ASTRO 122 formula sheet
I. CONSTANTS AND CONVERSION FACTORS
speed of light c= 299792 km/s,
Planck constant h= 6.62607 ×10−34 kg m2/s
Boltzmann constant k= 1.3806503 ×10−23 J/K
Stefan-Boltzmann constant σ= 5.6704 ×10−8W m−2K−1
Rydberg constant R= 1.097 ×107m−1
Mass of the proton mp= 1.007276u= 1.67262158 ×10−27 kg
Mass of the electron me= 0.0005486u= 9.10938188 ×10−31kg
Mass of the Hydrogen atom (with electron) mH= 1.007825u= 1.67353322 ×10−27 kg
Mass of the Helium atom (with 2 electrons) MHe = 4.002677u= 6.6466032 ×10−27 kg
1eV = 1.60218 ×10−19J
II. ANGLES AND DISTANCES
Conversion between radians, arcmin, and arcseconds
1rad = 57.2958 deg = 3437.750= 20626500
Small angle αdistance d-size Drelation
D=d×α(radians) = d×α(arcsec)/206265
III. PROPERTIES OF LIGHT, BLACK BODY RADIATION
Relation between wavelength λ, frequency fof light and energy Efof photons
fλ =c, Ef=hf =hc
λ
Blackbody radiation: wavelength λmax of the peak of Planck curve (Wien’s Law) and total energy flux
Fthrough the surface of the blackbody of temperature T (Stefan-Boltzmann Law) (temperature always
in Kelvin)
λmax = 0.00291K
Tm, F =σT 4
Total Luminosity Lof a spherical black body (a star) of radius Rand temperature T
L= 4πR2F= 4πσR2T4
