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Astr 421 Fall 2004

Galaxies Sylvain Veilleux

October 6, 2004 DUE: October 15, 2004

PROBLEM SET # 3

Problems 1 - 4.

Sparke & Gallagher, Problems 3.2, 3.3, 3.6, and 3.19

Problem 5.

Assume that the Sun is in the midplane of the Galaxy with a vertical component of motion equal to 7 km s$^{-1}$. Assume that the Sun moves through a constant-density region with $\rho$ = 0.13 M$_\odot$ pc$^{-3}$.

(a)
Apply Gauss's law in a plane-parallel layer to show that the Sun executes simple harmonic motion with a force constant proportional to $\rho_0$.

(b)
Estimate the maximum height above the plane that the Sun will reach.

(c)
In light of the derived value of z$_{\rm max}$, is the assumption of a constant density medium realistic?

(d)
Roughly how many vertical oscillations has the Sun made during its lifetime (4.6 billion years)?





Sylvain Veilleux 2004-10-05