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w3390
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Homework Statement
A star is moving in a circular orbit of radius r within a galaxy. What is it's orbital speed
v(r) as a function of [tex]\rho[/tex](r) and radius.
The galaxy is spherically symmetric with a mean density [tex]\rho(r)[/tex] and radius R.
Homework Equations
F = -Gm[tex]\int[/tex][tex]\frac{\rho(r')e_{r}}{r^{2}}[/tex]
The Attempt at a Solution
My attempt to find the orbital speed was to equate the equation mentioned above to F = ma, which in this case would be F = mv^2/r. From here I solved for v. However, I am confused about what to do for the integral. As I have it now, my answer looks like:
v(r) = [-Gr[tex]\int[/tex][tex]\frac{\rho(r')e_r}{r^2}[/tex]dV']^1/2
Is that correct?
Any help would be much appreciated.