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Physics 110, Problem set #2
Due April 14, 2010
1.
(25 pts) In lecture (3) I showed that perturbing a circular orbit in
2
/
1
r
central
force field will result in stable “oscillations” around the unperturbed solution.
These small oscillations are in fact the difference between a circular orbit and a
slightly elliptical one.
Repeat the calculation and show that a circular orbit is also
stable against perturbations in the
z
direction.
Use the methods and notations
used in the class.
2.
(25 pts) A mass is dropped from the top of a tower (height 10m) located on the
equator. Ignore the air friction. Approximate the Earth as a sphere,
with
24
10
6
×
=
⊕
M
Kg
,
6
10
4
.
6
×
=
⊕
R
m
,
2
1
3
11
10
7
.
6
−
−
−
×
=
s
Kg
m
G
.
Include the
effects of the Coriolis force, the centrifugal force, and the corrected gravitational
acceleration at a nonzero elevation. Think carefully about the relative
contributions of various effects and make approximations.
a.
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 Spring '09
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