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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