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#### EQUATIONS.C

Course: ASTRO 119, Fall 2009

School: Concordia Chicago

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CONVERSIONS EQUATIONS, AND CONSTANTS Compiled for Phy Sci 119, Fall quarter, 2005. FUNDAMENTAL CONSTANTS c=3x1010 cm/sec=300,000 km/sec (speed of light) G=6.67x10-8 cm3/g-sec2 (gravitational constant) k=1.38x10-16 ergs/oK (Boltzmann's constant) h=6.625x10-27 erg-sec (Planck's constant) Ionization energy of neutral hydrogen (H) =13.6 eV. mH=1.6x10-24 g (mass of proton or hydrogen atom) me=9x10-28 g (mass of...

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CONVERSIONS EQUATIONS, AND CONSTANTS Compiled for Phy Sci 119, Fall quarter, 2005. FUNDAMENTAL CONSTANTS c=3x1010 cm/sec=300,000 km/sec (speed of light) G=6.67x10-8 cm3/g-sec2 (gravitational constant) k=1.38x10-16 ergs/oK (Boltzmann's constant) h=6.625x10-27 erg-sec (Planck's constant) Ionization energy of neutral hydrogen (H) =13.6 eV. mH=1.6x10-24 g (mass of proton or hydrogen atom) me=9x10-28 g (mass of electron) mHc2=109 eV=1 Gev (rest mass of the proton) T=0.29cm-oK (Wien's law) =5.6x10-5 erg/(cm2-sec-oK4) [Stefan-Boltzmann constant] 1 radian=2x105 arcsec R=109,680 cm-1 the Rydberg constant. ASTRONOMICAL "CONSTANTS" 1 solar mass=2x1033 g 1 solar luminosity=4x1033 erg 1 solar radius=7x1010 cm. =0.007, the efficiency of conversion of mass to energy in converting H to He (nucleosynthesis). 1 Earth mass=5.6x1027 g 1 Earth radius=6.37x108 cm Age of the Universe=1.4 x 1010 years Main sequence lifetime of the Sun=1010 years. Current age of the Sun =4.8x1010 years CONVERSIONS 1 eV=1.6x10-12 erg 1 AU=1.5x1013 cm= one astronomical unit=Earth-Sun distance. 1 pc=2x105 AU=3x1018 cm 1 yr=3x107 sec 1 Angstrom=10-8 cm 1 Mpc=106 pc 1 km=105 cm K=1046 erg, the energy released by dropping 1 solar mass from infinity to a distance of 1AU from another one solar mass object. m-M=5logr-5, the magnitude equation M=M1-M2=-2.5 log L1/L2, where Lx and Mx are the luminosities and absolute magnitudes in a common filter band for two stars, 1 and 2. DISTANCES AND GRAVITY =1/d, where is the parallax in arcseconds, d is the distance to an object in parsecs (pc). l/d = (radians) the "skinny triangle", l is the arc of a long, skinny triangle; where d is the distance from the observer to the arc; and is the angle, in radians, made by the line of length l that delineate the arc (approximated as a straight line for this equation.) F=-GmM/r2, the force between two bodies of mass m and M, separated by distance r. F=-mv2/r, the force acting on any body in circular motion, never mind the nature of the force. U=- GmM/r, the potential energy of two bodies separated by distance r. K=(1/2)mv2 , the kinetic energy of a body of mass m moving at velocity v. K=-U=GmM/r=(1/2)mv2, the kinetic energy of two bodies in free-fall, E=0, E=0. K=-U/2, the Virial theorem, which applies to bodies in bound orbits. v=(GM/r)1/2, orbital velocity of a body of mass m at distance r around mass M v=(2GM/r)1/2 , the velocity of a body in free fall at a distance r from the body it is moving toward; also, the escape velocity of a body from a body of mass M, starting at distance r. P2=4 2R3/GM, where P is the period of two objects, in seconds, in circular orbits around a center of mass, R =the sum of the radii of the two orbits (in cm), M is the sum of the two masses (grams) and G is the gravitational constant as given above. P2=R3/M, the above equation in units years, of AU and solar masses. Binary Orbits: r1/r2=v1/v2=m2/m1 for stars of mass m1 and m2, orbiting the center of mass at velocities v1 and v2 at distances from the center of mass of r1 and r2: MJ=10T(T/n)1/2, MJ the Jean's mass in Solar masses, where T is the temperature in oK and n is the density of H atoms (particles per cubic centimeter) RJ=5(T/n)1/2, the radius of a cloud in parsecs that will just collapse (and which at temperature T and particle density n contains mass MJ). LIGHT AND THE ATOM (/ ) =(/ )=v/c, the Doppler shift (non-relativistic): =wavelength, =frequency, v=velocity, c=speed of light =c / ( frequency of a photon), where is the frequency, is the wavelength and c is the speed of light. E=h 1/=RZ2[(1/n12)-(1/n22)], where is the wavelength of the photon emitted, n1 is the Bohr quantum number for the inner most orbit and n2 is the Bohr quantum number for the outer most Bohr orbit being considered. R is the Rydberg constant, given above. For Balmer alpha, emission of hydrogen, Z=1, n1=2, n2=3 and =6563A. =fh /c, f=flux of photons of energy h per cm2 per sec. p=fh A, total power received by an antenna or telescope on Earth. THERMODYNAMICS and STARS (1/2)mv2=(3/2)kT, relation of velocity v in a gas of temperature T. T=0.29 cm-oK (Wien's law) F= T4, flux in ergs/cm2-sec from a Black Body of temperature T. L=4 R2 T4, luminosity in ergs/sec of a Black Body of radius R and temperature T L/Lo=(M/Mo)3.5 , the mass-luminosity relationship for stars on the main sequence. t/to=(M/Mo) -2.5, the main sequence life time of a star of mass M, where to and Mo are the values for the Sun (5 billion years and one solar mass). tcollapse=GM2/LR, an approximation to the collapse time ...

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