## PHYSICAL AND ASTRONOMICAL QUANTITIES

The following compilation of conversions, constants, and derived values is by no means complete. Rather, it pertains to the particular topic of galaxian astronomy, as discussed in the present book. When possible, values are given to 5 significant figures. Most quantities are given in the centimeter-gram-second (CGS) system that is favored by many astronomers, with conversions to the meter-kilogram-second (MKS or SI), English, and other systems when deemed useful. For a more detailed compilation of physical and astronomical quantities, see the book Astrophysical Formulae by Kenneth R. Lang (1999, 3rd Edition, Astronomy & Astrophysics Library [New York: Springer-Verlag]).

Conversions

Numbers:

p = 3.1416

e = 2.7183

n = nana = 10-9 (e.g. 1 nm = 10-9 m)

similarly (m = micro = 10-6), (m = milli = 10-3), (c = centi = 10-2), (k = kilo = 103),

(M = mega = 106; e.g. 1 Mpc = 106 pc), (G = giga = 109 ; e.g. 1 Gyr = 109 yrs).

Angle:

1 degree (o) = 60 arcminutes (') = 3600 arcseconds ("), where 360o = circle.

1 radian (rad) = 57.296o = 206265", where 2p radians = circle.

1 steradian = 1 rad2 = 3282.8 deg2 = 4.25 x 1010 arcsec2, where 4p steradians = sphere.

1 hour (hr) of Right Ascension (RA) = 60 minutes = 3600 seconds, where 24 hr = circle.

1 hr = 15o at constant Declination (Dec); 1 hr = 15o cos(Dec) along great circle.

Length:

1 cm = 108 Å = 107 nm = 104 mm = 101 mm = 10-2 m = 10-5 km;

1 mile = 5280 ft = 1.609 km = 1.609 x 105 cm; 1 ft = 12 inches; 1 inch = 2.54 cm.

1 Astronomical Unit (AU) = 1.4960 x 1013 cm = 92.975 x 106 miles.

1 light-year (ly) = 9.4605 x 1017 cm = 5.8797 x 1012 miles.

1 parsec (pc) = 3.0856 x 1018 cm = 3.2616 ly = 206265 AU.

Time (t):

1 sidereal year (yr) = 365.25636 d = 3.15581498 x 107 s.

1 solar year (yr) = 365.24219 d = 3.15569258 x 107 s.

Speed (v) {length per unit time}:

1 km/s = 5.7924 x 103 miles/hr = 3.337 ly/Myr = 1.023 pc/Myr.

Hydrogen in thermal equilibrium: v = (kT/mH)1/2 = 9.083 km s-1 (T/104K)1/2.

Mass (M or m):

1 kilogram (kg) = 103 g.

1 ounce (oz) = 1/16 pound = 28.571 g.

Density (r) {mass per unit volume}:

1 kilogram/meter3 (kg m-3) = 10-3 kg/L = 10-3 g/cm3.

Force (F):

1 Newton (N) = 105 dyne.

1 pound (lb) = 4.482 x 105 dyne.

Temperature (T):

0o Kelvin = -273.15o Centigrade.

0o Centigrade = 273.15o Kelvin = 32o Fahrenheit, where T(oF) = (9/5) T(oC) + 32o.

Pressure (P) {force per unit area = energy per unit volume}:

1 Pascal (Pa) = 1 N/m2 = 10 dyne/cm2 = 1.45 x 10-4 lb/in2.

1 atmosphere (atm) = mean atmospheric pressure on Earth at sea level.

1 atm = 1.013 x 106 dyne/cm2 = 1.013 x 105 Pa = 14.7 lb/in2.

Energy (E):

1 erg = work to lift 1.02 milloigrams of mass a height of 1 cm at Earth’s surface (sea level).

1 Joule (J) = 107 erg.

1 Calorie (cal) = 4.1839 erg.

1 electron-Volt (eV) = energy of one electron accelerated by 1 Volt potential difference.

1 eV = 1.6022 x 10-12 erg ==> l = 1.24 x 103 nm (E/eV)-1 = 1.24 x 104 Å (E/eV).

Proton rest energy: mpc2 = 938.3 MeV; Electron rest energy: mec2 = 0.511 MeV.

Power (P or L) {rate of doing work or expending energy; luminosity}:

1 Watt (W) = 1 Joule/s = 107 erg/s.

1 horsepower (hp) = 745.7 W = 7.457 x 107 erg/s.

Physical Quantities

 Symbol Meaning Value c Speed of light in vacuum 2.9979 x 1010 cm s-1 G Gravitational constant 6.6726 x 10-8 dyne cm2 g-2 h Planck’s constant 6.6261 x 10-27 erg s k Boltzmann’s constant 1.3806 x 10-16 erg K-1 e Charge of electron (e-) -4.8032 x 10-10 esu (CGS) -1.602 x 10-12 coulomb (SI) me Rest mass of electron 9.1094 x 10-28 g mp Rest mass of proton 1.6726 x 10-24 g mH Mass of hydrogen atom 1.6735 x 10-24 g lc = h/mec Compton wavelength (of e-) 2.4263 x 10-10 cm s = (2p5k4)/(15c2h3) Stefan-Boltzmann constant 5.6705 x 10-5 erg cm-2 s-1 K-4 sT = (8p/3)(e2/mec2)2 Thomson e- cross section 6.6525 x 10-25 cm2 lp T Wien’s Law constant 2.8977 x 10-1 cm K 2.8977 x 106 nm K 2.8977 x 107 Å K EH+ H ionization potential 13.6 eV ==> lH+ = 91.2 nm aB H recombination coefficient 2.59 x 10-13 cm3 s-1 at T = 10,000K

Astronomical Quantities

 Symbol Meaning Value M(Earth) Mass of Earth 5.9737 x 1027 g R(Earth) Radius of Earth 6378.1 km t(Earth) Sidereal year 365.26 days = 3.156 x 107 s v(Earth) Earth’s orbital speed 29.9 km/s a(Earth) Earth’s orbital radius (AU) 1.4960 x 1013 cm M(Sun) Solar mass 1.9891 x 1033 g R(Sun) Solar radius 6.9598 x 105 km Teff(Sun) Solar effective temperature 5780 K LBol(Sun) Solar bolometric luminosity 3.85 x 1033 erg/s mV(Sun), mB(Sun) Solar apparent magnitudes -26.73 mag, -26.08 mag MV(Sun), MB(Sun) Solar absolute magnitudes +4.83 mag, +5.48 mag Mbol(Sun) Solar bolometric magnitude +4.72 mag t(Sun) Solar orbital period 200 Myr v(Sun) Solar orbital speed 220 km/s RG(Sun) Galactocentric radius of Sun 8.5 kpc = 27.7 x 103 ly M(Gal) Dynamical mass of Galaxy > 4 x 1011 M(Suns)