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< R 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: 5/2 1+e#/Ro

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< R 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: 5/2 1+e#/Ro

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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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 zo): Po, rs 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 e(r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: 5/2 1+e-w/R Draw the expected and observed rotational velocity into the plot below: 2.0 1.5 1.0 0.05 10 Radius from Center r [R,] (d) Scientists believe the reasons for the difference to be dark matter: Determine the rotational velocity due to dark matter vpM (r) from Ro and draw it into the plot above. (e) Derive the dark matter mass MpM(r) enclosed in r and explain its distributed. (f) Explain briefly three theories that provide explanations for dark matter.…
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 (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…
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 zo): Po, rs 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 u (r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: Vobo (r) = /Gapoz0Ro (- 5/2 1+e-4r/Ro Draw the expected and observed rotational velocity into the plot below: 2.0 1.5 1.0 0.5 0.0 10 Radius from Center [R) (d) Scientists believe the reasons for the difference to be dark matter: Determine the rotational velocity due to dark matter vpM(r) from Ro and draw it into the plot above. (e) Derive the dark matter mass MpM(r) enclosed in r and explain its distributed. (f) Explain briefly three theories that provide…
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 zo): p(r) = 0, J Po, 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 v(r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: Vobs (r) = /GT P0 20 Ro 5/2 1+e-4r/Ro Draw the expected and observed rotational velocity into the plot below: 2.0 1.5 1.0 0.5 0.0 4 6 7 9. 10 Radius from Center r [Ro] (d) Scientists believe the reasons for the difference to be dark matter: Determine the rotational velocity due to dark matter vpM(r) from Ro and draw it into the plot above. (e) Derive the dark matter mass MDM(r) enclosed in r and explain its distributed. (f) Explain briefly three theories that provide…
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 zo): Po, rs 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: Vabo (r) = /Gapoz0Ro 5/2 +e-dr/Ro Draw the expected and observed rotational velocity into the plot below: 2.0 1.5 1.0 0.5 0.0 10 Radius from Center [R,) (d) Scientists believe the reasons for the difference to be dark matter: Determine the rotational velocity due to dark matter vpM(r) from Ro and draw it into the plot above. (e) Derive the dark matter mass MpM (r) enclosed in r and explain its distributed. (f) Explain briefly three theories that provide…
The most mass of our Milky Way is contained in an inner region close to the core with radius Re. 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 20): Po rs Ro pr) =30. r> Re (a) Derive an expression for the mass M(r) enclosed within the radius r. (b) Derive the expected rotational velocity of the Milky Way e(r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: 5/2 Draw the expected and observed rotational velocity into the plot below: 15 Radius from Center (A (d) Scientists believe the reasons for the difference to be dark matter: Determine the rotational velocity due to dark matter 'pr(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 ly in
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 zo): p(r) = Po, 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 v(r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: Vobs (r) = VGT P0žo Ro 5/2 1+e-4r/Ro 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 zo): { Po, 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: 5/2 1+e-4r/Ro Vobs (r) = VGapozo Ro Draw the expected and observed rotational velocity into the plot below: 2.0 1.5 0.0 3 2 6 10 Radius from Center r [R] (d) Scientists believe the reasons for the difference to be dark matter: Determine the rotational velocity due to dark matter vpm(r) from Ro and draw it into the plot above. (e) Derive the dark matter mass MpM(r) enclosed in r and explain its distributed. (f) Explain briefly three theories that provide explanations for…
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 zo): { r Ro Po, p(r) = 0, (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: Vobs (r) = VGT Po z0 Ro 5/2 1+e-4r/Ro 4 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 zo): Po, 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: VGT pozoRo 5/2 1+e-4r/Ro Vobs (r) Draw the expected and observed rotational velocity into the plot below: 2.0 1.5 1.0 0.5 0.0 1 7 8. 10 Radius from Center r [Ro) (d) Scientists believe the reasons for the difference to be dark matter: Determine the rotational velocity due to dark matter vpM (r) from Ro and draw it into the plot above. (e) Derive the dark matter mass MDM (r) enclosed in r and explain its distributed. (f) Explain briefly three theories that provide…
The most mass of our Milky Way is contained in an inner region close to the core with radius Re. 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 so): m rs R. dr) =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 (r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: 5/2 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 zo): p(r) = 0, { Po, 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 v(r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: VGT pozo Ro 5/2 1+e-4r/Ro Vobs (r) = 4 Draw the expected and observed rotational velocity into the plot below: 2.0 1.5 1.0 0.5 0.0 6 10 Radius from Center r [Ro] (d) Scientists believe the reasons for the difference to be dark matter: Determine the rotational velocity due to dark matter vpM (r) from Ro and draw it into the plot above. (e) Derive the dark matter mass MpM (r) enclosed in r and explain its distributed. (f) Explain briefly three theories that provide…