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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): 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

Stars and Galaxies (MindTap Course List)
Stars and Galaxies (MindTap Course List)
10th Edition
ISBN:9781337399944
Author:Michael A. Seeds
Publisher:Michael A. Seeds
Chapter16: Galaxies
Section: Chapter Questions
Problem 15P
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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): 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
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): 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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