2nd Midterm: Difficult Exam... Common Mistakes 1. Greenhouse Effect: CO2 absorbs IR light (not UV)....

2nd Midterm: Difficult Exam . . . 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 and flow at low temperatures in the outer solar system.

• 3. Titan retained its atmosphere because it’s cold: molecules don’t move fast enough to escape.

Announcements• Homework due a week from Friday (May 2): • Read Chapter 13: Planets Around Other Stars • Final Exam - comprehensive: May 20 @ 8am:

237 Hearst Gym • Telescope Observations: - Observing Starts: 8pm ! - Sketch 2 Objects & Star Chart (3 obs of Mars):

- Due Friday, May 2 (w/ HW) !

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

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

A Special Lecture by

Steven Beckwith

Be There !

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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http://en.wikipedia.org/wiki/Hellenic_civilization

http://en.wikipedia.org/wiki/Philosopher

http://en.wikipedia.org/wiki/460_BC

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



• 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.



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

Light Reflected off Planet

Area of Sphere: 4 R2

Cross Sectional Area of planet: r2

Fraction of Star lightThat hits planet:

a) r2

R

/ 4 R2

For Earth: Fraction is 10 -10

r

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 . . .

Quiz

The period of the sine wave is:

a) 2 dayb) 10 dayc) 20 dayd) 40 day

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



51 Peg



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



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



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

Quiz

From Doppler measurements, a star exhibits the sine wave variationIn velocity. The orbital plane is orientededge-on to us at Earth, causing the planet to block the star light.

a

b

c

dAt what point on the velocity plot

will the planet block the star light ?

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


Units: P in years, a in AU

Solve for a:a = 0.05 AU

Proximity: Temp = 1500 C

51 PegasiFirst Extrasolar Planet

Detecting Extrasolar PlanetsDetecting Extrasolar Planets




Momentum Conservation:Momentum Conservation:

MMSTARSTAR V VSTARSTAR = = MMplanetplanet V Vplanetplanet

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

2nd Midterm: Difficult Exam... Common Mistakes 1. Greenhouse Effect: CO2 absorbs IR light (not UV)....

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