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Lecture 11

AST 101 Lecture Notes - Lecture 11: Seismic Wave, Celestial Mechanics, Orbital Period


Department
Astronomy
Course Code
AST 101
Professor
Walter Freeman
Lecture
11

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Exam%scores%still%in%the%process%of%fixing
Most%errors%from%typos%some%yours,%some%mine%
Writing%assignment%due%October%10%(next%Monday)%Due%by%noon%TAs%
mailboxes%are%in%front%of%room%201%(main%office)%
Warmup%question%for%next%Tuesday%will%be%sent%out%tomorrow
Slides%are%here:%
https://walterfreeman.github.io/ast101/slides/lecture11.pdf
Announcements
Quotes%of%the%Day%Summary:%Newton%believed%everything%was%simple
Planets%travel%in%elliptical%orbits,%with%the%Sun%at%one%Focus
The%line%going%from%the%Su%to%the%planet%sweeps%out%equal%areas%in%equal%
times
The%time%that%a%planet%takes%to%go%around%the%sun%increases%as%the%3/2%
power%of%the%long%axis%of%the%ellipse
Kepler's%Laws,%Summarized
Kepler's%Second%Law
Each%colored%wedge%has%the%same%area,%and%the%planet%takes%the%same%
time to%go%through%each
Kepler’s%third%law%of%orbital%motion%says%that%the%square%of%a%planet’s
orbital%period is%proportional%to%the%cube%of%its semi-major%axis.%
Simply%put:%if%a%planet%is%further%from%the%Sun,%it%takes%longer%to%go%
around.
If%the%distance%is%doubled,%the%time%required%more%than%doubles
Planet Axis Orbital%Period
Saturn 10%AU 30%Years
Uranus 20%AU 84%Years
Earth 1%AU 1%Year
Finding%Uranus'%Orbital%Period%->%Math!%->%20^(3/2)%Period%=%~84%Years
Kepler's%Third%Law
Kepler%figured%out%what%had%eluded%everyone%else:%a%precise%description%
of%the%orbits%of%the%planets
But%he%thought%there%was%more:%that%the%planets'%orbits%were%caused by%
the%interplay%of%more%fundamental%agents
He%didn't%have%a%good%name%for%them:%we%now%call% them%"gravity"%and%
"inertia".
Where%are%we%now?
"It%is%useful%to%start%with%the%way%you%intuitively%believe% nature%to%work%
and%formulate%a%question%based%on%that%and%then%formulate%an%
experiment%to%discover%if%the%way%you%believe% nature%works%is%correct."%-
Anna
Focusing%on%the%perspective%of%Earth%only%leads%us%awry%in%Astronomy%
studies.%-Taylor
Student%Responses%to%Pre-Class%Question:
§The%Motion%of%the%Stars
§The%Near-Perfect-Spheres%of%the%planets%and%moons
§The%elliptical% motions%of%the%planets%(?)
§The%Colors%in%a%rainbow
Obviously%the%World%around%us%is%very%Diverse.%Some%things%in%it%look%
quite%simple:
§Seismic%waves%and%Earthquakes
§The%colors%in%the%Sun
§The%weather
§The%Diversity%of%rocks%in%the%Earth
§Even%the%simplest%living%things...language,%culture,%music,%art,%and%all%
the%creations%of%humankind
Others,%though,%are%maddeningly%complex:
Natural%Laws%vs.%Their%Consequences
The%Laws%of%the%Universe%are%simple%and%elegant
§i.e.%Lego%buildings
The%things%the%Universe%builds%out%of%them%are%often%complex!%
Elegance,%Revisited
1642-1727%(or%1726,%calendars%are%weird)
Finally%figured%out%the%laws%that%eluded%Kepler
§Forces%cause%objects%to%change%their%velocities
§Calculus%-The%Mathematics%of%Changes
§Gravity%is%such%a%force
§The%mathematical%description%of%gravity
§Principles%of%Optics
§The%mathematics%of%cooling
§…and%much%more
He%discovered
Isaac%Newton
"Forces%cause%objects%to%accelerate"
F%=%ma
F/m%=%a
F%is%force,%m%is%mass,%a%is%acceleration
Newton's%Biggest%Idea
Newton%showed%mathematically%what%Kepler%suspected
§Proportional%to%the%product%of%their%masses
§Inversely%proportional%to%the%distance%between%them%squared
All%objects%attract%all%other%objects%with%a%force%that%is:
§F=(Gm1m2)/r2
§This%is%all%of%celestial% mechanics
In%symbols:
The%Law%of%Gravity
Evolution)of)Science
Thursday,%October% 6,%2016
2:00%PM
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