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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
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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.