4-1 Dimensions
Eratosthenes measured the circumference of the earth in 240 BC.
Estimate was somewhere between 24,663 and 27,957 miles (actual
is 24,902 miles!).
Eratosthenes also figure out the year was 365 1/4 days,
suggested a leap year (which was adopted 200 years later),
and measured the tilt of the earth to within a degree.
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4-2 Dynamics
You will cover the phases of the Moon and eclipses in the homework (NAAP module).
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4-3 Interiors Propagation of Earthquake waves
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4-4 Surface Features Plate tectonics
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Age dating of rocks using radioactive decay.
−dn = λndt
dn/n = −λdt
Where n is the number of atoms, dn is the number that decay in
dt, and λ is a constant. This leads to
n/n0 = exp(−0.693t/τ )
(1)
where τ is the half-life, or the time when n = 1/2n0.
238U decays into 206P b with a half-life of 4.5 billion years - perfect
for estimating age of rocks. Measure ratio
n/n0 =238 U/(238U +206 P b)
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(2)
Problem 4.14
Potassium-40 decays into Argon-40 (which does not occur naturally)
with a half-life τ = 1.3 billion years. Assume that a rock sample contains
ratio of
40
40
Ar and
40
K in the
Ar/40K= 3. How old is the rock? What assumptions do you have to make in order
to calculate an age?
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4-5 Atmospheres
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4-6 Magnetic Fields
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Strength of dipole magnetic field drops as roughly 1/r3.
Lorentz force
~
F~ = q(~v × B)
(3)
Example: What happens to a proton moving to the right when it
enters a uniform B field directed out of page? Sketch its motion.
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Problem 4.7
Show that the circular period P (in seconds) for a charge in a uniform
magnetic field B does not depend upon the radius of the orbit. Evaluate this period for a
proton moving at speed v = 107 m/s in a magnetic field of 10−4 T. (For comparison, Earth’s
B field is 0.5 × 10−4 T.)
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