HW_09_S

# HW_09_S - Ph1a Solutions 9 Chefung Chan (cchan@caltech.edu)...

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Unformatted text preview: Ph1a Solutions 9 Chefung Chan (cchan@caltech.edu) 27 November 2004 Each homework problem is worth 5 points. Please disregard the point values listed on the problem itself. Use these instead. 9.1 FP4 (5 points) 9.1.a (1 point) The total energy E is given by: E = K + U = 1 2 mv 2- GMm r = 1 2 m parenleftbigg GM 5 R parenrightbigg- GMm 5 R E =- GMm 10 R Because E &lt; 0, the orbit will be elliptical. 9.1.b (1 point) The magnitude of the angular momentum vector L is | vector L | = | vector r vector p | = (5 R )( mv ) sin 135 | vector L | = m radicalBig 5 2 GMR 9.1.c (1.5 points) The equations for conservation of energy and angular momentum are respectively: E =- GMm 10 R = 1 2 mv 2 p- GMm r p | vector L | = m radicalBig 5 2 GMR = mv p r p Solving the second equation for r p gives r p = radicalBig 5 2 GMR/v 2 p Substituting into the energy equation:- GMm 10 R = 1 2 mv 2 p- GMm v p radicalBig 5 2 GMR v 2 p- 2 parenleftBigg radicalbigg 2 GM 5 R parenrightBigg v p + GM 5 R = 0...
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## This note was uploaded on 03/30/2010 for the course PH 1a taught by Professor Goodstein during the Fall '07 term at Caltech.

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HW_09_S - Ph1a Solutions 9 Chefung Chan (cchan@caltech.edu)...

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