Physics 112Star Systems

Lecture 2Motions of the Heavens

Kevin H. KnuthUniversity 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 basiccomponents:

YearMonthDay

The year is divided into12 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.

12. 18. 17. 16. 6. 6 Cimi 19 Kayab

Calendar RoundBatkun Count

Haab(Civil Calendar)

Day (1-19) Month (1-19)

Tzolkin (260 Day Calendar)

Day (1-13) Sign (1-20)

Batkun Count Batkun Katun Tun Uinal Kin

Kin = 1 DayUinal = 20 kinsTun = 18 UinalsKatun = 20 Tun

Batkun = 20 Katun

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 wordsolstitium meaning the pointwhere 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 wordsolstitium meaning the pointwhere 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 wordequinoxium meaning equalityof 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 wordequinoxium meaning equalityof 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 Observatory600 – 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

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.

Babylon(56 mi south of modern Baghdad)

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

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.

Note that all of these ratios are divisible by 6.

Clearly 6 was important to the Babylonians.

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.

At 60, the pattern starts all over again…

72 = = 60 + 10 + 2

Sexagesimal Number System (Base 60)

There is no symbol for zero.

So the number 60, is identicalto the number 1…

60 =

61 =

83 =

There is no decimal point either, so ½ = 30/60 = Indistinguishable from 30

Problems with the Babylonian System

All the simple fractions areeasily expressed as a singlenumber

1/2 = 30/60 =

1/3 = 20/60 =

1/4 = 15/60 =

1/5 = 12/60 =

1/6 = 10/60 =

Benefits of the Babylonian System

Of course, 1/7 is going to cause some problems, but it does in our system too…

1/7 = 0.142857142857…

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 portionThe name of the unit of measure indicates the scale

1 meter = 10 decimeters = 100 centimeters = 1000 millimeters1 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

RigelSaiph

Alnitak

Alnilam Mintaka

Bellatrix

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

MercuryVenusMarsJupiterSaturn

Note that Jupiter was the King of the Gods. He was also called Jove or Zeus.

By Jove!Zeus = Dios = GodJupiter = God the Father

Days of the Week

Coincidentally, there are 7 main objects in the SkyThese were associated with gods

More or less, we name the days of the week after them…

English Spanish French Object

Monday Moon’s Day Lunes LundiMoonTuesday Tīu’s Day* Martes MardiMarsWednesday Odin’s Day Miercoles MecrediMercuryThursday Thor’s Day Jueves Jeudi

JupiterFriday Frige’s Day*** Viernes VendrediVenusSaturday Saturn’s Day Sabado** SamediSaturn**Sunday Sun ‘s Day DomingoDimanche 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 Analemmahttp://antwrp.gsfc.nasa.gov/apod/ap061223.html

Martian Analemmahttp://antwrp.gsfc.nasa.gov/apod/ap061230.html

My apologies to those whose images I have neglected or was unable to reference.