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PHSC108_Hmwk6.pdf - PHSC 10800: Earth as a Planet Homework...

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PHSC 10800: Earth as a PlanetHomework #6Show all work for full credit.Assigned: November 12, 2018Due for Full Credit: November 19, 20181)Planet Velocities and Energy (33 pts)We talked about how planet formation involves the collisions of bodies(planetesimals, embryos) leading to the growth (and heating) of a planet.Let’s thinkabout the velocities and energies involved here.a) The speed of a body in its orbit around the Sun is given by the equation:V2= GM⦿[(2/r) - (1/a)]HereVis the speed of the body in m/s, G is the gravitational constant,M⦿is the mass ofthe Sun in kilograms,ais the semi-major axis of the body in meters, andris its currentdistance from the Sun in meters (remember, in an elliptical orbit, the distance betweenthe Sun and the body is always changing).Assume you have an asteroid with a semi-major axis of 3 AU and a perihelion of 1 AU (so it’s potentially an Earth crossing orbit).What would its speed be at 1 AU?If the Earth’s orbital speed is 30 km/s, what is thelowest velocity at which this asteroid could possibly impact the Earth (what is thedifference in orbital velocity, if both bodies are orbiting in the same direction)?What if itwas a comet, which has a semi-major axis of 20 AU and a perihelion of 1 AU?(Herewe’re ignoring the acceleration from Earth’s gravity to keep things simple.)b) The accretion of planets can involve very large, energetic impacts.The impactthat formed the Moon is typically assumed to have involved the collision of a Mars-sizedimpactor (about 10% the mass of the Earth) with the Earth at a velocity of 10 km/s.Ifthe kinetic energy of a moving body is given byEkinetic=(1/2)mv2where m is its mass andv its speed, what was the energy of the kinetic energy of the impactor?Give youranswer in Joules (J) where 1 J = 1 kg m2/s2.

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Term
Fall
Professor
Fred Ciesla
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