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): S Po, r< Ro 0, r> Ro p(r) = (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: Voba (r) = VGTP020 Ro 5/2 1+e-dr/R 4

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): S Po, r< Ro 0, r> Ro p(r) = (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: Voba (r) = VGTP020 Ro 5/2 1+e-dr/R 4

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 81AP: The nearest neutron star (a collated star made primarily of neutrons) is about 3.00 1018 m away...

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Question

Please answer the last three parts

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):
S Po, r< Ro
0, r> Ro
p(r) =
(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:
Voba (r) = VGTP020 Ro
5/2
1+e-dr/R
4

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Given

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Visible mass distribution of the Milky way

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Expected rotational velocity

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Expected rotational velocity vs observed rotational velocity

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Rotational velocity due to the dark matter

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Rotational velocity due to the dark matter

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Rotational velocity due to dark matter.

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Dark matter mass distribution function

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Theories in support of dark matter, Galaxy rotation curve and Gravitational lensing

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Large scale structure formation and the role of dark matter.

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