Download Complete Astronomy Formulas Cheat Sheet and more Cheat Sheet Astronomy in PDF only on Docsity! 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× 10−8Wm−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 = 3437.75′ = 206265′′ Small angle α distance d -size D relation D = d× α(radians) = d× α(arcsec)/206265 III. PROPERTIES OF LIGHT, BLACK BODY RADIATION Relation between wavelength λ , frequency f of light and energy Ef of photons fλ = c, Ef = hf = hc λ Blackbody radiation: wavelength λmax of the peak of Planck curve (Wien’s Law) and total energy flux F through the surface of the blackbody of temperature T (Stefan-Boltzmann Law) (temperature always in Kelvin) λmax = 0.0029 1K T m, F = σT 4 Total Luminosity L of a spherical black body (a star) of radius R and temperature T L = 4πR2F = 4πσR2T 4 IV. STRUCTURE OF ATOMS, ATOMIC SPECTRUM OF HYDROGEN Energy levels of Hydrogen atom and energy of transitions between the levels En = − 13.6eV n2 , En − EN = 13.6eV ( 1 N2 − 1 n2 ) Wavelength of the photon emitted or absorbed during atomic transition 1 λ = R ( 1 N2 − 1 n2 ) V. DOPPLER EFFECT Wavelength shift ∆λ of the photon that has wavelength in the laboratory λ if the light source and the observer moves with relative velocity v ∆λ λ = v c v = c · ∆λ λ Relative velocity v is considered positive if the distance between the light source and the observer increases. VI. OPTICS AND TELESCOPES Angular resolution diffraction limit αDiff of a telescope with aperture DA observing at wavelength λ αDiff (radians) = 1.22 λ DA , αDiff (arcsec) = 250000 λ DA VII. BRIGHTNESS OF STARS Inverse square law linking brightness b to luminosity L and distance d of the source (star). b = L 4πd2 , b1 b2 = ( L1 L2 )( d2 d1 )2
