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) = Teaud

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 ρpc / (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 /. SolveR ⩵ 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 ≡ GMRs

; Rs= 2 GMc2

ϵ ≡Eg

mc2 = GMm/Racc

mc2 = GMc2 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 kmsMpc

For Ho=67 (km/s)/Mpc, ho=67/100 = 2/3, sotage = 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 kmsMpc

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