2nd Midterm: Mean: 85 St.Dev: 11

For help:For help: See GSI or Prof. Manga or Prof. Marcy

2nd Midterm: Common Mistakes

1. Greenhouse Effect:• CO2 absorbs IR light (not UV).

• 2. Geological activity on Jupiter’s moons is due to their composition of ice: Allows melting at low temperatures in the outer solar system.

Volcanism and tectonics possible.

Announcements• Homework due a week from Friday: • Chapter 13 on Planets Around Other Stars Homework counts 50% of grade; Drop lowest score.

• Final Exam - comprehensive: May 20 @ 8am: 237 Hearst Gym

• Telescope Observations: Saturn, Mars, Orion Nebula. Observing Starts: 8pm ! Star Chart with 3 obs of Mars: Due May 1.

Wednesday, April 23, 5:30pmChevron Auditorium - International House

"The Dawn of Creation: The First Two Billion Years"

A Special Lecture by

Steven Beckwith

Extra Credit: 3 points for half-page summary of talk

Are there Other Planetary Systems ?Are there Other Planetary Systems ?

Are any of them Are any of them

like our Solar System ?like our Solar System ?

February 5, 1996

Now Exiting our Solar System to …Now Exiting our Solar System to …

The Milky Way Galaxy. .. . ..

. .. . . .. .

..

. . ..

. . ..

..

Now Leaving our Solar System . . .

Democritus:Greek philosopher (460 - 370 BC).

“ There are innumerable worlds of different sizes. These worlds are at irregular distances, more in one direction and less in another, and some are flourishing, others declining. Here they come into being, there they die, and they are destroyed by collision with one another. Some of the worlds have no animal or vegetable life nor any water. “

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Epicurus (341-270 B.C.)

“There are infinite worlds both like and unlike this world of ours ... we must believe that in all worlds there are living creatures and plants and other things we see in this world…”

Greek philosopher in Athens where he opened a school of philosophy

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• Bruno was enthusiastic about the Copernican theory that the planets circle the sun and he believed there are many other planets around other stars, some of them with life.

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Giordano Bruno 1584

Giordano Bruno lost the thread of truth and the Roman Church burned him for it.

http://www.gospelcom.net/chi/DAILYF/2002/02/daily-02-17-2002.shtml

Wrote; ‘De l'infinito, universo e mondi  (The Infinity, the Universe and Its Worlds)

Burned at the Stake February 17, 1600

By Catholic Church

Stars are a billion times brighter…

…than the planet

hidden in the glare.

Detecting Earths: Like detecting a firefly next to a nuclear explosion

Planet DetectionPlanet Detection

The Wobble of a Star:The Wobble of a Star:

Gravitational pullGravitational pullby the planetby the planet

Star moves slower, due to Star moves slower, due to conservation of momentum: mass x velocityconservation of momentum: mass x velocity

MMSTARSTAR V VSTARSTAR = M = Mplanetplanet V Vplanetplanet

1/2 m1/2 mPLPLVVPLPL2 2 == G mG mPLPLMMStarStar / r / r

VVPL PL ~ 10 ~ 10 km/skm/s

VVStarStar = = VVPLPL VVSTARSTAR ~ 10 ~ 10 m/sm/s xx (M(MPLPL /M /MJUPJUP))

Momentum:Momentum:

WobbleWobbleVelocityVelocity

MMPLPL

MMSTARSTAR

( )

Detecting a Star’s Wobble: Detecting a Star’s Wobble: Doppler EffectDoppler Effect

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Detecting the wobble Detecting the wobble of a Star, pulled of a Star, pulled around by its planet.around by its planet.

SpectrumSpectrumstarlightstarlight

12 years12 years . . . Jupiter . . . Jupiter

(Met

ers/

sec)

Need Telescope . . .

Echelle Spectrometer

CCD

Echelle

Grating

Collimator

StarlightStarlight

From TelescopeFrom Telescope

High Resolution ``Echelle”High Resolution ``Echelle”

SpectrometerSpectrometer

Spectrum of Star:Spectrum of Star:

Doppler EffectDoppler Effect

Doppler Shift:Doppler Shift: = v / c= v / c

4096 Pixels

Michel Mayor & Didier Queloz

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51 Peg

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Claim of First Detected Extrasolar Planet:Claim of First Detected Extrasolar Planet:5151PegasiPegasi

Orbital Period = 4.2 days ! Absurd Orbital Period = 4.2 days ! Absurd

One week Later . . .

4 Nights at Lick Observatory

October 11, 1995

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Period = 4.2 days

Kepler’s 3rd Law: P2 = a3

Units: P in years, a in AU

Solve for a:a = 0.05 AU

Proximity: Temp = 1500 C

Determination of Orbital Distance from Star to Planet

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Determination of Planet’s Mass

Conservation of Momentum: Conservation of Momentum: momentum of star = momentum of planetmomentum of star = momentum of planet

MMSTARSTAR V VSTARSTAR = = MMplanetplanet V Vplanetplanet

Solve for Mass of planet:Solve for Mass of planet:MMplanetplanet = M = MSTARSTAR V VSTARSTAR / V / Vplanetplanet

MSTAR : Star Masses are known (most are Sun-like)

VSTAR from Doppler shift: 55 m/s

What is Vplanet ?

Vplanet = 2 a / PYou know “a” from Kepler’s 3rd Law: P2 = a3

Can Determine Mplanet

Summary of Doppler Wobble MethodSummary of Doppler Wobble Method::Orbital PhysicsOrbital Physics

Kepler’s 3rd Law and Conservation of MomentumKepler’s 3rd Law and Conservation of Momentum

PP22 = 4 = 4 22/[G(M/[G(Mstarstar + M + Mplanetplanet)] a)] a33

P = orbital period a = orbital distance of planet from starP = orbital period a = orbital distance of planet from star

Simple Version of Kepler’s 3rd Law:Simple Version of Kepler’s 3rd Law:

PP22 = 4 = 4 22/GM/GMstarstar a a3 (3 (planet’s mass is negligible compared to star.)planet’s mass is negligible compared to star.)

Measure P from Doppler periodicity: Can solve for a.Measure P from Doppler periodicity: Can solve for a.

Circular Orbit: VCircular Orbit: Vplanetplanet = 2 = 2 a / P (Circumference/Time) a / P (Circumference/Time)

Momentum Conservation:Momentum Conservation:

MMstarstar V Vstarstar = M = MPlanetPlanet V Vplanetplanet

Mplanet = Mstar Vstar / VPlanet

Doppler Wobble Method:Unknown Orbital Inclination

Tilt of Planet’s Orbital Plane: UnknownTilt of Planet’s Orbital Plane: Unknown• Edge-on Orbit: Full Doppler EffectEdge-on Orbit: Full Doppler Effect• Face-on Orbit: No Doppler EffectFace-on Orbit: No Doppler Effect• General Tilt Angle: True Wobble speed is General Tilt Angle: True Wobble speed is greater than Doppler indicatesgreater than Doppler indicates

True planet mass is GREATER than theTrue planet mass is GREATER than themass found by the Doppler method. (25% greater mass found by the Doppler method. (25% greater

on Avg.)on Avg.)

We measure M sin i

Period = 4.2 days

Kepler’s 3rd Law: P2 = a3

Units: P in years, a in AU

Solve for a:a = 0.05 AU

Proximity: Temp = 1500 C

51 PegasiFirst Extrasolar Planet

16 Cygni 16 Cygni BBMass = 1.7 M

JUP (Min)

Orbit PeriodOrbit Period

2.2 yr2.2 yr

Not SinusoidalNot Sinusoidal

VelocitVelocit

yy

WobbleWobble

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Velocity

Orbit of Planet around 16 Cygni

16 Cygni: Planet & Moon

Life on Gas Giant Planets ?Life on Gas Giant Planets ?

FloatersFloaters

Earth-Like MoonEarth-Like Moon

Eccentric Orbit ! of Planet around 16 Cygni

Orbital Eccentricities

• <e> = 0.25• Tidal Circ.• Origin of Eccent.

Unknown

Origin of Eccentricities

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Planet - Planet Gravitational Interactions

Mass = 0.62 MMass = 0.62 MJUPJUP

70 Days70 Days

Upsilon AndromedaeUpsilon Andromedae::Velocity ResidualsVelocity Residuals

0.6 M0.6 MJUPJUP

2 M2 MJUPJUP

4 M4 MJupJup

Upsilon Andromedae:Upsilon Andromedae:

Triple Planet SystemTriple Planet SystemPlanets havePlanets haveNo NamesNo Names

..

..

..

..

.

..

..

..

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Upsilon AndromedaeUpsilon Andromedae