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The most mass of our Milky Way is contained in an inner region close to the core with radius Ro- Because the mass outside this inner region is almost constant, the density distribution can be written as following (assume a flat Milky Way with height z0): Po. rs Ro 0, r> Ro plr) = (a) Derive an expression for the mass M(r) enclosed within the radius r. (b) Derive the expected rotational velocity of the Milky Way v(r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: Vida (r) = VGapoz0Ro 5/2 1+etr/&, Draw the expected and observed rotational velocity into the plot below:

The most mass of our Milky Way is contained in an inner region close to the core with radius Ro- Because the mass outside this inner region is almost constant, the density distribution can be written as following (assume a flat Milky Way with height z0): Po. rs Ro 0, r> Ro plr) = (a) Derive an expression for the mass M(r) enclosed within the radius r. (b) Derive the expected rotational velocity of the Milky Way v(r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: Vida (r) = VGapoz0Ro 5/2 1+etr/&, Draw the expected and observed rotational velocity into the plot below:

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The most mass of our Milky Way is contained in an inner region close to the core with radius Ro- Because the mass outside this inner region is almost constant, the density distribution can be written as following (assume a flat Milky Way with height z0): Po. rs Ro 0, r> Ro plr) = (a) Derive an expression for the mass M(r) enclosed within the radius r. (b) Derive the expected rotational velocity of the Milky Way v(r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: Vida (r) = VGapoz0Ro 5/2 1+etr/&, Draw the expected and observed rotational velocity into the plot below:
Transcribed Image Text:The most mass of our Milky Way is contained in an inner region close to the core with radius Ro- Because the mass outside this inner region is almost constant, the density distribution can be written as following (assume a flat Milky Way with height z0): Po. rs Ro 0, r> Ro plr) = (a) Derive an expression for the mass M(r) enclosed within the radius r. (b) Derive the expected rotational velocity of the Milky Way v(r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: Vida (r) = VGapoz0Ro 5/2 1+etr/&, Draw the expected and observed rotational velocity into the plot below:
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Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you. If you want remaining sub-parts to be solved, then please resubmit the whole question and specify those sub-parts you want us to solve.

Step 2

Given the density and height of Milky Way.

(a)

The expression for the mass M(r) enclosed within radius r be calculated as,

Advanced Physics homework question answer, step 2, image 1

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