26
I E F C O D R I L A I N R D N X A E A E S I I C M L M V A A I A D R E L G E Einführung in die Astronomie I Jörn Wilms Sommersemester 2011 Büro: Dr. Karl Remeis-Sternwarte, Bamberg Email: [email protected] Tel.: (0951) 95222-13 http://pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro Erlangen-Nürnberg Friedrich-Alexander-Universität I E F C O D R I L A I N R D N X A E A E S I I C M L M V A A I A D R E L G E I E F C O D R I L A I N R D N X A E A E S I I C M L M V A A I A D R E L G E 1–1 Introduction I E F C O D R I L A I N R D N X A E A E S I I C M L M V A A I A D R E L G E 1–2 Preliminaries 1 Astronomie im Bachelorstudiengang Physik NF im Bachelor/Master: Zwei Module (Je 10 ECTS): NW1 (Grundkenntnisse) kann gewählt werden im 1./2., 3./4. oder 5./6. Semester NW2 (vertieft) kann gewählt werden u.a. im 4./5. Semester oder als NW im Masterstudium PW im Bachelorstudium: Modul für PW-1, PW-2, oder PW-3 PW im Masterstudium: geplant: PW-1, PW-2 und/oder PW-3 alternativ im Mas- terstudiengang I E F C O D R I L A I N R D N X A E A E S I I C M L M V A A I A D R E L G E 1–3 Preliminaries 2 Astronomie für LAG-Physik, BA Informatik und Mathematik physikalisches Wahlfach im LAG: NW-1 (10 ECTS): kann vorzugsweise gewählt werden im 5./6. Semester NF im Bachelor Informatik: Erweiterter NW-1 (15 ECTS): Besteht aus NW1 plus verpflichtende Übungen und kann gewählt werden im 5./6. Semester NF im Bachelor Mathematik: 35 ECTS: 1. und 2. Semester: Einführung in die Experimentalphysik I und 2 (je 7.5 ECTS) 3. und 4. Semester: Astonomie NW-1 (10 ECTS) 5. und 6. Semester: Astronomie NW-2 (10 ECTS), PW-1 (5 ECTS) weitere Fächer: Anfrage beim jeweiligen Prüfungsamt

KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

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Page 1: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

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ail:[email protected]

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13

http://pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro

Erlangen−Nürnberg

Friedrich−Alexander−Universität

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Page 2: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

WS

2009/1

0 u

nd S

S2010

1

1

NW

-1

Ein

füh

run

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n d

ie A

str

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to

Astr

on

om

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10 E

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: V

orlesung E

inf. in d

ie A

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it T

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WS

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as P

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nn

die

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zen

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rof. D

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t D

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f. D

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eber

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örn

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Mo

du

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nstitu

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alt

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odul gib

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um

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er

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sensch

aftlic

hen

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oden,

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es u

ns e

rlauben,

ihre

Entfern

ungen,

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ßenskale

n,

Massen u

nd p

hysik

alis

che N

atu

r zu v

ers

tehen.

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inzeln

en w

erd

en b

ehandelt:

Geschic

htlic

her

Hin

terg

rund d

er

Astr

onom

ie

Sonnensyste

m:

Pla

nete

nbew

egung u

nd K

eple

rsche

Gesetz

e,

Eig

enschaften d

er

Pla

nete

n u

nd d

er

kle

inen

Ob

jekte

im

So

nn

en

syste

m (

Ausw

ahl aus:

innere

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au

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n,

pla

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re O

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läch

en

, A

tmo

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ing

e),

extr

asola

re P

lanete

n.

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rne

: E

ntf

ern

un

ge

n,

Te

mp

era

ture

n,

Sp

ektr

en

, M

asse

n,

Hert

zspru

ng-R

ussell-

Dia

gra

mm

, in

ne

rer

Au

fba

u,

En

tste

hu

ng

un

d E

ntw

icklu

ng

, E

nd

sta

die

n d

er

Ste

rnentw

icklu

ng,

Doppels

tern

e.

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hstr

e u

nd a

ndere

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xie

n:

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au u

nd E

ntw

icklu

ng,

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ssifik

atio

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isch

er

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terie

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ala

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fen

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ählte M

eth

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er

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enutz

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skope,

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ete

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ers

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wic

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ur

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nd T

em

pera

ture

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astr

onom

ischer

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kte

able

iten.

können e

infa

che a

str

onom

ische M

essungen s

elb

st

durc

hfü

hre

n u

nd a

usw

ert

en.

erf

ahre

n e

in V

ers

tändnis

über

die

we

ite

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we

nd

ba

rke

it

WS

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nd S

S2010

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na

turw

isse

nsch

aft

lich

er

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tho

de

n d

urc

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de

r A

str

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otw

endig

e E

xtr

apola

tion v

on E

rgebnis

sen v

on

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essungen a

uf

astr

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kale

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entw

ickeln

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keiten z

ur

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atu

rwis

senschaftlic

her

Pro

ble

me,

ein

schlie

ßlic

h d

er

Fähig

keit z

ur

Bedie

nung

typ

isch

er

astr

on

om

isch

er

Instr

um

en

te.

7

Vo

rau

ssetz

un

gen

r d

ie T

eiln

ah

me

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e;

spezie

lles Z

ula

ssungsverf

ahre

n f

ür

Frü

hstu

die

rende.

8

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passu

ng

in

M

us

ters

tud

ien

pla

n

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Stu

die

nse

me

ste

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rüh

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sth

öre

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en

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ark

eit

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du

ls

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ngang P

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(nic

htp

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alis

cher

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ere

ich)

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hra

mt

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ysik

am

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na

siu

m (

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hlb

ere

ich

)

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die

rende a

ndere

r F

äch

er:

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hlb

ere

ich

10

Stu

die

n-

un

d

Prü

fun

gsle

istu

ng

en

Z

wei 60-m

inütige K

lausure

n z

u d

en V

orlesungen (

PL),

T

eiln

ahm

e a

m T

uto

rium

und a

n d

en P

raktikum

ste

rmin

en,

Durc

hfü

hru

ng d

er

Vers

uche,

Testa

te (

SL)

11

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ch

nu

ng

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od

uln

ote

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itte

lwert

der

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usurn

ote

n

12

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rnu

s d

es

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ge

bo

ts

Jährlic

h

13

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eit

sau

fwan

d

P

räsenzzeit:

180 h

E

igenstu

diu

m:

120 h

14

Dau

er

des M

od

uls

2 S

em

este

r (g

gf. 3

Sem

este

r, f

alls

das P

raktikum

im

W

inte

rse

me

ste

r a

bso

lvie

rt w

ird

) 15

Un

terr

ich

tssp

rach

e

Deuts

ch u

nd E

nglis

ch

16

Vo

rbere

iten

de

Lit

era

tur

H.

Ka

rttu

ne

n,

P.

Kro

ge

r, H

. O

ja, F

undam

enta

l A

str

onom

y,

Springer,

2003

M.

Kutn

er,

Astr

ono

my:

A P

hysic

al P

ers

pective,

Cam

bridge

Univ

. P

ress,

2003

I

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ine

mod

ulüb

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fung

.

=⇒

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izie

rtN

oten

gebu

ng!

=⇒

KLA

US

UR

am19

.Jul

i201

1

Kla

usur

führ

tzu

eine

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este

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ige

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nso

sind

Vor

schl

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und

Frag

enfü

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bung

ense

hrer

wün

scht

.

Page 3: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

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R

DN

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ed.,

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inge

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64(h

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),51

0pp

.G

ood

gene

ralo

verv

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ofas

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ende

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prep

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ion.

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ER

,200

3,A

stro

nom

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Phy

sica

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spec

tive,

2nd

ed.,

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niv.

Pre

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51,6

00pp

.M

oder

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ysic

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sed

text

book

,eas

yto

read

.R

ecom

men

ded.

BE

NN

ET

TE

TA

L.,

2009

,Ast

rono

mie

:D

ieko

smis

che

Per

spek

tive,

Pea

rson

Stu

dium

,e79

.95,

1200

pp.

Mod

ern

and

good

;Ger

man

tran

slat

ion

isno

tbad

,Rec

omm

ende

d.

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EF

CO

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Text

book

s

UN

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AS

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stro

nom

ie

und

Ast

roph

ysik

,7.

Aufl

age,

Ber

lin:

Spr

inge

r,e

60,5

77pp

.In

term

edia

tele

vel:

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dov

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lar

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Goo

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65,6

72pp

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term

edia

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vel,

self

cont

aine

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esch

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CA

RR

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toM

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Rea

ding

:A

ddis

on-W

esle

y,ca

.e

100

(har

dcov

er),

1400

pp.

Adv

ance

dle

vel,

expe

cts

good

phys

ics

back

grou

nd.

Rec

omm

ende

dif

you

wan

tto

spec

ializ

ein

astr

onom

y.

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

1–11

Con

tent

s1

Con

tent

s

03M

ayO

rgan

isat

ion,

Intro

duct

ion

10M

ayH

isto

ryof

Ast

rono

my

17M

ayP

lane

tsI

24M

ayP

lane

tsII

31M

ayP

lane

tsIII

07Ju

nP

lane

ts:

Tran

snep

tuni

ans,

Ast

eroi

ds,C

omet

s,M

eteo

rites

21Ju

nM

easu

rem

entM

etho

ds:

Tele

scop

es,C

oord

inat

es

28Ju

nS

tars

,Dis

tanc

es,L

umin

osity

,HR

D

05Ju

lS

tars

:B

inar

ies,

Mas

ses

&R

adii

12Ju

lE

xopl

anet

s

19Ju

lE

xam

!

26Ju

lS

tars

:F

orm

atio

n

Page 4: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–1

His

tory

ofA

stro

nom

y

Sto

nehe

nge:

2500

BC

;sol

arob

serv

ator

y?

Dis

kof

Neb

ra:

1600

BC

first

repr

oduc

tion

ofth

eni

ghts

ky,c

onst

ella

tion

ofM

oon

and

Ple

iade

s

mea

sure

sso

lstic

esan

deq

uino

xes=⇒

cale

ndar

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–4

His

tory

1

His

tory

Toge

ther

with

theo

logy

,ast

rono

my

ison

eof

the

olde

stpr

ofes

sion

sin

the

wor

ld.

Ast

rono

mic

alno

men

clat

ure

isst

illst

rong

lyin

fluen

ced

byth

istr

aditi

on.

=⇒

appr

ecia

tion

ofhi

stor

yof

astr

onom

yis

requ

ired

for

unde

rsta

ndin

gev

enof

toda

y’s

astr

onom

y.M

any

term

sus

edar

eba

sed

onth

ishi

stor

y,e.

g.m

agni

-

tude

sby

the

gree

kas

tron

omer

Hip

parc

os(∼

150

BC

)

Page 5: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–5

His

tory

1

Ear

lyC

osm

olog

y

Com

posi

teof

imag

esof

Mar

ssp

aced

∼a

wee

kap

art–

from

late

July

2005

(bot

tom

right

)th

roug

hF

ebru

ary

2006

(top

left)

.

Exp

lain

obse

rvat

ions

:

•da

ilym

otio

nsof

Sun

,

Moo

n,pl

anet

s&

star

s

from

Eto

W

•m

uch

slow

erm

otio

nof

Sun

&M

oon

with

re-

spec

tto

star

s

•oc

casi

onal

retr

ogra

de

mot

ions

ofpl

anet

s(E

to

W)

•so

lar

and

luna

rec

lipse

s

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–6

His

tory

1

Bab

ylon

Bab

ylon

ian

astr

onom

y:E

arlie

stas

tron

omy

(flou

rish∼

700

BC

)w

ithin

fluen

ceon

us:

=⇒

sexa

gesi

mal

syst

em[3

60:6

0:60

],24

h

day,

12×

30d

year

,...

=⇒

Obs

erva

tions

ofS

unan

dM

oon

=⇒

stel

lar

cons

tella

tions

,12

sign

sof

zodi

ac

=⇒

book

keep

ing

onso

lar

and

luna

r

eclip

ses,

Sar

oscy

cle:

18yr

11d

=⇒

desc

riptio

nof

plan

etm

ovem

ent

=⇒

cata

logi

ngst

ella

rpo

sitio

ns

Imag

e:M

ul.A

pin

cune

iform

tabl

et(B

ritis

hM

useu

m,

BM

8637

8,8

cmhi

gh),

desc

ribes

risin

gan

dse

tting

ofco

n-st

ella

tions

thro

ugh

the

baby

loni

anca

lend

ar.

Sum

mar

izes

astr

onom

ical

know

ledg

eas

ofbe

fore

∼69

0B

C.

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–7

His

tory

2

Gre

ek

Atla

sFa

rnes

e,2c

A.D

.,M

useo

Arc

heol

ogic

oN

azio

nale

,Nap

oli

Gre

ekA

stro

nom

ers:

“Mat

hem

atic

ians

deve

lopm

ento

fthe

geoc

entr

icw

orld

mod

el

•T

hale

s(6

24–5

47B

C):

Ear

this

flat,

surr

ound

edby

wa-

ter.

Fou

nder

ofN

atur

alP

hilo

soph

y

•P

ytha

gora

s(c

a.57

0–51

0B

C):

Ear

this

asp

here

.

“Eve

ryth

ing

isnu

mbe

r”A

harm

onic

univ

erse

(mus

ic)

re-

quire

sor

bita

lmot

ions

ince

rtai

nra

tios

ofin

tege

rnu

m-

bers

(see

Kep

ler:

Har

mon

ices

mun

di)

•P

lato

(427

–347

BC

):th

eci

rcle

isth

epe

rfec

tgeo

met

ric

form

,uni

form

circ

ular

mot

ion

iset

erna

l=⇒

“the

hex

of

circ

les”

•E

udox

us(4

08–3

55B

C):

Geo

cent

ric,p

lane

tsaf

fixed

to

conc

entr

iccr

ysta

lline

sphe

res.

27sp

here

sto

acco

unt

for

non-

unifo

rmm

otio

ns(d

oes

notw

ork

for

Mar

san

d

Ven

us).

Firs

trea

lmod

elfo

rpl

anet

ary

mot

ion!

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–8

His

tory

3

Gre

ek

Aris

totle

(384

–322

BC

,de

cael

o):

Refi

nem

ento

f

Eud

oxus

mod

el:

add

sphe

res

toen

sure

corr

ect

mot

ions

ofal

lpla

nets

:

>50

nest

edan

dlin

ked

sphe

res,

driv

enby

the

oute

rmos

tsph

ere.

=⇒

Cen

tral

philo

soph

yun

til∼

1450

AD

!

Page 6: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–9

His

tory

4

Gre

ek

Hip

parc

hus

(??

–∼

127

BC

):F

irstG

reek

obse

rver

:

•S

tar

cata

log:

850

star

s

•M

agni

tude

sof

star

s:0m

...6

m

•P

aral

lax

ofth

eM

oon

•Ta

ble

ofch

ords

(ear

lytr

igon

omet

ry)

•D

isco

very

ofpr

eces

sion

(shi

ftof

the

vern

aleq

uino

x)by

com

paris

onw

ith

Bab

ylon

ian

star

cata

log

•S

easo

nsha

veun

equa

llen

gth

•us

edge

ocen

tric

wor

ldm

odel

ofA

risto

tele

tom

ake

pred

ictio

ns(E

picy

cle)

.

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–10

His

tory

5

Gre

ek

(Ave

ni,1

993,

p.58

)

Pto

lem

aeus

(∼14

0AD

):S

ynta

xis

(aka

Alm

ages

t):

Refi

nem

ento

fAris

tote

lian

theo

ryin

tom

odel

usea

ble

for

com

pu-

tatio

ns

=⇒

Pto

lem

aic

Sys

tem

.

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–11

His

tory

6

Gre

ek

Dev

elop

men

toft

hehe

lioce

ntric

wor

ldm

odel

:A

rista

rchu

s(3

10–2

30B

C)

dete

r-

min

esof

the

radi

usof

the

Sun

1sta

ndla

stqu

arte

rof

Moo

n:

obse

rved

∠(M

oon,

Sun

)=

1/4

circ

le−

1/30

×1/

4ci

rcle=

87◦

=⇒

dist

ance

s:D(S

un−

Ear

th)=

19×

D(M

oon−

Ear

th)

Cas

sini

(167

2):

Par

alla

xof

Mar

s,w

hich

give

sD(S

un−

Ear

th)

=14

0M

io.

km(u

sing

Kep

ler’s

3rd

law

).

Sin

cean

gula

rdi

amet

ers

ofS

unan

dM

oon

are

alm

oste

qual

:

R(S

un)=

19×

R(M

oon)

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–12

His

tory

7

Gre

ek

Dev

elop

men

toft

hehe

lioce

ntric

wor

ldm

odel

:

Aris

tarc

hus

(310

–230

BC

)ra

dius

ofth

eS

un luna

rec

lipse

s:

Moo

nfit

sin

toea

rth

shad

owtw

ice

(infa

ct:

3.68

times

)

=⇒

Rad

ii:R

(Sun

)=9.

5×R

(Ear

th)

=⇒

com

mon

sens

e:sm

alle

rbo

dy

mov

esar

ound

the

larg

eron

e!

Hel

ioce

ntric

wor

ldm

odel

Page 7: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–13

His

tory

8

Gre

ek

Era

tost

hene

s(2

76–1

95B

C):

mea

sure

men

toft

heea

rth’

s

radi

us

Idea

:m

easu

recu

lmin

atio

n

ofth

eS

unat

two

plac

esof

know

ndi

stan

ce(N

toS

)on

the

sam

eda

y.

Sye

ne:

Sun

atze

nith

,Ale

xand

ria:

7.2◦

away

from

Zen

ith

=⇒

Dis

tanc

ebe

twee

nA

lexa

ndria

and

Sye

ne:d/(

2πR)=

7.2/

360

Mea

sure

d:50

00S

tade

s

Som

ehi

stor

ians

belie

veth

atth

isdi

stan

ceco

rres

pond

sto∼

820

km,s

oif

true

then

the

radi

usof

the

Ear

thw

ould

have

been

dete

rmin

edto

6264

km

infa

ct:

6378

km;r

epea

ted:

1671

:P

aris

-Am

iens

(J.P

icar

d)

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–14

His

tory

9

Gre

ek

The

dist

ance

toth

eM

oon

and

the

Sun

:

angu

lar

diam

eter

ofth

eM

oon

equa

lsw

idth

offin

ger

as

seen

from

1m

away

=⇒

Rm

oon/d

moo

n=

1/20

0

Luna

roc

culta

tions

:R

moo

n=

1/2R

eart

h

=⇒

Rea

rth/d

moo

n=

1/10

0

dm

oon=

100×

Rea

rth=

6264

00km

=⇒

dist

ance

toth

eS

un: d

sun=

19×

dm

oon=

11.9

Mio

km

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–15

His

tory

10

Ren

aiss

ance R

egio

mon

tanu

s:Jo

hann

esM

ülle

r

from

Kön

igsb

erg

(Fra

ncon

ia)

(143

6–14

76):

•S

tudi

esat

Leip

zig

(144

7)an

dV

ienn

a

(145

0):

Mat

hsan

dA

stro

nom

y

•E

pyto

ma

Joan

isde

mon

tere

gio

inal

-

mag

esti

ptol

emei

(146

1–14

63):

tran

s-

latio

nto

latin

with

muc

him

prov

edm

aths

•D

etr

iang

ulis

omni

mod

is(1

462–

1464

):

foun

datio

nof

mod

ern

trig

onom

etry

•E

phem

erid

esas

tron

omic

aeab

anno

1475

–150

6:

mos

tacc

urat

e

ephe

mer

ides

=⇒

Nav

igat

ion:

Col

umbu

s&

Vas

coda

Gam

a

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–16

His

tory

11

Ren

aiss

ance N

icol

aus

Cop

erni

cus

(147

3–15

43):

Ear

thce

ntre

dP

tole

mai

csy

stem

is

too

com

plic

ated

,aS

un-c

entr

edsy

s-

tem

ism

ore

eleg

ant.

Page 8: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–16

His

tory

12

Ren

aiss

ance

(Gin

geric

h,19

93,p

.165

)

Nic

olau

sC

oper

nicu

s(1

473–

1543

):

Ear

thce

ntre

dP

tole

mai

csy

stem

is

too

com

plic

ated

,aS

un-c

entr

edsy

s-

tem

ism

ore

eleg

ant:

De

revo

lutio

nibu

sor

bium

coel

estiu

m:

“In

noot

her

way

do

we

perc

eive

the

clea

rha

rmon

ious

linka

gebe

twee

nth

em

otio

nsof

the

plan

ets

and

the

size

sof

thei

ror

bs.”

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–16

His

tory

13

Ren

aiss

ance

(Gin

geric

h,19

93,p

.165

)

Nic

olau

sC

oper

nicu

s(1

473–

1543

):

Ear

thce

ntre

dP

tole

mai

csy

stem

is

too

com

plic

ated

,aS

un-c

entr

edsy

s-

tem

ism

ore

eleg

ant:

De

revo

lutio

nibu

sor

bium

coel

estiu

m:

“In

noot

her

way

do

we

perc

eive

the

clea

rha

rmon

ious

linka

gebe

twee

nth

em

otio

nsof

the

plan

ets

and

the

size

sof

thei

ror

bs.”

Cop

erni

can

prin

cipl

e:T

heE

arth

isno

tatt

hece

nter

ofth

eun

i-

vers

e.

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–17

His

tory

14

Ren

aiss

ance

Tych

oB

rahe

(154

6–16

01):

Vis

ualp

lane

tary

posi

tions

ofhi

ghes

tpre

cisi

onre

veal

flaw

sin

Pto

lem

aic

posi

tions

.

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–18

His

tory

15

Ren

aiss

ance

Ret

rogr

ade

mot

ion:

he-

lioce

ntric

vsge

ocen

tric

mod

el

Page 9: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–19

His

tory

16

Ren

aiss

ance

Joha

nnes

Kep

ler

(157

1–16

30):

Pla

n-

ets

orbi

ton

ellip

ses

arou

ndS

un,n

ot

onci

rcle

s,la

ws

ofm

otio

n.

Gal

ileo

Gal

ilei(

1564

–164

2):

Tele

-

scop

icob

serv

atio

ns,d

isco

very

of

four

moo

nsof

Jupi

ter

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–20

His

tory

17

Ren

aiss

ance

Joha

nnes

Kep

ler

(157

1–16

30):

•bo

rn27

.12.

1571

,Wei

lder

Sta

dt

•S

tudi

esT

übin

gen

with

Mae

stlin

•15

94–1

600:

Gra

z

•15

96:

Mys

teriu

mC

osm

ogra

phic

um

•16

00–1

612:

Pra

g,as

sist

anto

fTyc

ho

Bra

he,t

hen

Mat

hem

atic

ian

ofem

pero

r

Rud

olfI

I,di

scov

ered

Sup

erno

vaof

1604

,... 16

09:

Ast

rono

mia

Nov

a

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–21

His

tory

18

Ren

aiss

ance

Ast

rono

mia

Nov

a,K

apite

l1:

mot

ion

ofM

ars

in

the

epic

ycle

theo

rybe

twee

n15

60an

d15

96

Ast

rono

mia

nova

(Pra

g,16

09)

Crit

icof

the

epic

ycle

theo

ry:

“pa-

nis

quad

rage

sim

alis

(Ost

erbr

ezel

)

=⇒

Inel

egan

t!

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–22

His

tory

19

Ren

aiss

ance

Res

ulto

fKep

ler’s

inve

stig

atio

ns:

The

Kep

leria

nla

ws:

1.P

lane

tsm

ove

onel

liptic

alor

bits

,Sun

in

focu

s.

(“A

stro

nom

iaN

ova”

,160

9)

2.M

otio

nis

notu

nifo

rm,p

lane

tmov

esfa

st

whe

ncl

ose

toth

eS

un.

(“A

stro

nom

iaN

ova”

,160

9)

3.T

hird

law

com

es10

year

sla

ter

(“H

arm

onic

eM

undi

”,16

19)

Page 10: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–23

His

tory

20

Ren

aiss

ance

Tabu

lae

Rud

olph

inae

,162

7

Mos

tpre

cise

posi

tions

ofpl

anet

sev

er:

30×

smal

ler

erro

rsth

anbe

fore

(Gin

geric

h,19

93)

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–24

His

tory

21

Ren

aiss

ance

Moo

nsm

ove

arou

ndJu

pite

r

(=⇒

sim

ilar

tohe

lioce

ntric

mod

el!)

...

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–25

His

tory

22

Ren

aiss

ance

Dis

cove

ryof

phas

esof

Ven

us(I

lSag

giat

ore,

1623

)

Obs

erve

dph

ases

and

angu

lar

size

chan

ges

ofV

enus

Page 11: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–27

His

tory

24

Ren

aiss

ance

The

obse

rved

phas

ech

ange

sof

Ven

usca

nbe

expl

aine

dby

the

helio

cent

ric

wor

ldm

odel

,but

also

inTy

cho´

sge

ocen

tric

.

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–28

His

tory

25

mer

mer

,167

6

Ole

mer

(164

4–17

10):

mea

sure

men

toft

he

spee

dof

light

Tim

esof

occu

ltatio

nof

Iosh

iftby

upto

20m

inut

esdu

ring

the

year

.

(Pet

erH

orre

bouw

,Bas

isas

tron

omia

esi

veas

tron

o-m

iae

mac

hina

,Kop

enha

gen,

1735

)

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–29

His

tory

26

New

ton

(New

ton,

1730

)

Isaa

cN

ewto

n(1

642–

1727

):N

ewto

n’s

law

s,

phys

ical

caus

efo

rsh

ape

ofor

bits

isgr

avita

-

tion

(De

Phi

loso

phia

eN

atur

alis

Prin

cipi

aM

athe

-

mat

ica,

1687

).

=⇒

Beg

inof

mod

ern

phys

ics

base

das

tron

-

omy.

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–30

His

tory

27

Tele

scop

es

New

ton

tele

scop

e

Obj

ectiv

em

irror

Sec

onda

rym

irror

Cas

segr

ain

tele

scop

e

New

ton

(166

8),G

rego

ry(1

670)

,Cas

segr

ain

(167

2):

Mirr

orte

leco

pes

(mirr

orm

ade

polis

hed

met

al[c

oppe

r/zi

nkal

loy]

)

Page 12: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–31

His

tory

28

Her

sche

l

Will

iam

Her

sche

l(17

38–1

822)

:

•15

.11.

1738

:bo

rnin

Han

nove

r

•M

usic

ian

(Obo

ist)

•17

59:

emig

ratio

nto

Eng

land

•bu

ilds

larg

ere

flect

ing

tele

scop

es

•17

81:

Dis

cove

ryof

Ura

nus

•st

udy

ofN

ebul

ae

•S

tar

coun

ts(w

ithhi

ssi

ster

Car

olin

e)

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–32

His

tory

29

Her

sche

l

Geo

met

ryof

the

Milk

yW

ayac

cord

ing

toW

illia

mH

ersc

hel(

1785

)

Sun

iscl

ose

toth

ece

ntre

ofth

eM

ilky

Way

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–33

His

tory

30

Her

sche

l

1 A

U

d

p

=⇒

Wan

ted:

Mea

sure

men

tofa

year

lypa

ralla

x

ofa

star

.

Par

alla

x(s

mal

lang

les)

:

p=

1A

U

d(p

mea

sure

din

radi

an)

Pro

blem

sinc

ean

tigui

ty:p

issm

allb

ecau

seth

e

star

sar

eso

far

away

.

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–34

His

tory

31

Bes

sel

Frie

dric

hW

ilhel

mB

esse

l

(178

4–18

46)

Bes

sel(

1839

):fir

stdi

stan

cem

easu

rem

ento

fa

star

61C

yg:

Par

alla

x0.

3′′

=⇒

dist

ance

11lig

htye

ars

Page 13: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–35

His

tory

32

The

grea

tdeb

ate

Whi

rlpoo

lneb

ula

(Lor

dR

osse

,≈18

50)

19th

cent

ury:

Ast

rono

my

evol

ves

into

a

mod

ern

natu

rals

cien

ce:

•pr

ecis

est

ella

rpo

sitio

n(“

Dur

chm

uste

run-

gen”

=su

rvey

s)

•P

hoto

grap

hy

•S

pect

rosc

opy

(Ast

roph

ysic

s)

The

natu

reof

the

nebu

lae?

The

grea

tdeb

ate:

26.4

.192

0

prot

opla

neta

ryne

bula

e

or

isla

ndun

iver

se(“

Wel

teni

nsel

”):

Har

low

Sha

pley

vs.

Heb

erC

urtis

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

2–36

His

tory

33

Hub

ble

Mou

ntW

ilson

2.5

mTe

lesc

ope

Edw

inH

ubbl

e,19

22

2–36

Ave

ni,A

.F.,

1993

,A

ncie

ntA

stro

nom

ers,

(Was

hing

ton,

D.C

.:S

mith

soni

anB

ooks

)

Gin

geric

h,O

.,19

93,

The

Eye

ofH

eave

n–

Pto

lem

y,C

oper

nicu

s,K

eple

r,(N

ewYo

rk:

Am

eric

anIn

stitu

teof

Phy

sics

)

New

ton,

I.,17

30,

Opt

icks

,Vol

.4th

,(L

ondo

n:W

illia

mIn

nys)

,re

prin

t:D

over

Pub

licat

ions

,195

2

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–1

The

Pla

nets

:O

verv

iew

Page 14: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–2

Intr

oduc

tion

1

Wha

tis

apl

anet

?

Firs

t,ne

edto

look

atth

ede

finiti

onof

apl

anet

.

His

toric

alba

ckgr

ound

:

•an

tiqui

ty–1

781:

6pl

anet

s:M

ercu

ry,V

enus

,Ear

th,M

ars,

Jupi

ter,

Sat

urn

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–2

Intr

oduc

tion

2

Wha

tis

apl

anet

?

Firs

t,ne

edto

look

atth

ede

finiti

onof

apl

anet

.

His

toric

alba

ckgr

ound

:

•an

tiqui

ty–1

781:

6pl

anet

s:M

ercu

ry,V

enus

,Ear

th,M

ars,

Jupi

ter,

Sat

urn

•17

81:

Wilh

elm

Her

sche

ldis

cove

rsU

ranu

s=⇒

7pl

anet

s

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–2

Intr

oduc

tion

3

Wha

tis

apl

anet

?

Firs

t,ne

edto

look

atth

ede

finiti

onof

apl

anet

.

His

toric

alba

ckgr

ound

:

•an

tiqui

ty–1

781:

6pl

anet

s:M

ercu

ry,V

enus

,Ear

th,M

ars,

Jupi

ter,

Sat

urn

•17

81:

Wilh

elm

Her

sche

ldis

cove

rsU

ranu

s=⇒

7pl

anet

s

•18

01:

Giu

sepp

eP

iazz

i:C

eres

=⇒

8pl

anet

s

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–2

Intr

oduc

tion

4

Wha

tis

apl

anet

?

Firs

t,ne

edto

look

atth

ede

finiti

onof

apl

anet

.

His

toric

alba

ckgr

ound

:

•an

tiqui

ty–1

781:

6pl

anet

s:M

ercu

ry,V

enus

,Ear

th,M

ars,

Jupi

ter,

Sat

urn

•17

81:

Wilh

elm

Her

sche

ldis

cove

rsU

ranu

s=⇒

7pl

anet

s

•18

01:

Giu

sepp

eP

iazz

i:C

eres

=⇒

8pl

anet

s

•18

02:

Hei

nric

hO

lber

s:P

alla

s=⇒

9pl

anet

s,H

ersc

helc

oins

term

“ast

eroi

d”.

Page 15: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–2

Intr

oduc

tion

5

Wha

tis

apl

anet

?

Firs

t,ne

edto

look

atth

ede

finiti

onof

apl

anet

.

His

toric

alba

ckgr

ound

:

•an

tiqui

ty–1

781:

6pl

anet

s:M

ercu

ry,V

enus

,Ear

th,M

ars,

Jupi

ter,

Sat

urn

•17

81:

Wilh

elm

Her

sche

ldis

cove

rsU

ranu

s=⇒

7pl

anet

s

•18

01:

Giu

sepp

eP

iazz

i:C

eres

=⇒

8pl

anet

s

•18

02:

Hei

nric

hO

lber

s:P

alla

s=⇒

9pl

anet

s,H

ersc

helc

oins

term

“ast

eroi

d”.

•18

04:

Kar

lHar

ding

:Ju

no=⇒

10pl

anet

s

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–2

Intr

oduc

tion

6

Wha

tis

apl

anet

?

Firs

t,ne

edto

look

atth

ede

finiti

onof

apl

anet

.

His

toric

alba

ckgr

ound

:

•an

tiqui

ty–1

781:

6pl

anet

s:M

ercu

ry,V

enus

,Ear

th,M

ars,

Jupi

ter,

Sat

urn

•17

81:

Wilh

elm

Her

sche

ldis

cove

rsU

ranu

s=⇒

7pl

anet

s

•18

01:

Giu

sepp

eP

iazz

i:C

eres

=⇒

8pl

anet

s

•18

02:

Hei

nric

hO

lber

s:P

alla

s=⇒

9pl

anet

s,H

ersc

helc

oins

term

“ast

eroi

d”.

•18

04:

Kar

lHar

ding

:Ju

no=⇒

10pl

anet

s

•18

07:

Hei

nric

hO

lber

s:V

esta=⇒

11pl

anet

s

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–2

Intr

oduc

tion

7

Wha

tis

apl

anet

?

Firs

t,ne

edto

look

atth

ede

finiti

onof

apl

anet

.

His

toric

alba

ckgr

ound

:

•an

tiqui

ty–1

781:

6pl

anet

s:M

ercu

ry,V

enus

,Ear

th,M

ars,

Jupi

ter,

Sat

urn

•17

81:

Wilh

elm

Her

sche

ldis

cove

rsU

ranu

s=⇒

7pl

anet

s

•18

01:

Giu

sepp

eP

iazz

i:C

eres

=⇒

8pl

anet

s

•18

02:

Hei

nric

hO

lber

s:P

alla

s=⇒

9pl

anet

s,H

ersc

helc

oins

term

“ast

eroi

d”.

•18

04:

Kar

lHar

ding

:Ju

no=⇒

10pl

anet

s

•18

07:

Hei

nric

hO

lber

s:V

esta=⇒

11pl

anet

s

•18

45:

Kar

lHen

cke:

Ast

rea=⇒

12pl

anet

s

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–2

Intr

oduc

tion

8

Wha

tis

apl

anet

?

Firs

t,ne

edto

look

atth

ede

finiti

onof

apl

anet

.

His

toric

alba

ckgr

ound

:

•an

tiqui

ty–1

781:

6pl

anet

s:M

ercu

ry,V

enus

,Ear

th,M

ars,

Jupi

ter,

Sat

urn

•17

81:

Wilh

elm

Her

sche

ldis

cove

rsU

ranu

s=⇒

7pl

anet

s

•18

01:

Giu

sepp

eP

iazz

i:C

eres

=⇒

8pl

anet

s

•18

02:

Hei

nric

hO

lber

s:P

alla

s=⇒

9pl

anet

s,H

ersc

helc

oins

term

“ast

eroi

d”.

•18

04:

Kar

lHar

ding

:Ju

no=⇒

10pl

anet

s

•18

07:

Hei

nric

hO

lber

s:V

esta=⇒

11pl

anet

s

•18

45:

Kar

lHen

cke:

Ast

rea=⇒

12pl

anet

s

•18

46:

Joha

nnG

ottfr

ied

Gal

ledi

scov

ers

Nep

tune

=⇒

13pl

anet

s

Page 16: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–2

Intr

oduc

tion

9

Wha

tis

apl

anet

?

Firs

t,ne

edto

look

atth

ede

finiti

onof

apl

anet

.

His

toric

alba

ckgr

ound

:

•an

tiqui

ty–1

781:

6pl

anet

s:M

ercu

ry,V

enus

,Ear

th,M

ars,

Jupi

ter,

Sat

urn

•17

81:

Wilh

elm

Her

sche

ldis

cove

rsU

ranu

s=⇒

7pl

anet

s

•18

01:

Giu

sepp

eP

iazz

i:C

eres

=⇒

8pl

anet

s

•18

02:

Hei

nric

hO

lber

s:P

alla

s=⇒

9pl

anet

s,H

ersc

helc

oins

term

“ast

eroi

d”.

•18

04:

Kar

lHar

ding

:Ju

no=⇒

10pl

anet

s

•18

07:

Hei

nric

hO

lber

s:V

esta=⇒

11pl

anet

s

•18

45:

Kar

lHen

cke:

Ast

rea=⇒

12pl

anet

s

•18

46:

Joha

nnG

ottfr

ied

Gal

ledi

scov

ers

Nep

tune

=⇒

13pl

anet

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•18

47:

Kar

lHen

cke:

Heb

e=⇒

14pl

anet

s

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–2

Intr

oduc

tion

10

Wha

tis

apl

anet

?

Firs

t,ne

edto

look

atth

ede

finiti

onof

apl

anet

.

His

toric

alba

ckgr

ound

:

•an

tiqui

ty–1

781:

6pl

anet

s:M

ercu

ry,V

enus

,Ear

th,M

ars,

Jupi

ter,

Sat

urn

•17

81:

Wilh

elm

Her

sche

ldis

cove

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ranu

s=⇒

7pl

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•18

01:

Giu

sepp

eP

iazz

i:C

eres

=⇒

8pl

anet

s

•18

02:

Hei

nric

hO

lber

s:P

alla

s=⇒

9pl

anet

s,H

ersc

helc

oins

term

“ast

eroi

d”.

•18

04:

Kar

lHar

ding

:Ju

no=⇒

10pl

anet

s

•18

07:

Hei

nric

hO

lber

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esta=⇒

11pl

anet

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•18

45:

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lHen

cke:

Ast

rea=⇒

12pl

anet

s

•18

46:

Joha

nnG

ottfr

ied

Gal

ledi

scov

ers

Nep

tune

=⇒

13pl

anet

s

•18

47:

Kar

lHen

cke:

Heb

e=⇒

14pl

anet

s

•18

48:

And

rew

Gra

ham

:M

etis=⇒

15pl

anet

s

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–2

Intr

oduc

tion

11

Wha

tis

apl

anet

?

Firs

t,ne

edto

look

atth

ede

finiti

onof

apl

anet

.

His

toric

alba

ckgr

ound

:

•an

tiqui

ty–1

781:

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ercu

ry,V

enus

,Ear

th,M

ars,

Jupi

ter,

Sat

urn

•17

81:

Wilh

elm

Her

sche

ldis

cove

rsU

ranu

s=⇒

7pl

anet

s

•18

01:

Giu

sepp

eP

iazz

i:C

eres

=⇒

8pl

anet

s

•18

02:

Hei

nric

hO

lber

s:P

alla

s=⇒

9pl

anet

s,H

ersc

helc

oins

term

“ast

eroi

d”.

•18

04:

Kar

lHar

ding

:Ju

no=⇒

10pl

anet

s

•18

07:

Hei

nric

hO

lber

s:V

esta=⇒

11pl

anet

s

•18

45:

Kar

lHen

cke:

Ast

rea=⇒

12pl

anet

s

•18

46:

Joha

nnG

ottfr

ied

Gal

ledi

scov

ers

Nep

tune

=⇒

13pl

anet

s

•18

47:

Kar

lHen

cke:

Heb

e=⇒

14pl

anet

s

•18

48:

And

rew

Gra

ham

:M

etis=⇒

15pl

anet

s

•18

49:

Ann

ibal

ede

Gas

paris

:H

ygie

a=⇒

16pl

anet

s

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–2

Intr

oduc

tion

12

Wha

tis

apl

anet

?

Firs

t,ne

edto

look

atth

ede

finiti

onof

apl

anet

.

His

toric

alba

ckgr

ound

:

•an

tiqui

ty–1

781:

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anet

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ercu

ry,V

enus

,Ear

th,M

ars,

Jupi

ter,

Sat

urn

•17

81:

Wilh

elm

Her

sche

ldis

cove

rsU

ranu

s=⇒

7pl

anet

s

•18

01:

Giu

sepp

eP

iazz

i:C

eres

=⇒

8pl

anet

s

•18

02:

Hei

nric

hO

lber

s:P

alla

s=⇒

9pl

anet

s,H

ersc

helc

oins

term

“ast

eroi

d”.

•18

04:

Kar

lHar

ding

:Ju

no=⇒

10pl

anet

s

•18

07:

Hei

nric

hO

lber

s:V

esta=⇒

11pl

anet

s

•18

45:

Kar

lHen

cke:

Ast

rea=⇒

12pl

anet

s

•18

46:

Joha

nnG

ottfr

ied

Gal

ledi

scov

ers

Nep

tune

=⇒

13pl

anet

s

•18

47:

Kar

lHen

cke:

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e=⇒

14pl

anet

s

•18

48:

And

rew

Gra

ham

:M

etis=⇒

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anet

s

•18

49:

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ibal

ede

Gas

paris

:H

ygie

a=⇒

16pl

anet

s

•18

49:

Ann

ibal

ede

Gas

paris

:P

arth

enop

e=⇒

17pl

anet

s

Page 17: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–2

Intr

oduc

tion

13

Wha

tis

apl

anet

?

Firs

t,ne

edto

look

atth

ede

finiti

onof

apl

anet

.

His

toric

alba

ckgr

ound

:

•an

tiqui

ty–1

781:

6pl

anet

s:M

ercu

ry,V

enus

,Ear

th,M

ars,

Jupi

ter,

Sat

urn

•17

81:

Wilh

elm

Her

sche

ldis

cove

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ranu

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anet

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•18

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sepp

eP

iazz

i:C

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=⇒

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anet

s

•18

02:

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nric

hO

lber

s:P

alla

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anet

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ersc

helc

oins

term

“ast

eroi

d”.

•18

04:

Kar

lHar

ding

:Ju

no=⇒

10pl

anet

s

•18

07:

Hei

nric

hO

lber

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esta=⇒

11pl

anet

s

•18

45:

Kar

lHen

cke:

Ast

rea=⇒

12pl

anet

s

•18

46:

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nnG

ottfr

ied

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ledi

scov

ers

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tune

=⇒

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•18

47:

Kar

lHen

cke:

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e=⇒

14pl

anet

s

•18

48:

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rew

Gra

ham

:M

etis=⇒

15pl

anet

s

•18

49:

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ibal

ede

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ygie

a=⇒

16pl

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•18

49:

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ibal

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te18

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oduc

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14

Wha

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to(d

=24

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sI

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

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oduc

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15

Wha

tis

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•19

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deTo

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LGE

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16

Wha

tis

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d.

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Page 18: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–3

Intr

oduc

tion

17

Wha

tis

apl

anet

?

•19

30:

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deTo

mba

ugh:

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to(d

=24

00km

)=⇒

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hael

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wn

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0Q

uaoa

r(d

∼13

00km

)

•20

03:

Bro

wn

etal

.:90

377

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na(1

200

km.

d.

1800

km)

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wn

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.:20

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ka“X

ena”

)(d

∼24

00km

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=⇒

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s?!

?

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

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C

M LMV

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AI

AD

R

E

LGE

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18

Wha

tis

apl

anet

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•19

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deTo

mba

ugh:

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to(d

=24

00km

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dTr

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0Q

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∼13

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na(1

200

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wn

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19

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•20

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tern

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Def

init

ion

of

a P

lan

et i

n t

he

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lar

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tem

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nte

mp

ora

ry

ob

serv

atio

ns

are

chan

gin

g o

ur

un

der

stan

din

g o

fp

lan

etar

y

syst

ems,

and

it

is i

mp

ort

ant

that

ou

r n

om

encl

atu

re f

or

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ject

s re

flec

t o

ur

curr

ent

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g.T

his

ap

pli

es,

in p

arti

cula

r,to

th

e d

esig

nat

ion

"p

lan

ets"

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he

wo

rd "

pla

net

"o

rigi

nal

ly d

escr

ibed

"w

and

erer

s"th

at w

ere

kn

ow

n o

nly

as

mo

vin

g

ligh

ts i

n t

he

sky.

Rec

ent

dis

cove

ries

lea

d u

s to

cre

ate

a n

ew d

efin

itio

n,

wh

ich

we

can

mak

e u

sin

g cu

rren

tly

avai

lab

le s

cien

tifi

c in

form

atio

n.

Th

e IA

U t

her

efo

re r

eso

lves

th

at p

lan

ets

and

oth

er b

od

ies,

exce

pt

sate

llit

es,i

n o

ur

So

lar

Syst

em b

e d

efin

ed i

nto

th

ree

dis

tin

ct c

ateg

ori

es i

n t

he

foll

ow

ing

way

:

(1)

A p

lan

et1

is a

cel

esti

al b

od

y th

at

(a)

is i

n o

rbit

aro

un

d t

he

Sun

,

(b)

has

su

ffic

ien

t m

ass

for

its

self

-gra

vit

y to

ove

rco

me

rigi

d b

od

y fo

rces

so

that

it

assu

mes

a h

ydro

stat

ic e

qu

ilib

riu

m (

nea

rly

rou

nd

) sh

ape,

and

(c)

has

cle

ared

th

e n

eigh

bo

urh

oo

d a

rou

nd

its

orb

it.

(2)

A "

dw

arf

pla

net

"is

a c

eles

tial

bo

dy

that

(a)

is i

n o

rbit

aro

un

d t

he

Sun

,

(b)

has

su

ffic

ien

t m

ass

for

its

self

-gra

vit

y to

ove

rco

me

rigi

d b

od

y fo

rces

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it

assu

mes

a h

ydro

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ic e

qu

ilib

riu

m (

nea

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ape2

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(c)

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t cl

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d t

he

nei

ghb

ou

rho

od

aro

un

d i

ts o

rbit

,an

d

(d)

is n

ot

a sa

tell

ite.

(3)

All

o

ther

o

bje

cts3

,ex

cep

t sa

tell

ites

,o

rbit

ing

the

Sun

sh

all

be

refe

rred

to

coll

ecti

vely

as

"Sm

all

So

lar

Syst

em B

od

ies"

.

1T

he

eigh

t p

lan

ets

are:

Mer

cury

,V

enu

s,E

arth

,M

ars,

Jup

iter

,S

atu

rn,

Ura

nu

s,an

d

Nep

tun

e.

2.

An

IA

U p

roce

ss w

ill b

e es

tab

lish

ed t

o a

ssig

n b

ord

erli

ne

ob

ject

s in

to e

ith

er d

war

fp

lan

et

and

oth

er c

ateg

ori

es.

3.

Th

ese

curr

entl

y in

clu

de

mo

st o

fth

e S

ola

r Sy

stem

ast

ero

ids,

mo

st T

ran

s-N

eptu

nia

n

Ob

ject

s (T

NO

s),c

om

ets,

and

oth

er s

mal

l b

od

ies.

Page 19: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

3–3

RE

SO

LU

TIO

N 6

Plu

to

Th

e IA

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urt

her

res

olv

es:

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is

a "d

war

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by

the

abo

ve

def

init

ion

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d

is

reco

gniz

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as

the

pro

toty

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of

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ew c

ateg

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of

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ns-

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ian

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ject

s1.

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l b

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Ear

th-M

oon

syst

em

Pha

ses

ofth

em

oon

(cre

dit:

Uni

Kie

l)

Page 20: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

tota

lsol

arec

lipse

2006

Moo

nan

dS

unha

veve

rysi

mila

rap

pare

ntdi

amet

ers:

Ecl

ipse

s

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–8

Intr

oduc

tion

24

Ecl

ipse

s

•E

clip

tic:

orbi

talp

lane

ofth

eE

arth

arou

nd

the

Sun

.

•or

bita

lpla

neof

the

moo

nin

clin

edw

rt.

eclip

ticby

i=

5◦

•lin

eof

node

s:in

ters

ectio

nof

the

two

or-

bita

lpla

nes

•ec

lipse

soc

cur

only

whe

nM

oon

iscl

ose

to

one

ofth

eno

des

=⇒

two

eclip

sese

ason

spe

rye

ar

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–9

Pla

nets

:O

verv

iew

1

Ove

rvie

w

Div

isio

nof

Sol

arS

yste

min

totw

om

ajor

type

sof

plan

ets:

1.In

ner

“Ter

rest

rial”

Pla

nets

:M

ercu

ry,V

enus

,Ear

th/M

oon,

Mar

s:

=⇒

alls

imila

rto

Ear

th(“

rock

s”).

=⇒

nom

oons

(Ear

th/M

oon

bette

rca

lled

“tw

ins”

)

The

Inne

rP

lane

ts(S

SE

,NA

SA

)

Page 21: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–11

Pla

nets

:O

verv

iew

3

Ove

rvie

w

Div

isio

nof

Sol

arS

yste

min

totw

om

ajor

type

sof

plan

ets:

1.In

ner

“Ter

rest

rial”

Pla

nets

:M

ercu

ry,V

enus

,Ear

th/M

oon,

Mar

s:

=⇒

alls

imila

rto

Ear

th(“

rock

s”).

=⇒

nom

oons

(Ear

th/M

oon

bette

rca

lled

“tw

ins”

)

2.O

uter

Pla

nets

:Ju

pite

r,S

atur

n,U

ranu

s,N

eptu

ne:

=⇒

“gas

gian

ts”

=⇒

allh

ave

exte

nsiv

em

oon

syst

ems

Alth

ough

notp

lane

ts(i.

e.,m

otio

nno

taro

und

Sun

),la

rge

moo

nsof

gas

gian

ts

are

very

sim

ilar

inst

ruct

ure

tote

rres

tria

lpla

nets

.

The

Out

erP

lane

ts(S

SE

,NA

SA

)

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–13

Pla

nets

:O

verv

iew

5

Pla

nets

:P

rope

rtie

s

a[A

U]

Por

b[y

r]i

[◦]

eP

rot

M/M

�R/R

Mer

cury

'0.

387

0.24

17.

000.

205

58.8

d0.

055

0.38

3

Ven

us♀

0.72

30.

615

3.40

0.00

7−

243.

0d

0.81

50.

949

Ear

th�

1.00

01.

000

0.00

0.01

723.9

h1.

000

1.00

Mar

s♂

1.52

1.88

1.90

0.09

424.6

h0.

107

0.53

3

Jupi

ter

X5.

2011.9

1.30

0.04

99.

9h

318

11.2

Sat

urn

Y9.

5829.4

2.50

0.05

710.7

h95.2

9.45

Ura

nus

Z19

.283

.70.

780.

046

−17

.2h

14.5

4.01

Nep

tune

[30

.116

3.7

1.78

0.01

116.1

h17.1

3.88

(Plu

to\

39.2

248

17.2

0.24

46.

39d

0.00

20.

19)

Afte

rK

utne

r,A

ppen

dix

D;

a:

sem

i-maj

orax

isP

orb:

orbi

talp

erio

di:

orbi

tali

nclin

atio

n(w

rtE

arth

’sor

bit)

e:ec

cent

ricity

ofth

eor

bitP

rot:

rota

tiona

lper

iod

M:

mas

sR

:eq

uato

rialr

adiu

s1

AU

=1.

496×

1011

m.

Ear

thor

bit,

incl

inat

ion

ofth

ero

tatio

nax

isan

dth

ese

ason

sof

the

year

.

Per

ihel

ion:

Janu

ary

3.S

unis

clos

esti

nno

rthe

rnw

inte

r.

Page 22: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

2004

–200

9:S

easo

nson

Sat

urn:

6ye

ars

ofS

atur

nsor

bit.

Sea

sons

onS

atur

nK

ippe

nhah

n:U

nhei

mlic

heW

elte

n

Ura

nus:

rings

and

tilte

dro

tatio

nC

redi

t:La

wre

nce

Sro

mov

sky,

(Uni

v.W

isco

nsin

-Mad

ison

),K

eck

Obs

erva

tory

Ura

nus:

Sea

sons

Cre

dit:

Spa

ceS

cien

ce&

Eng

enee

ring

Cen

ter

(Uni

v.W

isco

nsin

-Mad

ison

)

Page 23: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

NA

SA

/ME

SS

EN

GE

R,2

008

Jan

Mer

cury

:

•no

tmuc

hla

rger

than

Moo

n

•de

nses

tofa

llte

rres

tria

lpla

nets

•no

evid

ence

for

atm

osph

ere

•R

otat

ion

perio

d:59

d,2/

3of

orbi

tal

perio

d.

•su

rfac

e:im

pact

crat

ers

•E

arly

info

rmat

ion

avai

labl

e

from

Mar

iner

10(t

hree

flyby

s,

1974

/197

5)

•N

AS

Am

issi

on“M

esse

nger

(laun

ched

2004

Aug

ust3

,flyb

ys20

08an

d20

09,

inor

bitf

rom

2011

on)

•E

SA

Mis

sion

Bep

iCol

ombo

,

plan

ned

for∼

2014

,arr

ival

2020

ES

A/V

enus

Exp

ress

Ven

us:

•si

mila

rsi

zeto

Ear

th,s

imila

rst

ruct

ure

•in

sola

tion∼

2×E

arth

•ve

rysl

owro

tatio

n(2

43d,

retr

ogra

de;

=⇒

noB

-fiel

d)

•ve

ryde

nse

atm

osph

ere:

surf

ace

pres

-

sure

∼90

×E

arth

•at

mos

pher

e:96

.5%

CO

2,3

.5%

N

=⇒

stro

nggr

eenh

ouse

effe

ct

=⇒

surf

ace

tem

pera

ture

∼46

0◦C

.

•ac

idra

in(y

es,s

ulph

uric

acid

!)

Info

rmat

ion

mai

nly

from

rada

rsu

rvey

ing

from

Ear

than

dfr

omM

agel

lan

(199

0–19

94),

plus

im-

ages

from

Pio

neer

Ven

usP

robe

(197

9).

Sev

eral

land

ings

(Ven

era,

1975

/198

1).

Cur

rent

lyst

ud-

ied

byE

SA

’sV

enus

Exp

ress

prob

e(la

unch

Apr

il20

05,a

rriv

alA

pril

2006

,mis

sion

until

end-

2012

).

Ear

th/M

oon,

seen

from

Mar

s(N

AS

A/M

alin

)

Ear

th:

•do

uble

plan

etsy

stem

•E

arth

surf

ace:

dom

inat

edby

plat

e

tect

onic

s,er

osio

n

•at

mos

pher

e:80

%N

2,2

0%O

2

=⇒

mod

erat

egr

eenh

ouse

effe

ct

=⇒

surf

ace

tem

pera

ture

>0◦

C.

•w

ater

pres

ent

Moo

n:

•ve

rysi

mila

rto

Mer

cury

,ove

rall

•M

aria

e(p

lain

sfr

omm

assi

veim

-

pact

s)an

dim

pact

crat

ers

•R

otat

ion

sync

hron

ous

toor

bit

arou

ndE

arth

Page 24: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

NA

SA

,Mar

sG

loba

lSur

veyo

r

Mar

s:

•sm

alle

rth

anE

arth

•ve

rylo

wde

nsity

(〈ρ〉∼

3g

cm−

3)

=⇒

smal

lcor

e,pr

obab

lyF

ean

d

Fe x

Sy,

•po

lar

caps

,sea

sons

•th

inat

mos

pher

e,cl

ouds

,fog

,...

•w

ater

subl

imes

=⇒

noliq

uid

wat

erto

day

•V

olca

nism

(larg

esh

ield

volc

anoe

s

=⇒

no(?

)pl

ate

tect

onic

s)

•at

mos

pher

e:95

%C

O2

=⇒

wea

kgr

eenh

ouse

effe

ct

•tw

om

oons

(cap

ture

das

tero

ids)

Ear

lyE

xplo

ratio

nth

roug

hM

arin

erm

issi

ons

and

Vik

ing

1an

dV

ikin

g2

orbi

ters

and

land

ers

in

1970

s,re

cent

ly,s

tron

gin

tere

st(N

AS

AM

ars

Glo

balS

urve

yor

[MG

S],

ES

AM

ars

Exp

ress

,plu

s

seve

rall

ande

rs).

Cur

rent

lybe

stsu

rvey

edpl

anet

exce

ptfo

rE

arth

.

The

jovi

anpl

anet

s,c ©

C.J

.Ham

ilton

NA

SA

/ES

A,C

assi

ni-H

uygh

ens

Jupi

ter:

•La

rges

tpla

neti

nso

lar

syst

em

•ra

pid

rota

tion=⇒

seve

rely

flat-

tene

d,ba

nded

atm

osph

ere

(Cor

iolis

forc

e),G

reat

Red

Spo

t

•st

rong

mag

netic

field

(str

ong

radi

o

emis

sion

)

•at

mos

pher

e:75

%H

,24%

He

(by

mas

s),v

ery

clos

eto

sola

r

•di

ffere

ntia

lrot

atio

n(r

otat

ion

pe-

riod

9h

50m

ateq

uato

r,9

h55

mat

pole

s)

•st

rong

mag

netic

field

•fo

urm

ajor

“Gal

ilean

”m

oons

plus

59

smal

lone

s(a

sof

Nov

2010

;cap

-

ture

das

tero

ids)

Ear

lyE

xplo

ratio

n19

70s

thro

ugh

Pio

neer

11an

d12

,and

then

thro

ugh

the

Voy

ager

prob

es.

In-

tens

ivel

yst

udie

dby

NA

SA

’sG

alile

opr

ojec

t(en

ded

2003

Sep

14).

NA

SA

/ES

AC

assi

ni,2

004

Oct

.N

AS

A/E

SA

Cas

sini

Sat

urn:

•si

mila

rto

Jupi

ter,

slig

htly

smal

ler

•ra

pid

rota

tion=⇒

flatte

ned,

band

edat

mo-

sphe

re

•at

mos

pher

e:75

%H

,24%

He

(by

mas

s),

mol

ecul

eset

c.si

mila

rto

Jupi

ter

•R

ings

!

•si

xm

ajor

moo

nspl

us61

smal

lone

s(a

sof

Nov

2010

;mai

nly

capt

ured

aste

roid

s)

•E

arly

Exp

lora

tion

in19

70s

with

Pio

neer

11

and

12an

dth

eV

oyag

erpr

obes

.

Stu

died

sinc

e20

04Ju

ly1

byN

AS

A/E

SA

Cas

sini

-Huy

gens

proj

ect(

dura

tion

until

2017

)

Page 25: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

Sat

urn’

sdu

strin

g(N

AS

AS

pitz

er):

exte

nds

from

128

to20

7RS,

40RS

thic

k.(V

erbi

scer

etal

.20

09,S

cien

ceO

ctob

er22

)

Dus

tsup

ply

byim

pact

son

moo

nP

hoeb

e,du

stpa

rtic

les

mig

rate

inw

ards

and

are

swep

tup

byIa

petu

s

NA

SA

Voy

ager

2,19

86Ja

n10

Ura

nus:

•at

mos

pher

eco

ld(5

9K

=−

214◦

C)

=⇒

amm

onia

has

froz

enou

t

•m

etha

ne,h

ydro

gen,

and

heliu

m

dete

cted

sofa

r(le

ssH

eth

anex

-

pect

edfr

omJu

pite

ran

dS

atur

n!)

=⇒

blui

shco

lor

•in

clin

atio

nof

rota

tion

axis

:98

(“ro

lling

onec

liptic

plan

e”).

•sm

allr

ing

syst

em

•fiv

em

ajor

moo

nsin

equa

toria

l

plan

epl

us22

smal

lone

s(a

sof

Nov

2010

;cap

ture

das

tero

ids)

Fly

byof

Voy

ager

2in

1986

Janu

ary,

sinc

eth

enon

lyre

mot

ese

nsin

gfr

omH

ubbl

eS

pace

Tele

-

scop

e(H

ST

)an

dgr

ound

base

din

stru

men

ts.

NA

SA

Voy

ager

2

Nep

tune

:

•at

mos

pher

esi

mila

rto

Ura

nus,

but

mor

eac

tive;

brig

htm

etha

necl

ouds

abov

ege

nera

lclo

udla

yer

•rin

gsy

stem

(5in

divi

dual

rings

)

•Tw

om

ajor

moo

ns(T

riton

,272

0km

diam

eter

(!)

and

Ner

eid

355

km),

11ca

ptur

edas

tero

ids

Fly

byin

1989

Aug

ustb

yV

oyag

er2,

only

HS

Tsi

nce

then

(sho

wed

in19

95th

atda

rksp

otha

s

vani

shed

,det

ecte

dne

wst

orm

syst

em)

Page 26: KLAUSUR am 19. Juli 2011pulsar.sternwarte.uni-erlangen.de/wilms/teach/intro/hand01.pdf · much slower motion of Sun & Moon with re- spect to stars occasional retrograde motions of

I

EF

CO

DRI

L

AI

N

R

DN

XAEA

ESII

C

M LMV

A

AI

AD

R

E

LGE

3–31

Pla

nets

:O

verv

iew

23

Str

uctu

re

Que

stio

nsth

atw

ew

illde

alw

ith:

•H

owdo

the

plan

ets

mov

e?K

eple

r’sla

ws

and

thei

rph

ysic

alin

terp

reta

tion

•W

hatd

opl

anet

ary

surf

aces

look

like?

crat

ers,

plat

ete

cton

ics,

volc

anis

m

•W

hati

sth

ein

tern

alst

ruct

ure

ofth

epl

anet

s?hy

dros

tatic

stru

ctur

e

•H

owdo

plan

etar

yat

mos

pher

esw

ork?

hydr

osta

ticst

ruct

ure

(aga

in)

•W

hati

sth

ena

ture

ofth

em

inor

bodi

es?

•H

owdi

dth

epl

anet

ary

syst

emfo

rm?

•Is

the

sola

rsy

stem

norm

al?

Are

ther

epl

anet

sel

sew

here

?(L

ater

)