unit 1 a - university of floridalada/ast1002/astlectclassnotes.pdf · the earliest calendars...
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Unit 1 a
How Big is Big?How far away is the Moon?
240,000 miles = 384,000 km = 1 light second
What does this really mean?How many McDonald’s hamburgers would it take to get
from here to the Moon?How long would it take to drive there?
How Big is Big?It would take 19 billion or 19000000000 or19x109 hamburgers to reach the Moon.
This is about 20% of the hamburgers thatMcDonalds has ever sold!
Driving 80 miles per hour, it would take3000 hours or about 4 months of non-stopdriving!
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How Big is Really Big?• The solar system - our nearest planetary
neighborhood– Size of Earth: 8,000 mile diameter– Size of Jupiter: 88,000 mile diameter– Size of the Sun : 800,000 mile diameter
Relative Sizes of the Sun and Planets
See also http://www.troybrophy.com/projects/solarsystem/index.html
How Big is Really Big?
• The solar system - our nearest planetaryneighborhood– Size of Earth: 8,000 mile diameter– Size of Jupiter: 88,000 mile diameter– Size of the Sun : 800,000 mile diameter– Distance from Sun to Mercury: 36,000,000 miles– Distance from Sun to Earth: 93,000,000 miles– Distance from Sun to Jupiter: 500,000,000 miles
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How Big is Big?• Distance to the nearest star:
20000000000000 miles• Diameter of Our Galaxy:
200000000000000000 miles• Distance to Andromeda Galaxy
20000000000000000000 miles• Distance to most distant Galaxy:
100000000000000000000000miles
• Size of helium atom:0.0000000000001 miles
Scientific Notation• Distance to the nearest star: 20000000000000 miles
= 2x1013
• Diameter of Our Galaxy: 200000000000000000 miles= 2x1017
• Distance to Andromeda Galaxy20000000000000000000 miles = 2x1019
• Distance to most distant Galaxy:100000000000000000000000 miles = 1x1023
• Size of helium atom: 0.0000000000001miles = 1x10-13
Scientific Notation
• Multiplication– 2x1010 X 4x105 = (2X4)x10(10+5) =8x1015
• Division– 10x1010 / 5x1015 = (10/5)x10(10-15) = 2x10-5
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Powers of 10
Question• The distance between stars in our galaxy is
very large compared to the size of the stars.Thus, the galaxy is mostly empty space.
• Why do galaxies get damaged when onegalaxy hits another?
Question
• The atoms in your body are even moreempty than the space within our solarsystem.
• Why is it that when you clap your handsthey do not just pass through eachother?
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Question
What daily motions do you observe ofdifferent celestial objects?
Daily MotionsSun
Daily MotionsStars
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Solar and Sidereal DaysWhy is the Solar Day longer than the Sidereal Day?
Coordinate system on Earth
Gainesville: 29.6510N, 82.3250W
Celestial Sphere
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Annual Motions of the Sun
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Annual Motion of Sun
Annual Motionof the Stars
Annual Motions of the Stars
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Where are we?
• The position of acelestial pole nearthe horizon, tells uswe must be nearthe Equator. Alsoconsider the anglesthe star trails makewith the horizon: 90degrees.
Question• You are kidnapped, drugged and placed in a dark room
for an indefinite period of time!• You escape and find a radio to call for help but you don’t
know where you are!• Luckily, it’s a clear night. You watch the stars for while
and you see the stars rising at a 20 degree angle withrespect to your horizon.
• What can you tell your rescuers about your location?
Seasons• With the annual motion of the Earth around the
Sun, we notice a cyclic pattern in the weather,know as the seasons.
• Observations:Seasons are reversed in the Northern andSouthern Hemispheres
•For example, you’re at the beach at Cape Cod inJuly, they’re skiing in New Zealand!
The region near the equator is hottest; poles are the coldest
The Sun’s position in the sky changes
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Reasons for the Seasons?
• What causes this pattern?• Two Possible Models:
– Distance of the Earth from the Sun?– Tilt of the Earth’s axis with respect to the
Earth’s orbital plane (ecliptic)
Reason for Seasons:Distance?
• Predictions:– Relation between Earth-Sun distance and
season• for example, the Earth should be closest to the
Sun in summer– Same season every where on Earth
• since the Earth is tiny compared to the Earth-Sun distance
Reason for Seasons:Distance?
• Observations:
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Reason for Seasons:Distance?
• Predictions don’t match Observations:– Seasons are reversed in the Northern and
Southern Hemispheres• For example, you’re at the beach at Cape Cod
in July, they’re skiing in New Zealand!– The Earth is closest to the Sun during
northern winter
Reason for the Seasons: Tilt?The Earth’s axis of rotation is tilted by 23.5
degrees with respect to the ecliptic pole
Reason for the Seasons: Tilt?• Predictions:
– Summer occurs in hemisphere pointedtoward the Sun
– Winter occurs in the hemisphere pointedaway from the Sun
– Therefore: Seasons are reversed innorthern and southern hemisphere
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Reason for the Seasons: Tilt
Reason for the Seasons: Tilt
Reason for the Seasons
• Demonstration
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Reason for the Seasons: Tilt
• Predictions match observations:– The northern hemisphere and southern
hemisphere seasons are reversed– The region near the equator is hottest;
poles are coldest
Question• When is the hottest time of year in Quito Ecuador?• If the Earth’s rotation axis was perpendicular to it’s
orbital plane (ecliptic), what would you expect theseasons to be like?
• If the Earth’s rotation axis was parallel to it’s orbitalplane (ecliptic), what daily and annual effects wouldthis have?
Example of the ScientificMethod
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Motion of the MoonEast to west in arc across sky
Eastward w.r.t. stars - half degreeper hour
Sidereal Period - 27.3 days
Moon rises ~ 50 minutes later each day
Phases of theMoonWhy does the Moon Shine?
Reflected sunlight
Half of the Moon isalways lit up
Fraction of lit surface wesee from Earth - phase
How much of the Moon is litup by Sun?
Synodic Period - 29.5 days
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Sidereal & Synodic Periods
Sidereal Period: 27.3 days
Synodic Period: 29.5 days
Phases of theMoon
• The changes in the Moon’s phaseare due to changes in the anglebetween the Sun, Moon and theEarth
– 0 degrees : New Moon
– 90 degrees: Quarter Moon(First or Third)
– 180 degrees: Full
Question • If the Sun sets at 6pm, whendoes a first quarter Moon rise?
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A First Quarter Moon rises at noon
Eclipses
• A solar eclipse occurs when the Moon movesbetween the Earth and the Sun
• A lunar eclipse occurs when the Earth movesbetween the Sun and the Moon and the Moon movesthrough the Earth’s shadow
• In ancient cultures eclipses were bad omens
The Moon Moves Over the Face of theSun
•
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The Sun is Nearly Covered
•
The Diamond Ring
Total Solar Eclipse
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Angular Size of Sun and Moon
• The Sun and Moon have very differentphysical sizes– Radius of Sun is 7x105 km– Radius of Moon is 1.7x103 km– So the Sun is 400 times bigger than the
Moon!!• How can they appear to be nearly the
same size during an eclipse?
Angular Size• Answer: the Moon and Sun,
coincidentally, have nearly the sameangular size
• Angular size of an object depends ontwo things– The physical size of the object– The distance to the object
Angular size (radians)= Physical Size
Distance
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An Annular Solar Eclipse
Question
• Why does an annular eclipse lookdifferent?
Shadows & Eclipses
• A total solar eclipse can seen from only a small region onthe Earth– entire disk of the Sun covered– In umbra or inner shadow the Moon
• Partial solar eclipses are seen over a larger area– only part of the Sun is covered by the Moon– in the penumbraor Moon’s outer shadow
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• The Moon’sshadow movesover the Earthduring a solareclipse
Paths of Solar Eclipses
Next solar eclipse visible from USAAug. 21st 2017
http://sunearth.gsfc.nasa.gov/eclipse/eclipse.html
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When and How Often Are Eclipses
partial, total orannular eclipse- 3 to 5 timeseach year
total eclipse -0 to 3 times ayear
Solar eclipses occurat new moon
New moon crossesecliptic
The Lunar Eclipse
• total lunar eclipse - the Moon moves completely throughthe Earth’s umbra
• partial lunar eclipse - the Moon moves partially throughthe Earth’s umbra
• Penumbral eclipse – the Moon passes through thepenumbra but does not come in contact with umbra
• Lunar eclipses are visible anywhere on the night-timeside of the Earth
A Lunar Eclipse
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Question
• Why is the Moon’s surface still visibleduring a total lunar eclipse?
When & How Often?• Lunar eclipses occur at FULL
Moon PHASE• Lunar eclipses do not occur
every month because theMoon’s orbital plane is tiltedwith respect to the ecliptic– a total lunar eclipse occurs
when the Moon crosses theecliptic at full Moon
– since the Earth’s shadow ismuch bigger than the Moon,total lunar eclipses occurmore often than solareclipses
Lunar eclipses occur 2 to 5 times per year
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Motion of the Planets• The planets are the brightest
objects in the night sky (with theexception of the Moon)
• Rise in the east and set in the west• Planet means “Wanderer”
– The planets move slowly amongthe stars staying near the ecliptic
– Different planets move at different speeds relative to thestars (of the visible planets,Mercury is the fastest, Saturn isthe slowest)
– They move in complex patternschanging their direction ofmotion
Motion of the Planets• Planets generally move eastward relative to the stars• Planets undergo retrograde motion
– motion relative to stars:• slows• reverses• moves westward relative to stars• slows again• reverses again• resumes its general eastward motion
• This motion is unique among all astronomical objects• This confused & perplexed people for centuries & led
people of many cultures to attribute superior powers tothe planets
Inferior Planets• Venus and Mercury• Stay near the Sun on
the sky• Are visible only near
sunrise and sunset(“morning & eveningstars”)
• Move away from theSun and then movetoward it
Mercury - (ca. 15th
century)
Mercury is holding abag for commerce andtwin snakes for healingpowers.
Reigns over Virgo &Gemini
Venus depicted in the AztecCodex: Aztec god, Xolotl(evening star) at thecrossroads of fate. Laterbecame twin of Quetzalcoatl(morning star & supreme god)
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Superior Planets• The visible superior
planets are Mars,Jupiter and Saturn
• Can appear far fromthe Sun but remainnear the ecliptic
Mars & VenusFresco from Pompeii(ca. 1 A.D.)
Mars is the war-god& Venus, the god oflove.
Saturn (ca. 18th century) - Arabicillustration showing agriculturalactivities under direction of Saturn
Planets, Gods & Days ofWeek
• English names for mostof the days of the weekcome from Norse gods
• Tuesday : Tiwes - godof war
• Wednesday: Woden -god of day & night
• Thursday: Thor - god ofthunder - head god
• Friday: Frega - goddessof spring
15th centuryengraving ofdays of theweek andtheirastrologicalcounterparts
Ancient Astronomy• Since pre-historic times, ancient
people have observed andrecorded the regular & cyclicpatterns in the sky
• To explain these motions, a dualdevelopment in human thoughtbegan:– search for natural &
unchanging laws– creation of mythology
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The Earliest Calendars• During the stone age (50,000 years ago) people first
began to leave a record in carvings and paintings.These included:– Pictures of constellations– The first calendars
25,000 year old Ishango bone (Congo, Africa)with possible lunar phase calendar
14 Phases of the moon seen in cave paintingsin Lascaux, France (18,000 BC)
Early Calendars-Alignments• Many archaeological sites reveal alignments with prominent celestial
events.• Archeoastronomy is the study and interpretation of such alignments.
– The reality of such alignments can be scientifically verified– The cultural significance (e.g. purpose) has been lost to time– However, it is reasonable to assume that at least one purpose was to
predict the seasons, possibly for agriculture, hunting, migration…..
Hopi sunrisecalendar
•Observed by a“Sun priest” atPueblo
•Used to anticipateceremonials
Stonehenge c.a. 2800BC
• Constructed and reconstructed on SalisburyPlain in England over thousands of yearsbeginning about 2,800 BC
• Probably used as a calendar and almanac ofsolar and lunar motion
• Stones were brought from many miles awayshowing its importance
• There are many other similar Neolithic (newstone age) sites throughout Britain
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STONEHENGE
The Great Pyramid c.a.2600BC
• Celestial bodies had greatsignificance in Egyptian cultureand was integrated into theirreligion
• Pyramids are the tombs ofEgyptian Pharaohs, who werebelieved to be divine gods whowere connected to the stars
• The side of the Pyramids were very accurately alignednorth-south
•The passages and shafts within the Pyramids may havebeen aligned with astronomical bodies (Orion and a PoleStar)
•The Pole star was called an “imperishable star” since itnever sets and the spirit of the Pharaoh would journey there
The Great Pyramids• The Great Pyramids of Gaza
may have been arranged in thepattern of the constellation ofOrion
• Orion had special significance inancient Egypt & represented thegod Osiris
• Osiris is the god of birth, death &resurrection
• By placing such a configurationon the ground, the god wasbrought to Earth
• The pyramids were placed alongthe Nile, which may haverepresented the Milky Way
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Chichén Itzá c.a. 600-830AD• Chichén Itzá was an important Mayan & Toltec
ceremonial site on the Yucatan• Prominent alignments with Venus & Sun rise &
set were made through windows in the tower ofthe Caracol
Venus, as the morning star, was prominent in Mayan religion and representedtheir most important godQuetzaloatl
Chichén Itzá c.a. 600-830AD
• Widows in the top of pyramid arealigned with sunrises at the solstices
• There are also alignments (notshown) with the sunset points of theequinoxes
– step shadow projects onto northern orsouthern staircase
El Castillo - a Mayan pyramid at Chichén Itzá
North America - ChacoCanyon
• Chaco Canyon was home to the Anasazi People from900 - 1300 A.D.
• Anasazi means “ancient ones” in Navajo• Atop of Fajada Butte, are 3 large stone slabs and a
petroglyph know as the Sun Dagger• The stones are aligned such that at noon on the
solstices & equinoxes, 1 or more daggers of the Sun’slight strike the petroglyph key locations.
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Other North American Sites
• Casa Grande in Southern Arizona• A Hohokam pueblo built about 1000 A.D.• Hohokam means “those who have gone”• Windows are aligned with solar and lunar events
• Medicine Wheel in Wyoming• Built by Native Americans of the High Planes
• Rocks laid out in a 90 foot circle
• Radial spokes are aligned with the positions ofsunrise and sunset at the solstices and are alsoaligned with the rising & setting positions ofbright stars
Asian Alignment Sites
• Located in Gao ChengZhen, China, this giantgnomon was 1st built 2000years ago (Han Dynasty)
• Light passes through a 40 fthigh window - wall’s shadowis measured on a largehorizontal scale
• City of Vijayanagara in India - 14th century• Layout of city is aligned N-S & alignments withPole Star and other Astronomical objects
Constellations
PatternsOfStars
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Constellations
StableOver Human History
ConstellationsReflect the cultures × of the peoplewho created them
The oldest constellations used by astronomers today originated ~ 3000 BC in Mesopotamia
Southern hemisphere constellations used by astronomers originated in the 17th century by sailors
Constellations
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Orion the Hunter• Orion is a prominent winter
constellation• Located near the Celestial Equator so
it can been seen from eitherhemisphere
• Located near the Milky Way
Orion• Greek Mythology
– Orion, son of Poseidon and a great,fearless hunter
– His arrogance angered the goddess Herawho sent a scorpion to kill him
– The Moon god Artemis placed him in thesky far away from Scorpio
• Jewish - the Biblical Samson• Arab - Al Jabbar the giant• China - Hunter and warrior Tsan• Brazilian - A Cayman “cousin of the gator”• Egypt - The God Osiris
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Ursa Major & Minor• Ursa Major is the most prominent northern
circumpolar constellation• Ursa Major contains the “Big Dipper” asterism• Ursa Minor contains the “Little Dipper”
asterism
Ursa Major
Ursa Minor Big Dipper
Ursa Major & Minor• Two stars in the front end of the Big
Dipper point to Polaris• Greco-Roman Mythology
– Callisto & Zeus were lovers & had ason, Arcas. Hera, Zeus’ wife, was angryand turned Callisto into a bear. Yearslater, Arcas was hunting & was about tokill his mother, so Zeus stepped in &threw them both into the sky. Hera stillwanted revenge so she made the paircontinually circle the sky, never beingable to refresh themselves in the River-Ocean that encircle the Earth.
Ursa Major• Aztec - Tezcatlipoca- Peg legged god
associated with death & the north• Hindu - the seven Rishi or primordial sages• Chinese - chariot carrying sages• Basques - 2 bullocks followed by 2 thieves,
watched by a herdsman & his 2 servants• Egyptian - ox pulling a man with a
hippopotamus and alligator on his back• Seen as a bear in many cultures despite its
long tail. Perhaps this is due to the notion thatit prowls around the sky like a bear.
Persian Representation
Arab Representation
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Early Views of the Cosmos
• Ancient world pictures ofthe cosmo– geocentric - Earth
centered– finite - had boundary
• typically a shell ofstars closed offthe universe
• Ancient cosmologiespaid little attention tocelestial motions even ifcelestial cycles werecarefully observed
Nut,Egyptiangoddess ofsky, archedover Geb,god of Earth
Coloredwood cut byFrenchastronomerFlammarioncirca 1880
Babylonians
• The Babylonians were among the firstpeople known to have keptastronomical records– careful observers– kept continuous written records of
observations on clay tablets– observations used for making calendars
& predicting celestial motions• Babylonian Cosmos:
– finite cosmos– no specific shape to Earth– stars attached to a shell far beyond
Earth– Sun entered through a gate at edge of
Universe Babylonian tablet recordingastronomical informationcirca 550 B.C.
Ancient Views of the Cosmos• Egyptian:
– Earth is flat– Sky is like a flat plate support by 4 mountains– Sun is carried across the sky in a boat from
east to west. At night Sun is carried back tothe east through the Underworld
• India:– Earth is a circular disk surrounded by the
ocean– great mountain in center of world– Sun goes around mountain once a day
• China:– sky is a round dome, surrounding Earth– Earth is square– Sun travels in a big tilted circle
Egypt
India
China
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Early Greeks• Ancient Greek astronomers were the first to attempt to
explain the workings of the heavens in a careful,systematic way using naked eye observations andmodels
• Greeks enjoyed philosophy which to them meant theattempt to understand all things in nature
• They used their highly developed mathematical skills(geometry & trigonometry) & logic to makeremarkable discoveries about their universe
Aristotle & A Spherical Earth• Aristotle (384-322 B.C.) showed by proof
that the Earth was spherical:1 He observed that the Earth’s shadow is
curved during a lunar eclipse– “The shapes that the Moon itself shows are
of every kind -straight, gibbous, and concave- but in eclipses the outline is always curved:and since it is the interposition of the Earththat makes the eclipse, the form of this linewill be caused by the form of the Earth’ssurface which is therefore spherical” -Aristotle’s treatise On the Heavens
Painting ofAristotle byRembrandt
Aristotle & A Spherical Earth
2 Aristotle learned from travelers that theheight of the Pole star above the horizonvaries as you travel from North to South• Going North: Polaris gets higher with
respect to the horizon• Going South: Polaris gets lower with
respect to the horizon• Go far enough south -- Polaris no longer
visible
⇒Earth must be spherical!
Flat Earth Spherical Earth
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Question
• Aristotle also reasoned that the Earthwas spherical by watching ships leaveport and sail off towards the horizon. – What would you observed about a ship
sailing away from you if you lived on a:• Flat Earth ?• Spherical Earth ?
Aristarchus of Samos(310-230 B.C.)
• Estimated relative sizes of the Moon & Earth– timed duration of lunar eclipses– compared the time it takes the Moon to enter
the Earth’s shadow with the time it takes theMoon to cross the Earth’s shadow
• Estimated distance to Moon– measured angular size of Moon & compared
this to the estimate of the Moon’s size relativeto Earth’s diameter
• Estimated distance to Sun– assumed Moon’s orbit was circular & uniform– measured intervals between 1st and 3rd
quarter phases of the Moon & for 1 completephase cycle
– compared these intervals to determine theMoon-Earth - Sun angle
Aristarchus of Samos(310-230 B.C.)
• Estimated size of Sun– from total Solar Eclipse using
relationship between angulardiameter, size and distance
Aristarchus estimated all these quantities in terms of the Earth’s diameter
⇒ Aristarchus found that the Sun was much bigger & much farther awaythan the Moon⇒ He therefore concluded that the Sun, not the Earth was at the center ofthe Universe
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7.20 5000 stadia=
Eratosthenes (c. 200 B.C.)Eratosthenes estimated the Earth’s diameter, and therebytook the relative measurements of Aristarchus and placedthem on an absolute scale
3600 Earth’s circumference7.20 5000 stadia
Hipparchus (c. 150 B.C.)• Erected an observatory on Rhodes & built instruments to
measure as accurately as possible the direction of objectsin sky
• compiled catalog of stellar coordinates - 850 entries• discovered precession - Earth’s axis of rotation (about the
celestial sphere) continually changes• refined Aristarchus’ technique to measure Moon’s size &
distance– 29.5 Earth diameters (actual distance = 30 Earth diameters)
• determined length of year to within 6 minutes• carefully observed motions of Moon, Sun & planets• predicted lunar eclipses to within 1 hour• 1st to deal with the problem of parallax for solar eclipses &
predicted the paths of totality for solar eclipses• Developed a geometrical, geocentric model of the
Universe
Scientific Models• Conception of a physical model to explain the workings of nature
is a creative act of science• Models apply known laws of nature to explain observations• Key aspects of a scientific model
⇒ models explain what is seen⇒ models predict observations accurately⇒ simplify your understanding of nature
• Validity of models is tested by checking how well predictions fit thebest & new observations
• Scientific models are not static but evolve when new & betterobservations become available
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Modeling the Cosmos• Key Observations to Explain
– Motion of Sun• East to West in about 12 hours from
sunrise to sunset• West to East along ecliptic ~ 10 per day• variation in speed along the ecliptic• variation of length of day & height of Sun
with season– Motion of Moon
• East to West in about 12 hours 25 minutesfrom Moonrise to Moonset
• West to East within 50 of ecliptic• sidereal & synodic periods
Modeling the Cosmos• Key Observations to Explain
– Motion of Stars• East to West in ~ 12 hours
from star rise to star set• star rise is ~ 4 minutes
earlier each day• circumpolar stars• stars in fixed position
relative to one another• precession• yearly motion relative to
Sun
Modeling the Cosmos• Key Observations to Explain
– Motion of Planets• East to West in ~ 12 hours from rising
to setting; interval varies depending onrate of planet’s motion with respect tostars
• West to East, within 70 of ecliptic• Average speed varies along ecliptic
– fastest for Mercury– slowest for Saturn
• Variation in speed along ecliptic foreach planet
• Retrograde motion from West to Eastat a time specific for each planet