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The Physics of Star Formation Authored by : Dr. Harold Alden Williams Montgomery College at the Takoma Park/Silver Spring Campus, Planetarium Director and Physics and Geology Laboratory Coordinator A few important equations in Newtonian hydrodynamics • • • • • Continuity equation, conservation of mass Equation of Motion, force/volume, in the fluid continuum Energy Equation Equation of State Newtonian Gravity, Poisson’s Equation Equation of Continuity, conservation of mass dr + rÑ × v = 0 dt wherer is the mass density, t is the time, v is the fluid velocity. Newton’s Second Law, conservation of momentum written here in per unit volume. dv r = f = -ÑP - rÑF dt Where is the mass density, is the fluid velocity, is the time, is the force per unit volume, is the pressure, is the gravitational potential. r vt f P F Relationship between total derivative with respect to time and partial derivatives with respect to time for any function g(x;t) dg(x;t) ¶g(x;t) = + v iÑg(x;t) dt ¶t Newton’s Second Law, conservation of momentum in conservative form using previous equation ¶M + Ñ i(Mv) = -ÑP - rÑF ¶t Text Where is the mass density, is the fluid velocity, r is the time, vis the momentum density tis the pressure, M = rv is the gravitational potential. P F Energy Equation e The Energy Equation is the internal energy density is the velocity v is the pressure P is the local heating functions G L is the local cooling function is Cthe thermal conductivity T isTthe temperature de + eÑ iv = -PÑ iv + G - L + Ñ i(CTÑT) dt Three ways to do science 1. Observation or Experiments, requires large expensive telescopes and/or research grants, doable with graduate student helpers. 2. Theory, largely algebra and calculus, cheap, doable in an undergraduate institution even a community college. 3. Simulation, solving equations on a computer at a super computers center, doable with graduate student helpers in a few institutions with super computer centers.