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Lecture 2: Our Place in the UniverseLecture 2: Our Place in the Universe

Prof. Jonathan Fortney

September 28, 2010

Astro 18: Planets and Planetary Systems

UC Santa Cruz

Asteroid Ida and satellite Dactyl

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Topics for this classTopics for this class

• Some definitionsSome definitions

• What is our place in the universe?What is our place in the universe?

• The earth and its place within the Solar SystemThe earth and its place within the Solar System

• The Solar System’s place in the Milky Way GalaxyThe Solar System’s place in the Milky Way Galaxy

• Our galaxy in the universe at largeOur galaxy in the universe at large

• Geometry of the Solar SystemGeometry of the Solar System

• Plane of the planets’ orbitsPlane of the planets’ orbits

• Tilt of the earth’s axisTilt of the earth’s axis

• The sky at nightThe sky at night

• The cosmic distance scaleThe cosmic distance scale

• The expansion of the universe and the Big BangThe expansion of the universe and the Big Bang

Please remind me to take break at

12:45

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• A large, glowing ball of gas that generates A large, glowing ball of gas that generates heat and light through nuclear fusionheat and light through nuclear fusion

What is a Star?What is a Star?

• Nuclear Fusion:– Energy

generation mechanism in which two light atoms join together (fuse) to form a heavier atom

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1. Planet: Intuitive Definition1. Planet: Intuitive Definition

• A moderately large object that orbits a star.A moderately large object that orbits a star.

• It shines mostly by reflected light from its parent star. It shines mostly by reflected light from its parent star.

Mars Neptune

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2. Planet: International 2. Planet: International Astronomical Union DefinitionAstronomical Union Definition

• A celestial body that A celestial body that

(a) is in orbit around the Sun(a) is in orbit around the Sun

(b) has sufficient mass for its self-gravity to overcome (b) has sufficient mass for its self-gravity to overcome rigid body forces, so that it assumes a hydrostatic rigid body forces, so that it assumes a hydrostatic equilibrium (nearly round) shape, and equilibrium (nearly round) shape, and

(c) has cleared the neighbourhood around its orbit.(c) has cleared the neighbourhood around its orbit.

• Note that by design, this definition only applies Note that by design, this definition only applies to planets in our Solar System. Definition of to planets in our Solar System. Definition of planets in other Solar Systems was postponed planets in other Solar Systems was postponed until future deliberations of the IAU.until future deliberations of the IAU.

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Moon (or satellite)Moon (or satellite)

An object that An object that orbits a planet.orbits a planet.

Ganymede (orbits Jupiter)

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AsteroidAsteroid

A relatively small A relatively small and and rockyrocky object object that orbits a star.that orbits a star.

Ida

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CometComet

A relatively A relatively small and small and icyicy object that object that orbits a star.orbits a star.

Tail (gas

and dust)Comet nucleusComet nucleus

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GalaxyGalaxy

• A very large grouping of stars in space, held A very large grouping of stars in space, held together by gravity and orbiting a common center.together by gravity and orbiting a common center.

• Masses: 10Masses: 1077 - 10 - 101313 times the mass of our Sun times the mass of our Sun

M31, The Great Galaxy in Andromeda

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Notation: Orders of magnitudeNotation: Orders of magnitude

• 101022 = 100 = 1 with 2 zeros after it = 100 = 1 with 2 zeros after it

• 101033 = 1000 = 1 with 3 zeros after it = 1000 = 1 with 3 zeros after it

• 101099 = 1 with 9 zeros after it = 1 billion = 1 with 9 zeros after it = 1 billion

• 10101111 = 1 with 11 zeros after it = 100 billion = 1 with 11 zeros after it = 100 billion

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Suppose you tried to count the more than 100 billion Suppose you tried to count the more than 100 billion stars in our galaxy, at a rate of one per second… stars in our galaxy, at a rate of one per second…

How long would it take you?How long would it take you?

A.A. a few weeksa few weeks

B.B. a few monthsa few months

C.C. a few yearsa few years

D.D. a few thousand yearsa few thousand years

Thought QuestionThought Question

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How did I know this?How did I know this?

• A year has about 3 x 10A year has about 3 x 1077 seconds seconds

• 100 billion stars = 10100 billion stars = 101111 stars stars

or “a few thousand years”or “a few thousand years”

1011 stars ×1 secstar

×1 year

3×107sec≈

1011

3×107 years≈103

⎛⎝⎜

⎞⎠⎟×103years

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Our Sun moves randomly relative to the other Our Sun moves randomly relative to the other stars in the local Solar neighborhood…stars in the local Solar neighborhood…

• … and orbits the galaxy every 230 million years.

• Typical relative speeds of more than 70,000 km/hr (!)

• But stars are so far away that we cannot easily notice their motion

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The real Milky WayThe real Milky Way

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Detailed study of Milky Way’s rotation reveals Detailed study of Milky Way’s rotation reveals presence of “dark matter” (!)presence of “dark matter” (!)

Most of Milky Way’s light comes from its disk and bulge …

…. but most of the mass is in its dark halo. We don’t yet know what it’s made of.

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UniverseUniverse

• The sum total of all matter and The sum total of all matter and energyenergy

• That is, everything within and That is, everything within and between all galaxiesbetween all galaxies

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How big is the Universe?How big is the Universe?

• The Milky Way is one of about 100 billion galaxies.

• 1011 stars/galaxy x 1011 galaxies = 1022 stars in the universe

As many stars as grains of (dry) sand on all Earth’s beaches…

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What is our place in the universe?What is our place in the universe?

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Geometry of the Earth relative to Geometry of the Earth relative to the Solar Systemthe Solar System

• The Sun and all the planets except Pluto lie in a The Sun and all the planets except Pluto lie in a “plane” called the “Ecliptic plane”“plane” called the “Ecliptic plane”

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But Earth’s rotation axis is But Earth’s rotation axis is notnot perpendicular to this planeperpendicular to this plane

• Earth’s rotation axis is inclined at 23.5 degreesEarth’s rotation axis is inclined at 23.5 degrees

• North rotational pole points to the North Star, PolarisNorth rotational pole points to the North Star, Polaris

Note that both rotation and motion around Sun are counterclockwise, if you are looking from above the N pole

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How is Earth moving in our solar system?

• Contrary to our Contrary to our perception, we are perception, we are not “sitting still.”not “sitting still.”

• We are moving with We are moving with the Earth in several the Earth in several ways, and at ways, and at surprisingly fast surprisingly fast speeds…speeds…

The Earth rotates around its axis once every day.

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The “Celestial Sphere”The “Celestial Sphere”

Stars at different Stars at different distances all distances all appear appear to lie on to lie on the “celestial the “celestial sphere.”sphere.”

Ecliptic is Sun’s Ecliptic is Sun’s apparent path apparent path through the through the celestial sphere. celestial sphere.

Because our Solar Because our Solar System lies almost System lies almost in a plane, planets in a plane, planets follow paths along follow paths along ecliptic as well.ecliptic as well.

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The Local SkyThe Local Sky

Zenith: The point directly overhead

Horizon: All points 90° away from zenith

Meridian: Line passing through zenith and connecting N and S points on horizon

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Results of the tilt of Earth’s axisResults of the tilt of Earth’s axis

• SeasonsSeasons

• Apparent motions of stars in skyApparent motions of stars in sky– and how these vary with where you are on the Earthand how these vary with where you are on the Earth

• Apparent paths of planets and Sun along the Apparent paths of planets and Sun along the eclipticecliptic

• Precession of the Earth’s axisPrecession of the Earth’s axis– in 15,000 AD, the “North Star” won’t be Polaris any in 15,000 AD, the “North Star” won’t be Polaris any

more, it will be Vega (the brightest star in the Summer more, it will be Vega (the brightest star in the Summer Triangle) Triangle)

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Seasons: Key conceptsSeasons: Key concepts

• Earth's rotation axis is tilted with respect to its Earth's rotation axis is tilted with respect to its orbital planeorbital plane

• Tilt angle changes the angle of sunlight striking Tilt angle changes the angle of sunlight striking the Earth's surfacethe Earth's surface

• At a fixed location on the Earth, the angle of the At a fixed location on the Earth, the angle of the sunlight varies with timesunlight varies with time

• Seasons!Seasons!

• Other planets have different tilts, and thus Other planets have different tilts, and thus different types of seasonsdifferent types of seasons

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Seasons: summer is when your Seasons: summer is when your hemisphere is tipped toward Sunhemisphere is tipped toward Sun

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Seasons: summer is when your Seasons: summer is when your hemisphere is tipped toward Sunhemisphere is tipped toward Sun

Note: Earth is closest to Sun in January, farthest in July!

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What causes the seasons, cont’dWhat causes the seasons, cont’d

Tilt of Earth’s Tilt of Earth’s axis causes axis causes sunlight to be sunlight to be spread out spread out differently in differently in summer and summer and winterwinter

Click hereClick here

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Most extreme seasons in Solar Most extreme seasons in Solar System: 42-year summer!System: 42-year summer!

• Uranus is tipped on its Uranus is tipped on its side:side:

– Rotation axis lies almost in Rotation axis lies almost in its orbital planeits orbital plane

• Uranus takes 84 Earth-Uranus takes 84 Earth-years to go around the years to go around the SunSun

• So the North polar So the North polar regions of Uranus have regions of Uranus have summer (in this case, summer (in this case, continuous sunlight) for continuous sunlight) for 42 Earth-years!42 Earth-years! rotational pole

orbital plane

Uranus

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First ConcepTestFirst ConcepTest

I will pose a question on next slide.

First, each of you will have one minute to think about the answer (three multiple choices). This is not a trick question: think conceptually.

Then, break into groups of 2 or 3

You will have two minutes to convince your neighbors of the best answer. Discuss!

I will then ask for a show of hands for the three multiple choices, and we will discuss the results.

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ConcepTest OneConcepTest One

You are having an argument with a friend about what causes Earth’s seasons. Your friend insists the difference between summer and winter is that the Earth is closer to the Sun in summer than it is in winter. Which of the following is the best fact you can use to convince your friend that his/her explanation must be wrong? Why?

a) days are shorter in winter than in summer

b) if you are above the Arctic Circle in winter, there is a long period of time when the sun never rises

c) when it is winter in the Northern Hemisphere, it is summer in the Southern Hemisphere

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What does the universe look like What does the universe look like from Earth?from Earth?

With the naked With the naked eye, we can see eye, we can see more than 2,000 more than 2,000 stars as well stars as well as the Milky as the Milky Way (the plane Way (the plane of our Galaxy). of our Galaxy).

All the stars All the stars we see are in we see are in our own Galaxyour own Galaxy

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ConstellationsConstellations

A constellation is A constellation is a a regionregion of the of the sky. sky.

In our Western In our Western Civilization, 88 Civilization, 88 constellations constellations fill the entire fill the entire sky.sky.

Different cultures Different cultures have invented have invented different different constellations for constellations for themselves.themselves.

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Nightly motion of stars is straight up and Nightly motion of stars is straight up and down if you are at the equatordown if you are at the equator

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Nightly motion of stars is straight up Nightly motion of stars is straight up and down if you are at the equatorand down if you are at the equator

© Richard Pogge, Ohio State University.

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Nightly motion of stars is horizontal Nightly motion of stars is horizontal if youare at the North Poleif youare at the North Pole

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Nightly motion of stars is horizontal Nightly motion of stars is horizontal if youare at the North Poleif youare at the North Pole

© Richard Pogge, Ohio State University.

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Nightly motion of stars if youNightly motion of stars if youare at latitude 40 deg Northare at latitude 40 deg North

• Note: Latitude of Santa Cruz is 36.974 NorthNote: Latitude of Santa Cruz is 36.974 North

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Nightly motion of stars at lat 40 deg Nightly motion of stars at lat 40 deg North, looking to EastNorth, looking to East

© Richard Pogge, Ohio State University.

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Nightly motion of stars at latitude Nightly motion of stars at latitude 40 deg North, looking to North40 deg North, looking to North

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Nightly motion of stars at latitude Nightly motion of stars at latitude 40 deg North, looking to North40 deg North, looking to North

© Richard Pogge, Ohio State University.

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Where are we?Where are we?

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The Cosmic Distance Scale The Cosmic Distance Scale

• What is a light-year?What is a light-year?First discuss speed of light.First discuss speed of light.

• Light doesn’t travel infinitely fast. Light doesn’t travel infinitely fast.

• If light propagates in a vacuum (as in outer space), its If light propagates in a vacuum (as in outer space), its speed is a very specific number:speed is a very specific number:

c = 300,000 km/sec = 3 x 10c = 300,000 km/sec = 3 x 101010 cm/sec cm/sec

• At this speed, light would circle the Earth eight times in At this speed, light would circle the Earth eight times in 1 second1 second

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Since speed of light is constant, Since speed of light is constant, can use it to measure can use it to measure distancedistance

• distance = speed x timedistance = speed x time

• Use “dimensional analysis”:Use “dimensional analysis”:

– Write down units of each quantity in an equationWrite down units of each quantity in an equation– Then cross out places where the same unit is in a Then cross out places where the same unit is in a

numerator and denominatornumerator and denominator

• Example:Example:

€

L km( ) = ckm

sec

⎛

⎝ ⎜

⎞

⎠ ⎟× t sec( )

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Since speed of light is constant, Since speed of light is constant, can use it to measure can use it to measure distancedistance

• distance = speed x timedistance = speed x time

• Use “dimensional analysis”:Use “dimensional analysis”:

– Write down units of each quantity in an equationWrite down units of each quantity in an equation– Then cross out places where the same unit is in a Then cross out places where the same unit is in a

numerator and denominatornumerator and denominator

• Example:Example:

€

L km( ) = ckm

sec

⎛

⎝ ⎜

⎞

⎠ ⎟× t sec( )

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Define a light-yearDefine a light-year

• A light-year is the distance that light travels in A light-year is the distance that light travels in one Earth-yearone Earth-year

• How big is it?How big is it?

1 light-year = speed of light × 1 year

= 300,000 km

sec⎛⎝⎜

⎞⎠⎟× (1year) ×

365 days1 year

⎛⎝⎜

⎞⎠⎟×

24 hrs1 day

⎛⎝⎜

⎞⎠⎟×

60min1 hr

⎛⎝⎜

⎞⎠⎟×

60 sec1 min

⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥

= 9.46 trillion km

= 9.46 ×1012 km

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Some examples of light travel-timeSome examples of light travel-time

• The Moon:The Moon:– It takes light 1 sec to travel from the moon to the It takes light 1 sec to travel from the moon to the

Earth, so the Moon 1 light-sec away Earth, so the Moon 1 light-sec away

• The Sun:The Sun:– It takes light 8 minutes to travel from the Sun to the It takes light 8 minutes to travel from the Sun to the

Earth, so the Sun is 8 light-minutes awayEarth, so the Sun is 8 light-minutes away

• The nearest star, Proxima Centauri:The nearest star, Proxima Centauri:– It takes light about 4 years to travel from Proxima It takes light about 4 years to travel from Proxima

Centauri to the Earth, so this star is 4 light-years Centauri to the Earth, so this star is 4 light-years awayaway

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Implications of the finite speed of Implications of the finite speed of lightlight

• Because it takes light a finite amount of time to reach Because it takes light a finite amount of time to reach us,us,

the farther away we look in distance, the the farther away we look in distance, the further back we look in timefurther back we look in time

• In 1987 when we saw a supernova explosion in the In 1987 when we saw a supernova explosion in the Large Magellanic Cloud (a neighboring galaxy150,000 Large Magellanic Cloud (a neighboring galaxy150,000 light-years away), the supernova had actually exploded light-years away), the supernova had actually exploded 150,000 years ago 150,000 years ago

• When we look at galaxies that are more and more When we look at galaxies that are more and more distant from us, we are seeing them at younger and distant from us, we are seeing them at younger and younger stages of their evolutionyounger stages of their evolution

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At great distances, we see objects as they were At great distances, we see objects as they were when the universe was much youngerwhen the universe was much younger

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Example: new stars being formed in Example: new stars being formed in the Orion Nebulathe Orion Nebula

• The Orion The Orion Nebula is 1,500 Nebula is 1,500 light-years away.light-years away.

• We see the Orion We see the Orion Nebula as it Nebula as it looked 1,500 looked 1,500

years ago.years ago.

• The “new stars” The “new stars” that we see that we see actually formed actually formed 1,500 years ago1,500 years ago

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Example: the Andromeda Example: the Andromeda GalaxyGalaxy

• This photo shows the Andromeda Galaxy as it This photo shows the Andromeda Galaxy as it looked about 2 1/2 million years ago. looked about 2 1/2 million years ago.

Question: When will we be able to see what it looks like now?Question: When will we be able to see what it looks like now?

M31, The Great Galaxy in Andromeda

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ConcepTest TwoConcepTest Two

If the speed of light were half what it is now, then a “light-If the speed of light were half what it is now, then a “light-year” would year” would

a) take half as long to traverse at light speeda) take half as long to traverse at light speed

b) take the same amount of time to traverse at light b) take the same amount of time to traverse at light speedspeed

c) last twice as many monthsc) last twice as many months

d) last half as many monthsd) last half as many months

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The expansion of the universe and The expansion of the universe and the Big Bangthe Big Bang

• Observation:Observation:– Virtually every galaxy outside our Local Group is moving away Virtually every galaxy outside our Local Group is moving away

from usfrom us– The farther away a galaxy is, the faster it is moving away from The farther away a galaxy is, the faster it is moving away from

usus– How is the observation made? From Doppler shift of spectral How is the observation made? From Doppler shift of spectral

lines (will discuss in later lecture). lines (will discuss in later lecture). » Color of light becomes redder if the object emitting the Color of light becomes redder if the object emitting the

light is moving away from us.light is moving away from us.

• Recession velocities are large:Recession velocities are large:– tens of thousands to 100’s of thousands of km/sectens of thousands to 100’s of thousands of km/sec

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What’s going on?What’s going on?

• EntireEntire universe is expanding universe is expanding– (It’s not that everybody hates us....)(It’s not that everybody hates us....)

• Furthermore, at Furthermore, at everyevery place in the universe, it place in the universe, it looks like the rest of the galaxies are all looks like the rest of the galaxies are all receding, and more distant galaxies are receding, and more distant galaxies are receding fasterreceding faster

• Analogies to help understand this:Analogies to help understand this:– A jungle gym that whose bars are all getting longerA jungle gym that whose bars are all getting longer– A sponge cake that is expanding as it bakesA sponge cake that is expanding as it bakes

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““Local Sponge Cake” ExampleLocal Sponge Cake” Example

• EveryEvery raisin sees all the raisin sees all the other raisins moving other raisins moving away from itaway from it

• More distant raisins More distant raisins move away fastermove away faster

Click hereClick here

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The Big BangThe Big Bang

• This is as far back as we can hope to measureThis is as far back as we can hope to measure

• EveryEvery place in the universe was (almost) place in the universe was (almost) infinitely dense and infinitely hotinfinitely dense and infinitely hot

• Ever since the Big Bang, the universe has been Ever since the Big Bang, the universe has been expanding, becoming less dense (on the expanding, becoming less dense (on the average), and cooling offaverage), and cooling off

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ConcepTest ThreeConcepTest Three

There must be some very large distance such that light There must be some very large distance such that light from a galaxy at that distance hasn’t reached us during from a galaxy at that distance hasn’t reached us during the age of the universe. The expansion velocity of the age of the universe. The expansion velocity of galaxies at that distance, relative to us, must begalaxies at that distance, relative to us, must be

a) zeroa) zero

b) infiniteb) infinite

c) less than the speed of lightc) less than the speed of light

d) the speed of light or greaterd) the speed of light or greater

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The Universe in motion...The Universe in motion...

Earth rotates on axis: > 1,000 km/hr

Earth orbits Sun: > 100,000 km/hr

Solar system moves among stars: ~ 70,000 km/hr

Milky Way rotates: ~ 800,000 km/hr

Milky Way moves in Local Group

Universeexpands

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Orders of magnitude movieOrders of magnitude movie

Click here

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What have we learned?What have we learned?

• How can we know that the universe was How can we know that the universe was like in the past?like in the past?– When we look to great distances we are When we look to great distances we are

seeing events that happened long ago seeing events that happened long ago because light travels at a finite speedbecause light travels at a finite speed

• Can we see the entire universe?Can we see the entire universe?– No, the observable portion of the universe is No, the observable portion of the universe is

about 14 billion light-years in radius because about 14 billion light-years in radius because the universe is about 14 billion years oldthe universe is about 14 billion years old

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Our Celestial AddressOur Celestial Address

Earth and Planetary Sciences B210Earth and Planetary Sciences B210

UCSCUCSC

Santa CruzSanta Cruz

CaliforniaCalifornia

USAUSA

The EarthThe Earth

The Solar SystemThe Solar System

The Milky Way GalaxyThe Milky Way Galaxy

The Local Group of GalaxiesThe Local Group of Galaxies

The Local Supercluster of GalaxiesThe Local Supercluster of Galaxies

The UniverseThe Universe

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Reading assignmentsReading assignments

• Thursday Sept 30th. Bennett:Thursday Sept 30th. Bennett:

– Chapter 3 sections 3.2 through 3.5 Chapter 3 sections 3.2 through 3.5 – Chapter 4 (all)Chapter 4 (all)

• Prior to your first lab section next week:Prior to your first lab section next week:

» The Cosmic Perspective: Appendix C (“A Few The Cosmic Perspective: Appendix C (“A Few Mathematical Skills”)Mathematical Skills”)

• Tuesday October 5th. More discussion of Tuesday October 5th. More discussion of Bennett Chapter 4Bennett Chapter 4

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Homework assignmentsHomework assignments

• Due todayDue today

– Homework 1 (Please include photo!)Homework 1 (Please include photo!)– Stellarium Activity Part 1Stellarium Activity Part 1

• Due Thursday Sept 30Due Thursday Sept 30thth (in preparation for (in preparation for stargazing that night)stargazing that night)

– Stellarium Activity Part 2 – posted on class webpageStellarium Activity Part 2 – posted on class webpage

• Due Tuesday October 5thDue Tuesday October 5th

– Homework 2 (will be posted on class webpage)Homework 2 (will be posted on class webpage)

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Labs and sections will start next Labs and sections will start next weekweek

• Jenn Burt will circulate sign-up sheets for Jenn Burt will circulate sign-up sheets for timeslots of:timeslots of:

• Sections (two timeslots – you only have to come Sections (two timeslots – you only have to come to one section)to one section)

• Labs (every other week)Labs (every other week)

• Then we will look for classroomsThen we will look for classrooms

• Results will be posted on web, and announced in Results will be posted on web, and announced in class on Thursdayclass on Thursday

Our first stargazing Our first stargazing session will be this session will be this Thurs nightThurs night

• Wear warm clothes!Wear warm clothes!

• Bring a flashlight if Bring a flashlight if you have oneyou have one

• Bring binoculars if Bring binoculars if you have themyou have them

• Weather? Check the Weather? Check the astronomy club astronomy club website right before website right before you come to confirmyou come to confirm