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Problem 1. A particle is orbiting a star of mass M in a circular orbit. (a,...

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Physics

Problem 1. A particle is orbiting a star of mass M in a circularorbit. (a, 2 POINTS) Find the equation that provides the orbitalspeed at a given distance r from the center of the star. (b, 1POINT) From the result at (a), calculate at what distance rS theparticle should be from the center of the star for its orbitalspeed to be equal to the speed of light, c (in this case, theparticle would be a photon). (c, 1 POINT) Calculate that distance,rS for a star of mass equal to M = 10M, where the mass of the Sunis M = 1.99 × 1030 kg and c = 2.997925 × 105 km/s. (d, 4 POINTS) Ifthe particle is a star orbiting the Galaxy, find and plot thefunction that describes the speed of the star as a function of itsdistance from the center of the Galaxy, r. You must calculate thisin two cases, if the star is inside or outside the Galaxy. Assumethe Galaxy is a homogeneous sphere of maximum radius RGalaxy anddensity ρ0. (e, 2 POINTS) If the Sun is inside the Galaxy, itsorbital speed is 220 km/s and its distance from the center is 25 ×1019 m, what is the mass in kilograms of the part of the Galaxycontained within the orbit of the Sun?

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