• date post

14-Aug-2020
• Category

## Documents

• view

0

0

Embed Size (px)

### Transcript of sec. 18 a. owocki/phys333/QQ-secs18-24.pdfآ  b. In[\$]:= c=.; v = z c Out[\$]= 1. c c. In[\$]:= ckms...

• sec. 18

a.

Ein= Eout

σ T⊙4 4πR⊙2 πR2

4πd2 = σ T4 4π R2

T= T⊙2 2R⊙ d

for Earth, d=1 au

Te= T⊙ 2

2R⊙ au

In general,

T(d) = Te au d

b.

pcbau = (180. / π) 60 * 60; Tpcsun = 280 K / Sqrt[pcbau]

Out[\$]= 0.616518 K

• c.

In[\$]:= Tpchotstar = (60 000 / 6000) Tpcsun

Out[\$]= 6.16518 K

a.

In[\$]:= mp = 1.67 × 10-24 g; n = 100 cm-3; ρ = 2 mp n

Out[\$]= 3.34 × 10-22 g

cm3

b.

In[\$]:= a =.; σ = π a2; m = (4 / 3) π a3 ρd; κ = Xd σ / m

Out[\$]= 3 Xd

4 a ρd

In[\$]:= μm = 10-4 cm; κd = κ /. Xd → 2 × 10-3, ρd -> 1 g  cm3, a -> 0.1 μm 

Out[\$]= 150. cm2

g

2 QuickQuestions-secs18-24.nb

• In[\$]:= aucm = 1.49 × 1013 cm;

ℓ = 1

κd ρ pc / (pcbau * aucm)

Out[\$]= 6.49458 pc

c.

In[\$]:= d = 30 pc; τuv = d / ℓ

Out[\$]= 4.61924

d.

In[\$]:= Auv = 1.08 τuv

Out[\$]= 4.98878

In[\$]:= λuv = 0.1 μm; nm = μm / 1000; λv = 500 nm; τv = τuv (λuv / λv)

Out[\$]= 0.923848

In[\$]:= λir = 2 μm; τir = τuv (λuv / λir)

Out[\$]= 0.230962

sec. 19

In[\$]:= G =.; R =.; g = G M  R2;

tg = t /. SolveR ⩵ g t2  2, t[[2]]

Out[\$]= 2 R3/2

G M

QuickQuestions-secs18-24.nb 3

• = π

2

R3

GM ; same except for factor 2 ≈ 1.41 vs.

π

2 ≃ 1.57

tg (R)

tff =

π / 2

2 = 1.11

In[\$]:= π  2 2. 

Out[\$]= 1.11072

sec. 20

In[\$]:= s =.; aukm = aucm km  105 cm;

pckm = pcbau * aukm ; kpckm = 1000 pckm; Rgalkm = 8 kpckm; Vo = 220 km / s; Ps = 2 π Rgalkm / Vo; yrs = 365.25 * 24 * 60 * 60 s; PMyr = Ps Myr  106 yrs

Out[\$]= 222.513 Myr

In[\$]:= E21 = 1.2 μm eV / λ /. λ → 21 cm

Out[\$]= 5.71429 × 10-6 eV

4 QuickQuestions-secs18-24.nb

• a.

In[\$]:= au =.; d =.; s = au ( α / arcsec) (d / pc) /. {α -> 1 arcsec , d -> 8000 pc}

Out[\$]= 8000 au

b.

In[\$]:= au =.; s =.; d =.; αc = arcsec (s / au) / (d / pc) /. {s -> 1 pcbau au , d -> 8000 pc}

Out[\$]= 25.7831 arcsec

In[\$]:= pcbau

Out[\$]= 206265.

sec. 22

c2

2 ≡ GM Rs

; Rs= 2 GMc2

ϵ ≡ Eg

mc2 = GMm/Racc

mc2 = GM c2 Racc

= Rs2Racc ; for Racc= 5Rs , ϵ=0.1

QuickQuestions-secs18-24.nb 5

• a.

In[\$]:= λLyα = 91.5 nm; λobs = 183 nm; λem = λLyα ; z = λobs - λem

λem

Out[\$]= 1.

b.

In[\$]:= c =.; v = z c

Out[\$]= 1. c

c.

In[\$]:= ckms = 3 × 105 km / s; v = z ckms; Ho = 67. (km / s) / Mpc; d = v / Ho

Out[\$]= 4477.61 Mpc

sec. 24

a.

For empty universe, R(t) = 1 + Hot , so age where R-tage)=0 gives tage = 1 /Ho=

10 Gyr ho

where ho≡ Ho

100 kmsMpc

For Ho=67 (km/s)/Mpc, ho=67/100 = 2/3, so tage =

10 Gyr ho

= 10 Gyr 2/3

= 15 Gyr

6 QuickQuestions-secs18-24.nb

• For empty universe, R(t) = 1 + Hot , so age where R-tage)=0 gives tage = 1 /Ho=

10 Gyr ho

where ho≡ Ho

100 kmsMpc

For Ho=67 (km/s)/Mpc, ho=67/100 = 2/3, so tage =

10 Gyr ho

= 10 Gyr 2/3

= 15 Gyr

b.

For critical universe R(t) = ( 1 +( 3/2) Hot )2/3 so age where R-tage)=0 gives tage = (2 / 3) /Ho=

10 Gyr ho

= (2/3) 10 Gyr 2/3

= 10 Gyr

Appendices

QuickQuestions-secs18-24.nb 7