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/GM %3D It e cas o te coso where e= m GM So d= h? %3D 2. Let T be the period of a planet about the sun; that is, T is the time required for it to travel once around its elliptical orbit. Suppose that the lengths of the major and minor axes of the ellipse are 2a and 2b. (a) Use part (d) of Problem 1 to show that T = 2wab/h. h? (b) Show that GM b2 ed 472 a³. GM (c) Use parts (a) and (b) to show that T2 This proves Kepler's Third Law. [Notice that the proportionality constant 47/(GM) is inde- pendent of the planet.]

/GM %3D It e cas o te coso where e= m GM So d= h? %3D 2. Let T be the period of a planet about the sun; that is, T is the time required for it to travel once around its elliptical orbit. Suppose that the lengths of the major and minor axes of the ellipse are 2a and 2b. (a) Use part (d) of Problem 1 to show that T = 2wab/h. h? (b) Show that GM b2 ed 472 a³. GM (c) Use parts (a) and (b) to show that T2 This proves Kepler's Third Law. [Notice that the proportionality constant 47/(GM) is inde- pendent of the planet.]

College Physics
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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the handwritten in the whiteboard is the information given and please explain how did you get b^2=a^2(1-e^2) and ed=a(1-e^2) to solve question no 2b

/GM %3D It e cas o te coso where e= m GM So d= h? %3D
Transcribed Image Text:/GM %3D It e cas o te coso where e= m GM So d= h? %3D
2. Let T be the period of a planet about the sun; that is, T is the time required for it to travel once around its elliptical orbit. Suppose that the lengths of the major and minor axes of the ellipse are 2a and 2b. (a) Use part (d) of Problem 1 to show that T = 2wab/h. h? (b) Show that GM b2 ed 472 a³. GM (c) Use parts (a) and (b) to show that T2 This proves Kepler's Third Law. [Notice that the proportionality constant 47/(GM) is inde- pendent of the planet.]
Transcribed Image Text:2. Let T be the period of a planet about the sun; that is, T is the time required for it to travel once around its elliptical orbit. Suppose that the lengths of the major and minor axes of the ellipse are 2a and 2b. (a) Use part (d) of Problem 1 to show that T = 2wab/h. h? (b) Show that GM b2 ed 472 a³. GM (c) Use parts (a) and (b) to show that T2 This proves Kepler's Third Law. [Notice that the proportionality constant 47/(GM) is inde- pendent of the planet.]
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