h6 - ν and κ respectively You are to assume a Plummer...

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Homework # 6, due 22 Mar 1. Demonstrate that the temperature applicable to a stellar system is T = m < v 2 ( x ) > 3 k where it is assumed that the stars have equal mass m , v ( x ) is the velocity of a star relative to the center-of-mass, and <> represents an average. 2. Calculate the gravitational potential a distance z from a steet of matter with uniform surface density Σ, and show that the vertical force is independent of z . 3. In this problem, you are asked to compute the frequencies of the Sun’s orbital excursions from its mean position perpindicular and parallel to the Galactic plane,
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Unformatted text preview: ν and κ , respectively. You are to assume a Plummer model for the Galctic gravitational potential. Find the Plummer parameter a from the observed values of the Oort A and B constants, A = 15 km s-1 kpc-1 , B =-12 km s-1 kpc-1 , assuming the Galactocentric distance of the Sun is R = 8 . 5 kpc and its circular velocity is V = 220 km s-1 . Also determine the total mass of the Galaxy and the fraction which is interior to the solar circle. Explain the ratio κ/ν that you find....
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