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Life on Other Planets?

Four hundred years ago an advocate of the idea that planets orbited starsother than our Sun was burned at the stake. Giordano Bruno, a rebellious,independent Dominican monk (until he was kicked out of the order)further infuriated religious leaders by asserting in the late 16th centurythat beings like humans inhabited these other worlds. Let us now beginour study of extrasolar planets.

Jerry Gilfoyle ExtraSolar Planets 1 / 20

How Do We Find Extra-solar planets?

1 Look here first.2 Look here second.


https://www.youtube.com/watch?v=DY3LYQv22qY

https://facultystaff.richmond.edu/~ggilfoyl/cm/links/spinningMolecule1.3gp


1 Look here first.

2 Look here second.





1 Look here first.2 Look here second.




A Planet Around 51 Pegasus

Consider the data below which shows the oscillations in the speed of thestar 51 Pegasus implying the existence of an unseen, orbiting companion.What is the period of the oscillation? How is this period related to thedistance from 51 Pegasus to the unseen companion? What do theseresults imply about the maximum mass of the unseen companion? Assumethe mass of 51 Pegasus is ms = 2.2 × 1030 kg from its spectral type andthat it is a distance rpeg = 51ly from Earth.

Mayor and Queloz, Nat. 378 355


‘Wobbling’ Stars

Consider a solar system consisting only of the Sun and Jupiter orbitingabout their center of mass. What is the size of the Sun’s ‘wobble’ as itorbits the center of mass? Compare the wobble with the radius of the Sun.If an alien species on a small planet (similar to Earth) orbiting 51 Pegasustried to observe the Sun’s wobble what would be the angular size of thewobble? The distance from 51 Pegasus to the is 51 ly.

Jupiter’s mass 1.90 × 1027 kgSun’s mass 1.99 × 1030 kgSun-Jupiter distance 7.8 × 1011 mSun’s radius 6.96 × 108 m1 light-year 9.46 × 1015 m

More on wobbling stars here.


https://en.wikipedia.org/wiki/Doppler_spectroscopy

The Doppler Effect


https://www.youtube.com/watch?v=h4OnBYrbCjY

Wobbling Stars


https://en.wikipedia.org/wiki/Doppler_spectroscopy

Measuring Stellar Velocities

The velocities of distant starstowards or away from the Earthare measured using small blue-or red-shirts of the absorptionlines like those shown here inthe spectra of a variety of stars.Several methods are used tokeep the spectra precisely cal-ibrated for the long periodsneeded to record the observa-tions.


51 Pegasus Location in the Sky


Is 51 Peg’s Planet Eccentric?

ε =

√1 +

2El2

µα2= 1 − 2

rarp

+ 1

ε = 0

0 < ε < 1

ra pr

Red - Circular orbit

Blue - Elliptical orbit

v=0

Time

Velo

city


https://en.wikipedia.org/wiki/Elliptic_orbit

51 Pegasus’ Planet Data


Orbital period: 4.2293 ± 0.0011dVelocity resolution: 13 m/s


Stellar Spectra

The spectral class is a method for classifying stars based on the pattern ofabsorption lines (which reveal the elements in the star’s photosphere) andtheir intensity (which reflects the abundance). These measurements canbe translated into the temperature and density of the star’s photosphere.

G-type

A-type

K-type


The Main Sequence

The main sequence of theHertzsprung-Russell diagram isthe curve where the majority ofstars are located in this diagram.This line is so pronounced be-cause both the spectral typeand the luminosity depend on astar’s mass only to zeroth orderas long as it is fusing hydrogen.


The Method of Trigonometric Parallaxes

To place a star on the Hertzsprung-Russell diagram the absolute luminosityhas to be determined. This step requires measuring the distance from theEarth to the star. Nearby stars appear to move with respect to moredistant background stars due to the motion of the Earth around the Sun.This apparent motion (it is not ”true” motion) is called Stellar Parallax.


Getting the Mass of the Star

The luminosity of main sequence stars is proportional to their mass asshown in the plot below. Thus identifying the spectral type places the staron the main sequence and then measurments of its luminosity can bedirectly related to its mass.


Orbital Plane Tilt

51 Pegasus

UnseenCompanion

Orbital Plane

Telescope

θ tilt


A Planet Around 51 Pegasus

Consider the data below which shows the oscillations in the speed of thestar 51 Pegasus implying the existence of an unseen, orbiting companionnow called 51 Pegasus b. What is the period of the oscillation? How isthis period related to the distance from 51 Pegasus to 51 Peg b? What dothese results imply about the maximum mass of the unseen companion?Assume the mass of 51 Pegasus is ms = 2.2 × 1030 kg from its spectraltype and that it is a distance rpeg = 51ly from Earth.



Planet Comparison

JupiterMSun= 392,000MEarth

Me

rcu

ry

Ve

nu

s

Ea

rth

Ma

rs

0 1 2 3 4 50

100

200

300

400

Distance from the Sun (A.U.)

Ma

ss(M

/M⊕)


Planet Comparison

JupiterMSun= 392,000MEarth

51 Pegasus b

Me

rcu

ry

Ve

nu

s

Ea

rth

Ma

rs

0 1 2 3 4 50

100

200

300

400

Distance from the Sun (A.U.)

Ma

ss(M

/M⊕)

HOT JUPITER!


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