Orbits and Planetary Motion. Directions: Answer the following problem involving orbits and planctary motion. Refer to information given in the box below. Show your solution 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 of the 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 planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas) • The ratio of the squares of the periods (T) of any two planets is equal to the ratio of the cubes of their average distances from the sun (R). (The Law of Harmonies):= 3. Consider a planet with mass Mplanet to orbit in nearly circular motion about the sun of mass Maun: Prove that T? = using the following equations and GMn conditions on orbital motion Mpianet • Net centripetal force: Fnet = - • Gravitational force: Fgrar • Ferav = Fnet • Obtain the equation of speed along a circular path, v. • Substitute the equation of speed, v to the period of revolution: T = • Simplify the equation, square both sides and it should yield T² = GMplanet Moun GM Dage 3 of 3
Orbits and Planetary Motion. Directions: Answer the following problem involving orbits and planctary motion. Refer to information given in the box below. Show your solution 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 of the 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 planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas) • The ratio of the squares of the periods (T) of any two planets is equal to the ratio of the cubes of their average distances from the sun (R). (The Law of Harmonies):= 3. Consider a planet with mass Mplanet to orbit in nearly circular motion about the sun of mass Maun: Prove that T? = using the following equations and GMn conditions on orbital motion Mpianet • Net centripetal force: Fnet = - • Gravitational force: Fgrar • Ferav = Fnet • Obtain the equation of speed along a circular path, v. • Substitute the equation of speed, v to the period of revolution: T = • Simplify the equation, square both sides and it should yield T² = GMplanet Moun GM Dage 3 of 3
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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Transcribed Image Text:Show your solution and answer. Remember that the earth-moon distance is still
in kilometers.
Orbits and Planetary Motion. Directions: Answer the following problem involving
orbits and planetary motion. Refer to information given in the box below. Show your
solution 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 of
the 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 planet
will 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 the
ratio of the cubes of their average distances from the sun (R). (The Law of
Harmonies):
3. Consider a planet with mass Mplanet to orbit in nearly circular motion about the
sun of mass Mgun: Prove that T? = using the following equations and
GMsun
conditions on orbital motion
Net centripetal force: Fet = Mptanet V
Gravitational force: Farav
GMplanet Msun
Farav = Fnet
Öbtain the equation of speed along a circular path, v.
Substitute the equation of speed, v to the period of revolution: T =
Simplify the equation, square both sides and it should vield T2 = 4nR*
GMsun
Page 3 of 3
Show your derivation to prove that T = R
GM
Rubric for Scoring:
General Physics 1
Scoring for Problem Solving (per item)
Answered but Incorrect (3-4) Answered and Correct (5)
Unanswered (2)
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