Physics 341: Problem Set #7
due October 28
You are encouraged to work in groups on these problems, but each student must write up
the solutions individually. You must also list your collaborators on your solutions, and cite
any external sources you used (other than the course notes or textbook).
I will give partial credit for partial answers, but only if you show your work and explain your
reasoning. Be careful with units.
1. Recall that the surface brightness of an exponential disk has the form
I
(
R
)=
I
0
e

R/h
R
where
I
0
is the central surface brightness and
h
R
is the disk scale length. The total
brightness is given by integrating this proFle from
R
= 0 to
R
=
1
:
I
total
=
Z
1
0
I
(
R
)2
⇡
RdR
(a) Show that the total brightness of the exponential disk is
I
total
=2
⇡
I
0
h
2
R
Show your work!
Hint:
Let
x
=
R/h
R
and rewrite the integral in terms of
x
and
dx
. Note that from integration by parts,
R
xe

x
dx
=

(
x
+1)
e

x
plus a constant.
(b) What fraction of the total light is within one disk scale length (
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 Spring '11
 Gawsier
 Physics, Dark Matter, Mass, Work, rotation curve

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