Tun Uinal Kin
Kin = 1 Day
Uinal = 20 kins
Tun = 18 Uinals
Katun = 20 Tun
Batkun = 20 Katun
Tzolkin
(260 Day Calendar)
Day (1-13) Sign (1-20)
Calendar Round
6 Cimi
19 Kayab
Haab
(Civil Calendar)
Day (1-19) Month (1-19)
http://webexhibits.org/calendars/calendar-mayan.html
Northern Hemisphere
The modern civilizations mostly developed in the Northern
Hemisphere, and our notions of time and seasons reflect this.
SUMMER – The Sun is high in the sky during the day
The days are long
WINTER –
The Sun is low in the sky during the day
The days are short
 2009 Pearson Education Inc.
SEASONS
 2009 Pearson Education Inc.
Summer Solstice
SUMMER SOLSTICE (about June 22)
The longest day of the year in the northern hemisphere
The Sun reaches its maximum height in the sky on this day
This angle (declination) is denoted the Tropic of Cancer
It is at (23° 27') latitude.
Sol = Sun
The word solstice comes
from the Latin word
solstitium meaning the point
where the Sun stops.
Winter Solstice
WINTER SOLSTICE (about Dec 21)
The shortest day of the year in the northern hemisphere
The Sun’s maximum height at noon, is as low as it will get
This angle (declination) is denoted the Tropic of Capricorn
It is at (-23° 27') latitude.
Sol = Sun
The word solstice comes
from the Latin word
solstitium meaning the point
where the Sun stops.
Spring (Vernal) Equinox
SPRING EQUINOX (about March 21)
This is one of the midway points between the solstices.
Day and Night are both exactly 12 hours.
The Sun is directly over the Equator
The word equinox comes
from the Latin word
equinoxium meaning equality
of night and day
Fall (Autumnal) Equinox
FALL EQUINOX (about September 23)
This is one of the midway points between the solstices.
Day and Night are both exactly 12 hours.
The Sun is directly over the Equator
The word equinox comes
from the Latin word
equinoxium meaning equality
of night and day
Solstices and Equinoxes
The Solstices and Equinoxes enabled the ancients to tell the
time of year to within the accuracy of a day.
They did this by carefully monitoring shadows.
Stonehenge 3100 BC – 1600 BC
El Caracol: The Mayan Observatory
600 – 1000 AD
Analemma
An analemma is the shape
of the path that the Sun
traces out in the sky over
the course of a year.
It is found by noting the
position of the sun at the
same time each day.
http://www.analemma.com
Analemma on Mars
Excursion to Babylon
Sumer and Babylon
Babylon
(56 mi south of modern Baghdad)
Sumer was the first civilization…home of the first cities.
First written language was probably in Sumer around 3100 BC
In 2500 BC, by Royal Edict, all weights and measures were
standardized in Babylon.
Babylonian Measures
Length
1 finger ~ 2/3 inch
1 cubit = 30 fingers
1 cord (surveyors rope) = 120 cubits = 3600 fingers
Weight
1 grain ~ 45 milligrams
1 shekel = 180 grains ( ¼ ounce)
1 talent = 3600 shekels (67 pounds)
You may note that these numbers are divisible by 6 and 10.
This is a recurring theme in the Babylonian system…
Babylonian Measures
Angles
1 Circle = 360 Degrees
1 Degree = 60 Minutes of Arc
1 Minute of Arc = 60 Seconds of Arc
We still use these measures today!
Babylonian Measures
Time
1 Day = 24 Hours
1 Hour = 60 Minutes
1 Minute = 60 Seconds
360 Days per Year
12 Months with 30 Days each
Every 5th year an extra month was added to keep the
calendar aligned with the astronomical observations.
Babylonian Measures
Time
1 Day = 24 Hours
1 Hour = 60 Minutes
1 Minute = 60 Seconds
Note that all of these
ratios are divisible by 6.
Clearly 6 was important
to the Babylonians.
360 Days per Year
12 Months with 30 Days each
Every 5th year an extra month was added to keep the
calendar aligned with the astronomical observations.
Our Number System
Look at the numbers 1, 13, 147
The symbol 1 means something different in each number.
Its meaning depends on its position in the number.
1=1
13 = 1x10 + 3
147 = 1x100 + 4x10 + 3
=
1x102 + 4x101 + 3x100
We call our number system, a Base 10 system since each
symbol represents a number between 0 and 9 and is
multiplied by the base 10 taken to the power of the place in
the expression.
678,197 = 6x105 + 7x104 + 8x103 + 1x102 + 9x101 + 7x100
Our Number System
John Napier of Merchistoun, Scotland (1550 – 4 April 1617)
invented the Decimal Point enabling us to write fractional
amounts efficiently.
1/2 becomes 0.5
1/10 becomes 0.1 = 10-1
1/100 becomes 0.01 = 10-2
1/3 becomes 0.33333…
(which goes to show that our system isn’t perfect either!)
We often use this to write very large or very small numbers.
The speed of light is 3.0 x 108 meters/second
Roman Number System
Look at the numbers 1, 13, 147 again
The Romans used different symbols for different quantities.
1 = I
13 = XIII
147 = CXLVII
13 = 10 + 3 = X + III
147 = 100 + 40 + 7 = C + XL + VII
The Romans didn’t have a symbol for 0, which is why they
had to use separate symbols for everything.
Babylonian Writing System (Cuneiform)
The Babylonians wrote on soft clay tables
which were then baked to make the writing
permanent.
(don’t make fun…we “burn” DVDs)
Their written number system (cuneiform)
took advantage of this by using stencils
with two basic patterns that are repeated
to make more complex numbers.
Sexagesimal Number System (Base 60)
At 60, the pattern starts all over again…
72 =
= 60 + 10 + 2
Problems with the Babylonian System
There is no symbol for zero.
So the number 60, is identical
to the number 1…
60 =
61 =
83 =
There is no decimal point either, so ½ = 30/60 =
Indistinguishable from 30
Benefits of the Babylonian System
All the simple fractions are
easily expressed as a single
number
1/2 = 30/60 =
1/3 = 20/60 =
1/4 = 15/60 =
Of course, 1/7 is going to cause
some problems, but it does in our
system too…
1/7 = 0.142857142857…
1/5 = 12/60 =
1/6 = 10/60 =
Metric System
Today’s metric system improves on the Babylonian system.
It is base 10, instead of 60.
But we have extra conveniences:
We use 0 to represent zero (nothing)
We use a decimal point to indicate a fractional portion
The name of the unit of measure indicates the scale
1 meter = 10 decimeters = 100 centimeters = 1000 millimeters
1 kilometer = 1000 meters
Our scientific notation takes advantage of this.
The Moon
When can you see the Moon?
The Moon
When can you see the Moon?
It depends on state of the Lunar Cycle.
The Moon can be out in either the Daytime or the Nighttime.
Lunar Phases
The Moon goes through phases,
which are subdivided into quarters
Timing of the Lunar Cycle
Lunar Cycle repeats about every 28 days.
Each month has just a little more than 28 days.
So the cycle repeats roughly every Month.
Dividing the cycle into 4 stages, gives us 7 days per stage.
Each seven day block is called a Week.
Since 360 = 30 x 12
And
30 ~ 28
There are a little more than 12 lunar cycles per year.
This is why we have 12 Months per Year
The Phases are a Lighting Effect
Sun-Based Calendar
We use a Sun-based calendar, so the lunar phases do not
exactly coincide with the months.
The Jewish and Muslim calendars are Moon-based calendar,
which is why Passover (and subsequently Easter) as well as
Ramadan are on different days each year in our calendar. The
Jewish calendar includes a leap month once every few years
to help synchronize it with the solar year, so that Passover is
on a different day each year in the Muslim calendar, as well.
Constellations
What is a constellation?
Constellations
What is a constellation?
Constellation comes from the Latin constellationem, which
means “set with stars”
A constellation is simply a group of stars defined by tradition.
We use them in Astronomy to denote a neighborhood in the
sky. The constellation tells you about which direction to look
in the sky.
Other groupings of stars are called Asterisms.
The Big Dipper is an Asterism, it belongs to the constellation
Ursa Major (The Big Bear).
Constellations
Lets go look at some constellations with Celestia
We will travel to some of the Stars and see what happens to
the constellation
http://www.shatters.net/celestia/
Many Stars Have Names
Star Names can be:
Arabic
Greek
Roman
English
Named after Constellation
Catalog Number
Betelgeuse
Bellatrix
Alnilam Mintaka
Alnitak
Saiph
Rigel
Constellation of Orion
Constellation and Signs of the Zodiac
Constellations denote
neighborhoods or
directions in space
The Signs of the
Zodiac are the
constellations that the
Sun passes through
throughout the year.
Astronomy and Astrology
Astronomy and Astrology used to be the same study.
Both were used to predict when the seasons would happen,
when eclipses would happen, when the lunar cycles would
happen and so on.
But the two split when Astrology tried to predict too much from
the motions in the sky.
To this day…
Astronomy is a Science
Astrology is a Pseudo-Science
Planets
It turns out that the Sun is
not the only one
apparently moving through
the constellations of the
Zodiac.
Long ago, people noticed
other “stars” that did this.
The Greeks called them
Planets which means
“Wanderers”
They were then named
after the Gods of
Olympus.
Planets
Mercury
Venus
Mars
Jupiter
Saturn
Note that Jupiter was the
King of the Gods. He was
also called Jove or Zeus.
By Jove!
Zeus = Dios = God
Jupiter = God the Father
Days of the Week
Coincidentally, there are 7 main objects in the Sky
These were associated with gods
More or less, we name the days of the week after them…
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
English
Spanish
French
Object
Moon’s Day
Tīu’s Day*
Odin’s Day
Thor’s Day
Frige’s Day***
Saturn’s Day
Sun ‘s Day
Lunes
Martes
Miercoles
Jueves
Viernes
Sabado**
Domingo
Lundi
Mardi
Mecredi
Jeudi
Vendredi
Samedi
Dimanche
Moon
Mars
Mercury
Jupiter
Venus
Saturn**
Sun
*Tiu was the Germanic version of the God of War or Mars
**In Hebrew Shabtai = Saturn, this is the origin of the word Sabbath
***Germanic equivalent of Venus
Planets
Lets go look at some planets with Celestia
We will examine them from multiple viewpoints
References
M. Fowler, “Galileo and Einstein”
http://galileoandeinstein.physics.virginia.edu/
Earth Analemma
http://antwrp.gsfc.nasa.gov/apod/ap061223.html
Martian Analemma
http://antwrp.gsfc.nasa.gov/apod/ap061230.html
My apologies to those whose images I have neglected or was unable to reference.