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Astrophysics I Equation Cheat Sheet , Cheat Sheet of Astrophysics

Reed CollegeAstrophysics

Useful overview of the Astrophysics I Equations

Typology: Cheat Sheet

2019/2020

Uploaded on 11/27/2020

ekaant
ekaant 🇺🇸

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Equation Sheet - Astrophysics I - Fall 2014
∆θ= 1.22λ/D SNR = Nstar/qNtotal Ntotal =Nstar +p×nsky
d= 1/p D =θd λν =c E =hν
Bν=2hν3
c2
1
ehν/kT −1λmax T= 0.29 cm K hνmax = 2.8kT
L= 4πr2
∗σT 4=f4πd2
M1r1=M2r2ω2=G(M1+M2)
a3(M1+M2) sin3i=τ(v1obs +v2obs)3
2πG
dM
dr = 4πr2ρ(r)dP
dr =−GMρ
r2
dL
dr = 4πr2ρǫ dT
dr =3Lκρ(r)
16πr2acT 3
l= 1/nσ = 1/ρκ Pgas =nkT =ρ
¯mkT EK=f
2kT Prad =1
3aT 4
EG= 2µc2(παZAZB)2α=e2
¯h≈1/137
F=q1q2/r2λ=h/p ∆x∆px> h
dN =2s+ 1
exp E−µ(T)
kT + 1
d3pdV
h3ne=8π
3h3p3
f
P=1
3Zn(p)pvdp Pe=3
8π2/3h2
5me
n5/3
e=3
π2/3h2
20mem5/3
pZ
A5/3
ρ5/3
Pe=8πc
3h3
p4
f
4=3
8π1/3hc
4m4/3
pZ
A4/3
ρ4/3
rwd ≈h2
20mem5/3
pGZ
A5/3
M−1/3rwd = 2.3×109cm Z
A5/3 M
M⊙!−1/3
Mch = 1.4M⊙
Erot =1
2Iω2I=2
5Mr2L=B2r6ω4
6c3sin2θ
pf2

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Equation Sheet - Astrophysics I - Fall 2014

∆θ = 1. 22 λ/D SNR = Nstar/

√

Ntotal Ntotal = Nstar + p × nsky

d = 1/p D = θd λν = c E = hν

B

ν

2 hν

3

c

2

e

hν/kT − 1

λ max

T = 0.29 cm K hν max

= 2.8kT

L = 4πr

2

∗

σT

4

= f 4 πd

2

M

1

r 1

= M

2

r 2

ω

2

=

G(M

1

+ M

2

a

3

(M

1

+ M

2

) sin

3

i =

τ (v 1 obs

  • v 2 obs

3

2 πG

dM

dr

= 4πr

2

ρ(r)

dP

dr

GM ρ

r

2

dL

dr

= 4πr

2

ρǫ

dT

dr

3 Lκρ(r)

16 πr

2 acT

3

l = 1/nσ = 1/ρκ P gas

= nkT =

ρ

m ¯

kT E K

f

kT P rad

aT

4

EG = 2μc

2

(παZAZB )

2

α =

e

2

¯h

F = q 1

q 2

/r

2 λ = h/p ∆x∆p x

h

dN =

2 s + 1

exp

(

E−μ(T )

kT

)

d

3 pdV

h

3

ne =

8 π

3 h

3

p

3

f

P =

∫

n(p)pvdp Pe =

(

3

8 π

) 2 / 3 h

2

5 m e

n

5 / 3

e

(

3

π

) 2 / 3 h

2

20 m e

m

5 / 3

p

(

Z

A

) 5 / 3

ρ

5 / 3

P

e

8 πc

3 h

3

p

4

f

(

3

8 π

) 1 / 3

hc

4 m

4 / 3

p

(

Z

A

) 4 / 3

ρ

4 / 3

r wd

h

2

20 m e

m

5 / 3

p G

(

Z

A

) 5 / 3

M

− 1 / 3

r wd

= 2. 3 × 10

9

cm

(

Z

A

) 5 / 3

(

M

M⊙

) − 1 / 3

M

ch

= 1. 4 M

⊙

Erot =

Iω

2

I =

M r

2

L =

B

2

r

6

ω

4

6 c

3

sin

2

θ

r s

2 GM

c

2

= (3 km)

M

M

⊙

(ds)

2

=

(

2 GM

rc

2

)

(cdt)

2

−

(

2 GM

rc

2

) − 1

(dr)

2

− (rdθ)

2

− (r sin θdφ)

2

F

tide

m

2 GM

2

∆r

r

3

dE th

(

GM dM

r

GM dM

r + ∆r

)

dE

dt

GM

M

dr

r

2

= 2(2πr)σT

4

dr

T (r) =

(

GM

M

8 πσ

) 1 / 4

r

− 3 / 4

L ≈

GM

M

2 r in

L

E

4 πcGM m p

σ T

= (1. 3 × 10

38

erg/s)

M

M

⊙

ρJ =

4 πM

2

(

3 kT

G m¯

) 3

Rrec = α(T )x

2

n

2

Rion = nphotonn(1 − x)σionc rstrom =

(

3 Q∗

4 παn

2

) 1 / 3

n 2

n 1

g 2

g 1

e

−hν/kT

G = 6. 67 × 10

− 8 erg cm g

− 2 h = 6. 63 × 10

− 27 erg s c = 3. 0 × 10

10 cm/s

k = 1. 38 × 10

− 16 erg/K = 8. 62 × 10

− 5 eV/K

σ = 5. 67 × 10

− 5

erg cm

− 2

K

− 4

a = 4σ/c = 7. 6 × 10

− 15

erg cm

− 3

K

− 4

m p

= 1. 67 × 10

− 24 g m e

= 9. 1 × 10

− 28 g

e = 4. 8 × 10

− 10

statcoulombs 1 statcoulomb = 1 erg

1 / 2

cm

1 / 2

σ T

= 6. 7 × 10

− 25 cm

2

1 pc = 3. 086 × 10

18

cm

CGS units: erg = g cm

2 s

− 2 = dyne cm

Sun:

M

⊙

= 2. 0 × 10

33 g R ⊙

= 7. 0 × 10

10 cm L ⊙

= 3. 8 × 10

33 erg/s

T

E⊙

= 5800 K ρ¯ ⊙

= 1.4 g cm

− 3 T C⊙

= 15 × 10

6 K ρ C⊙

= 150 g cm

− 3