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Carefully write down the fit equation and consider the following questions.
1.
Is a linear function a good fit to the data?
2.
Compare the fit equation to the equation for a straight line:
y
=
mx
+
c
. What can you conclude
about the relationship between
T
and
a
?
3.
Assume that the planets are actually undergoing uniform circular motion (not a bad
approximation in most cases) in which the radius of the planet’s orbit is equal to the semimajor
axis
a
. Decide what provides the centripetal force and then apply Newton’s 2
nd
law to derive a
general
equation relating the orbital period
T
to the semimajor axis,
a
. This should involve the
mass of the Sun,
M
~
and Newton’s gravitational constant,
G
.
4.
Compare your equation to your linear fit to the log
T
– log
a
graph. What is the significance of
the numerical coefficients of the fit (i.e.
m
and
c
)?
5.
Use the coefficients of your linear fit to determine the mass of the Sun. Compare your result to
the actual mass (you can find this in Appendix C of the textbook).
Write out your answers neatly and attach a printout of your graph.
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 Fall '09
 LIND

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