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AST (90)

AST 101 (70)

Walter Freeman (30)

Lecture 11

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**preview**shows half of the first page. to view the full**3 pages of the document.**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%–TA’s%

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

1.

The%line%going%from%the%Su%to%the%planet%sweeps%out%equal%areas%in%equal%

times

2.

The%time%that%a%planet%takes%to%go%around%the%sun%increases%as%the%3/2%

power%of%the%long%axis%of%the%ellipse

3.

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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