## Some Useful Numbers

Parsecs: 1 pc = 3.086 x 1013 km = 206265 AU ; 1 pc3 = 2.94 x 1055 cm3
Time: 1 year = 3.156 x 107 s
Hubble time: H0-1 = 13.6 Gyr for H0 = 72 km s-1 Mpc-1
Solar mass: 1 M = 1.989 x 1030 kg
Proton mass: 1 mp = 1.6726 x 10-27 kg = 0.938 GeV c-2
Mass density: 1 M pc-3 = 39.77 GeV cm-3 = 6.77 x 10-23 g cm-3

Newton's constant:
G = 6.67 x 10-8 cm3 s-2 g-1 = 1.327 x 1011 km3 s-2 M-1 = 4.3 x 10-6 kpc km2 s-2 M-1

Surface brightness conversion between linear Σ in L pc-2 and logarithmic μ in magnitudes arcsecond-2:
μ = 21.57 + M -2.5logΣ
where M is the absolute magnitude of the sun in the relevant band, not to be confused with the solar mass M.

Distance modulus: m-M = 5logD-5 when D is in pc; becomes 5logD+25 when D is in Mpc. There is also a term for the k-correction due to the redshifting of the source spectrum when the cosmic redshift becomes substantial.

HI flux-to-mass conversion: MHI = 2.36 x 105 D2 FHI
gives the mass of atomic hydrogen in M given D, the distance in Mpc and FHI, the 21 cm flux integral in Jy km s-1

Baryonic Tully-Fisher Relation:
Mb = A*Vf4
with A ≈ 50 M km-4 s4
In MOND, A = X/(Ga0) with the geometric factor X ≈ 0.8 and (Ga0)-1 = 63 M km-4 s4.

MOND acceleration constant:
a0 = 1.2 x 10-10 m s-2 = 3700 km2 s-2 kpc-1

Critical surface density
Σ* = a0/G = 860 M pc-2 = 1.8 kg m-2 (about the surface density of a stiff piece of construction paper)