Have a homework question about power law density distributions that I could use a little help on...(adsbygoogle = window.adsbygoogle || []).push({});

Given a power-law distribution, ρ(R) [itex]\propto[/itex] [itex]R^{-\propto}[/itex], show that a flat rotation curve can be obtained if [itex]\propto[/itex] = 2 and that solid body rotation is obtained if [itex]\propto[/itex] = 0.

Also, I'm really not sure what this next question is asking for... Any help?

Suppose the rotation curve of the Milky Way is flat out to 2[itex]R_{0}[/itex]. What mass does that imply out to that distance? If all the luminosity of the Milky Way is contained inside 2[itex]R_{0}[/itex] what is the mass-to-light ratio of the Milky Way in solar units? What is the significance of this value?

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# A few questions about using power laws

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