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44.56:
a) For this model,
,
so
,
H
R
HR
R
dt
dR
HR
dt
dR
=
=
=
presumed to be the same for
all points on the surface.
b) For constant
,
θ
.
Hr
HR
dt
dR
dt
dr
=
=
=
c) See part
(a),
.
0
R
dt
dR
H
=
d) The equation
R
H
dt
dR
0
=
is a differential equation, the solution to
which, for constant
,
)
is
0
0
0
t
H
e
R
R(t
H
=
where
0
R
is the value of
R
at
0
=
t
. This equation
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Unformatted text preview: may be solved by separation of variables, as ) ( ln H R dt d R dt dR = = and integrating both sides with respect to time. e) A constant H would mean a constant critical density, which is inconsistent with uniform expansion....
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This note was uploaded on 02/23/2009 for the course PHYSICS 750:116 taught by Professor Brahmia during the Spring '09 term at Rutgers.
 Spring '09
 Brahmia
 Physics

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