Physics 341: Problem Set #4
due October 7
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. We showed in class that we can derive the total mass from a visual binary orbit,
M
=
m
1
+
m
2
=
4
π
2
d
3
˜
α
3
GP
2
where
M
is the total mass, ˜
α
is the angular semimajor axis in radians (˜
α
= ˜
α
1
+ ˜
α
2
),
P
is the orbital period, and
d
is the distance to the system.
Often for visual orbits of stars, we know ˜
α
and
P
very precisely, but the distance
d
is
much more uncertain. Let’s call the fractional uncertainty on the distance
f
d
, meaning
that we think the true distance is within
d
=
d
0
±
f
d
d
0
(where
d
0
is our best guess
and
f
d
²
1). For example, if
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 Fall '08
 Keeton
 Physics, Work, Sirius, fractional uncertainty

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