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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: r< Ro p(r) 0, r> Ro (a) Derive an expression for the mass M(r) enclosed within the radius r. (b) Derive the expected rotational velocity of the Milky Way u(r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: 5/2 Vada (r) = VGapoz0Ro 1+e-r/R Draw the expected and observed rotational velocity into the plot below: 2.0 1.5 1.0 0. 0.0 6 10 Radius from Center r [RI (d) Scientists believe the reasons for the difference to be dark matter: Determine the rotational velocity due to dark matter upM (r) from Ro and draw it into the plot above. (e) Derive the dark matter mass Mpar (r) enclosed in r and explain its distributed. (f) Explain briefly three theories that provide explanations for dark matter. Rotational Velocity e lyGrlo)

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: r< Ro p(r) 0, r> Ro (a) Derive an expression for the mass M(r) enclosed within the radius r. (b) Derive the expected rotational velocity of the Milky Way u(r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: 5/2 Vada (r) = VGapoz0Ro 1+e-r/R Draw the expected and observed rotational velocity into the plot below: 2.0 1.5 1.0 0. 0.0 6 10 Radius from Center r [RI (d) Scientists believe the reasons for the difference to be dark matter: Determine the rotational velocity due to dark matter upM (r) from Ro and draw it into the plot above. (e) Derive the dark matter mass Mpar (r) enclosed in r and explain its distributed. (f) Explain briefly three theories that provide explanations for dark matter. Rotational Velocity e lyGrlo)

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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: r< Ro p(r) 0, r> Ro (a) Derive an expression for the mass M(r) enclosed within the radius r. (b) Derive the expected rotational velocity of the Milky Way u(r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: 5/2 Vada (r) = VGapoz0Ro 1+e-r/R Draw the expected and observed rotational velocity into the plot below: 2.0 1.5 1.0 0. 0.0 6 10 Radius from Center r [RI (d) Scientists believe the reasons for the difference to be dark matter: Determine the rotational velocity due to dark matter upM (r) from Ro and draw it into the plot above. (e) Derive the dark matter mass Mpar (r) enclosed in r and explain its distributed. (f) Explain briefly three theories that provide explanations for dark matter. Rotational Velocity e lyGrlo)
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: r< Ro p(r) 0, r> Ro (a) Derive an expression for the mass M(r) enclosed within the radius r. (b) Derive the expected rotational velocity of the Milky Way u(r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: 5/2 Vada (r) = VGapoz0Ro 1+e-r/R Draw the expected and observed rotational velocity into the plot below: 2.0 1.5 1.0 0. 0.0 6 10 Radius from Center r [RI (d) Scientists believe the reasons for the difference to be dark matter: Determine the rotational velocity due to dark matter upM (r) from Ro and draw it into the plot above. (e) Derive the dark matter mass Mpar (r) enclosed in r and explain its distributed. (f) Explain briefly three theories that provide explanations for dark matter. Rotational Velocity e lyGrlo)
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