Fermi Problems and Scale of the Universe

Advanced Introduction to Astronomy

Spring 2014 Pomona College

by Dr. Bryan E. Penprase

An Example of a “Flipped” Class!!

Fermi ProblemsFermi Problems

Enrico Fermi, U. of Chicago Physics professor (and pioneer

of nuclear physics) at the chalkboard

Fermi ProblemFermi Problem

How many cars are in Claremont?

35,000 = Population of Claremont

2.28 = average cars / household in the US

2.5 = average household size in US

Best Guess:

a). 15,000b). 20,000c). 35,000d) 50,000e). 60,000

Fermi ProblemFermi Problem

How many cars are in Claremont? Best Guess:

a). 15,000b). 20,000c). 35,000d) 50,000e). 60,000

Classic Fermi ProblemClassic Fermi Problem

How Many Piano Tuners are there in Chicago?

Population of Chicago = 2.7 million (2013)

Number of families - 1 million (using 2.7 = avg family size)

Number of pianos?

~7% would be at income level with kids -> 75,000 pianos

Fermi CalculationsFermi Calculations

each piano tuned every 3 years -> 25,000 tuned per year

tuner can do about 5 per day -> 5*360 days = 1800 per year

need 25,000 / 1800 = 14 full-time tuners in Chicago

Fermi ProblemFermi Problem

How many planets are in the universe?

1011 = Average Stars per galaxy

1011 = number of galaxies (estimated)

2.3 = average number of planets per star

(based on current research)

a). 1011

b). 2x1011

c). 1022

d) 2x1022

e). 4x1023

Best Guess:

Fermi ProblemFermi Problem

How many planets are in the universe?

1011 = Average Stars per galaxy

1011 = number of galaxies (estimated)

2.3 = average number of planets per star

(based on current research)

a). 1011

b). 2x1011

c). 1022

d) 2x1022

e). 4x1023

Best Guess:

The Size of Things

Moving Through Space to the Edge of the Universe

by Dr. Bryan E. Penprase

Near Earth Environment

Geosynchronous Orbit

Limit of Human Travel(1.25 light seconds)

Solar System

1 AU = 8 light minutes

Limit of Human Spacecraft(Voyager 1: 125 AU; Voyager 2: 102 AU)

unexplored

Nearby Stars (with parallax)

Nearest star (3 light years)

Next Spiral Arm(500 pc)

Nearby Galaxies

LMC and SMC (50kpc)

Andromeda Galaxy (0.9 Mpc)

Galactic Center (8.5 kpc)

Virgo Cluster of Galaxies (10 Mpc)

Edge of the Universe

Distant GalaxiesLarge Scale Structure

(100 Mpc)

First “free” photons (13.7 billion lyrs-300klyrs)

Half way back to origin of time and space (z=1)

Most distant quasars“Dark Ages” (unexplored)

Our Place in the Universe

Our Place in the Universe (continued)

The Cosmic Distance Ladder - The first rungs (to Milky Way Center)

ParallaxVenus Transit - measure of AUStellar ParallaxEarly studiesModern techniques (Hipparcos + SIM)

Distance Ranging•Radar studies of planets•Laser lunar ranging•Timing of Spacecraft signals

Secondary Techniques•Standard Candles•Cepheids + Spectroscopic Parallax

This part will include history of transit expeditions; especially poor French dude Voyager exercise to recreate parallax; Retrograde loops and order of mag calculations; definition of parsec; intro to proper motionHistory of telescopes and first proper motion and parallax measurementsModern techniques -- Hipparcos sattelite and upcoming Kepler and SIM missionsIf time allows -- do simulation with the Partiview program where one sees stars moving.Ask David Haley to be sure “Digital Universe” is installed on laptops; can do 3D imageing and proper motions both.

This part will include history of transit expeditions; especially poor French dude Voyager exercise to recreate parallax; Retrograde loops and order of mag calculations; definition of parsec; intro to proper motionHistory of telescopes and first proper motion and parallax measurementsModern techniques -- Hipparcos sattelite and upcoming Kepler and SIM missionsIf time allows -- do simulation with the Partiview program where one sees stars moving.Ask David Haley to be sure “Digital Universe” is installed on laptops; can do 3D imageing and proper motions both.

This part will include some interesting information on early radar studies; some calculations for distances to different planets. Try to find some good footage of lunar ranging (email our friend teaching with us - ask for talk slides or movie)Include information on spacecraft and alternate theories of gravity

This part will include some interesting information on early radar studies; some calculations for distances to different planets. Try to find some good footage of lunar ranging (email our friend teaching with us - ask for talk slides or movie)Include information on spacecraft and alternate theories of gravity

Include basic concept of standard candle. Give some information on number of photons from different sources. Sun for example - kw + photons per square cm per second.Then scale for sun at distance of 1 pc. Include idea of flux units and basis for inverse square lawThis will set us up for discussion of light on next class (Tuesday).

Include basic concept of standard candle. Give some information on number of photons from different sources. Sun for example - kw + photons per square cm per second.Then scale for sun at distance of 1 pc. Include idea of flux units and basis for inverse square lawThis will set us up for discussion of light on next class (Tuesday).

Flying through the Big Dipper

Flying through Orion