A hodge-podge of equations:
4π 2 3
a
GM
r
2GM
=
r
2GM m
dr
r3
r
GM
vcirc =
r
P2 =
vesc
rlim < 2.5(
dF =
ρ̄p 1/3
) Rp
ρ̄m
2 1
v 2 = GM ( − )
r
a
0.29
T (K)
λmax (cm) =
L = 4πR2 σT 4
rperi = a(1 − e)
rapo = a(1 + e)
Bλ (T ) =
2hc2 /λ5
ehc/λkT − 1
13.6
En = − 2 eV
n
Teq = T∗ (1 − a)
kT
mg
P (z) = P0 e−z/H
H=
Vt = 4.74µ(00 /yr)d(pc)
R∗
2r
Rs =
L σ
4π cGm
µ(r) = µ0 + 1.09(r/h)
v = H0 d
1
R
!2
2GM
c2
re ∼ σ 1.24 hIi−0.82
MI = −8.7(log(vc ) − 2.5) − 23.5
M=
1+z =
Ṙ
R
r
< MV >= −2.43 log P − 1.62
[F e/H] = log(F e/H)∗ − log(F e/H)
M=
1
4
5hRiσ 2
G
tH = 1/H0
8
Λ
k
− πGρ − = − 2
3
3
R
2T + U = 0
Possibly Useful Constants and Conversions:
• Solar Blue Magnitudes: mB = −26.14, MB = +5.42
• Solar Visual Magnitudes: mV = −26.8, MV = +4.76
• Gravitational constant: if time is measured in years, distances in AU, and masses
−2
in solar masses, G = 39.5 AU3 M−1
yr
• Gravitational constant: if time is measured in Myr, distances in pc, and masses
−2
in solar masses. G = 4.43 × 10−3 pc3 M−1
Myr
• Stefan-Boltzmann constant σ = 7.18 × 10−17 if luminosities are measured in solar
luminosities, temperature is measured in Kelvin, and sizes are measured in solar
radii.
• 1 parsec (pc) = 206,265 AU
• 1 arcsecond (00 ) = 1/3600 degrees = 4.85 × 10−6 radians
• 1 Angstrom (Å) = 10−8 cm
• 1 year = 3.15 × 107 s
• 1 km/s ≈ 1 pc/Myr