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

Problem 1. A particle is orbiting a star of mass M in a circular orbit. (a, 2 POINTS) Find the equation that provides the orbital speed at a given distance r from the center of the star. (b, 1 POINT) From the result at (a), calculate at what distance rS the particle should be from the center of the star for its orbital speed to be equal to the speed of light, c (in this case, the particle 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 Sun is M = 1.99 × 1030 kg and c = 2.997925 × 105 km/s. (d, 4 POINTS) If the particle is a star orbiting the Galaxy, find and plot the function that describes the speed of the star as a function of its distance from the center of the Galaxy, r. You must calculate this in two cases, if the star is inside or outside the Galaxy. Assume the Galaxy is a homogeneous sphere of maximum radius RGalaxy and density ρ0. (e, 2 POINTS) If the Sun is inside the Galaxy, its orbital 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 Galaxy contained within the orbit of the Sun?

Expert Solution

genius_generous answered 1 year ago

Two stars of mass M?1 and M?2<M?1 are orbiting eachother in a circular orbit. The heavy...

Two stars of mass M?1 and M?2<M?1 are orbiting eachother in a circular orbit. The heavy star experiences a supernova explosion, losing most of its mass in a spherically symmetric outflow (i.e. without losing angular momentum) and leaving behind a small neutron star of mass M??NS. Show that if the mass lost is larger then half of the total mass of the system, the binary is disrupted.

Two stars of mass M1 and M2<M1 are orbiting eachother in a circular orbit. The heavy...

Two stars of mass M1 and M2<M1 are orbiting eachother in a circular orbit. The heavy star experiences a supernova explosion, losing most of its mass in a spherically symmetric outflow (i.e. without losing angular momentum) and leaving behind a small neutron star of mass MNS. Show that if the mass lost is larger then half of the total mass of the system, the binary is disrupted.

An object of mass m is in a circular orbit another heavier object of mass M....

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Q10. Assume that the Earth is orbiting the sun in a perfectly circular orbit. If the...

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4) A planet is orbiting a star at a distance of 1.20 × 1011 m with...

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A rocket with mass 5.00×103 kg is in a circular orbit of radius 7.30×106 m around the earth. The rocket's engines fire for a period of time to increase that radius to 8.70×106 m , with the orbit again circular. A)What is the change in the rocket's gravitational potential energy? Does the potential energy increase or decrease? B) How much work is done by the rocket engines in changing the orbital radius

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A rocket with mass 4.00×103 kg is in a circular orbit of radius 7.40×106 m around the earth. The rocket's engines fire for a period of time to increase that radius to 8.90×106 m, with the orbit again circular. a) What is the change in the rocket's kinetic energy? Does the kinetic energy increase or decrease? b) What is the change in the rocket's gravitational potential energy? Does the potential energy increase or decrease? c) How much work is done...

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