Orbits and Planetary Motion. Directions: Answer the following problem involvingorbits and planetary motion. Refer to information given in the box below. Show yoursolution and box your final answer|Kepler's three laws of planetary motion can be described as follows:• The path of the planets about the sun is elliptical in shape, with the center ofthe sun being located at one focus. (The Law of Ellipses)An imaginary line drawn from the center of the sun to the center of the planetwill sweep out equal areas in equal intervals of time. (The Law of Equal Areas)The ratio of the squares of the periods (T²) of any two planets is equal to theratio of the cubes of their average distances from the sun (R³). (The Law ofHarmonies):3. Consider a planet with mass Mplanet to orbit in nearly circular motion about thesun of mass Msun. Prove that T² = 4"*R²using the following equations andGMsunconditions on orbital motionMptanet v²• Net centripetal force: Fnet =Gravitational force: FgravGMplanetMsunR2Fgrav = FnetObtain the equation of speed along a circular path, v.Substitute the equation of speed, v to the period of revolution: T = 2Simplify the equation, square both sides and it should yield T :GMsun47²R³Show your derivation to prove that T²%3DGM sun

Answered: Image /qna-images/answer/fa562511-2138-422d-95bb-6f7ae76fce2b.jpg

. Consider a planet with mass Mptanet to orbit in nearly circular motion about the sun of mass Msun: Prove that T² = * using the following equations and GMsun conditions on orbital motion Net centripetal force: Fnet Mptanet v² R GMplanetMsun Gravitational force: Fgrav = Fgrav = Fnet Obtain the equation of speed along a circular path, v. Substitute the equation of speed, v to the period of revolution: T 2mR Simplify the equation, square both sides and it should yield T² 4x²R %3D GMsun

. Consider a planet with mass Mptanet to orbit in nearly circular motion about the sun of mass Msun: Prove that T² = * using the following equations and GMsun conditions on orbital motion Net centripetal force: Fnet Mptanet v² R GMplanetMsun Gravitational force: Fgrav = Fgrav = Fnet Obtain the equation of speed along a circular path, v. Substitute the equation of speed, v to the period of revolution: T 2mR Simplify the equation, square both sides and it should yield T² 4x²R %3D GMsun

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 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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