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Problem set 2 for ASTR 221: Stars and Planets
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Due 5pm Friday Sept 20
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Individual questions (hand in one solution each):
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(1) (from Carroll and Ostlie) (a) If all of the angular momentum
that is tied up in the rest of the solar system could be returned to
the Sun, what would its rotation period be? Refer to the data in Fig
23.8 (CandO) which is in our class notes. The moment-of-inertia ratio
of the Sun is 0.073. (b) What would the equatorial velocity of
the photosphere be? (c) How short could the rotation period be
before material would be thrown off from the Sun's equator?
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(2) (also from Carroll and Ostlie) Verify that Kepler's third law in
the form of Eq 2.37 in Carroll and Ostlie applies to the four moons
that Galileo discovered orbiting Jupiter -- Io, Europa, Ganymede and
Callisto, by doing the steps below.
(a) Plot log10(P) vs log10(a) for each of the moons
(b) From the graph, show that
the slope of the best-fit straight line through the data is 3/2.
(c) Calculate the mass of Jupiter from the value of the Y-intercept.
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(3)(a) Assume that a spherical dust grain located 1AU from the Sun has a
radius of 0.1 micron and a density of 3 g/cm**3. In the absence of
gravity, estimate the acceleration of that grain due to radiation
pressure. Assume that the solar radiation is completely absorbed.
(b) What is the gravitational acceleration on the grain?
Note that for certain sizes of grain, this is a way of clearing the solar system of dust just using radiation pressure.
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(4) Comet 1943I, which last passed through perihelion on Feb 27, 1991,
has an orbital period of 512 years and an orbital eccentricity of
0.999914 (!). This is one of a class of so-called sun-grazing
comets.
(a) What is the comet's semi-major axis?
(b) Determine its perihelion and aphelion distances from the Sun.
(c) What is the most likely source of this object, the Oort Cloud or
the Kuiper belt?
Carroll and Ostlie (on reserve in the library) p 29, 30 may be useful
here.
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