##
Some Useful Numbers

Parsecs:
1 pc = 3.086 x 10^{13} km = 206265 AU ;
1 pc^{3} = 2.94 x 10^{55} cm^{3}

Time: 1 year = 3.156 x 10^{7} s

Hubble time: H_{0}^{-1} = 13.6 Gyr for
H_{0} = 72 km s^{-1} Mpc^{-1}

Solar mass:
1 M_{⊙} = 1.989 x 10^{30} kg

Proton mass:
1 m_{p} = 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} cm^{3} s^{-2} g^{-1} =
1.327 x 10^{11} km^{3} s^{-2} M_{⊙}^{-1} =
4.3 x 10^{-6} kpc km^{2} 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: M_{HI} = 2.36 x 10^{5} D^{2} F_{HI}

gives the mass of atomic hydrogen in M_{⊙} given
D, the distance in Mpc and F_{HI}, the
21 cm flux integral in Jy km s^{-1}

Baryonic Tully-Fisher Relation:

M_{b} = A*V_{f}^{4}

with A ≈ 50 M_{⊙} km^{-4} s^{4}

In MOND, A = X/(Ga_{0}) with the geometric factor X ≈ 0.8 and
(Ga_{0})^{-1} = 63 M_{⊙} km^{-4} s^{4}.

MOND acceleration constant:

a_{0} = 1.2 x 10^{-10} m s^{-2} =
3700 km^{2} s^{-2} kpc^{-1}

Critical surface density

Σ_{*} = a_{0}/G = 860 M_{⊙} pc^{-2}
= 1.8 kg m^{-2} (about the surface density of a stiff piece of
construction paper)