# sln4 - EAS 4510 HW#4 Solutions Spring 2005 1) Problem 1.4...

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EAS 4510 HW#4 Solutions Spring 2005 1) Problem 1.4 BMW: Six constants of integration are required for a complete solution to the two-body (relative motion) problem. Why, in general, is a completely determined closed solution of the N-body problem an impossibility if 3 N ? __ _ CM of n body system fixed CM PV t P =+ (6 const. from linear momentum) O HK = (3 const. from cons. of angular momentum) TV ξ += (1 const. from cons. of total mech. energy) This yields 10 constants of motion for the n-body system, which is two short of the minimum of 12 constants needed to solve the 3-body relative motion problem. For an n-body relative motion problem, a minimum of 6(n-1) constants are needed. 2) 1.6 BMW: Find an equation for the velocity of a satellite as a function of total specific mechanical energy and distance from the center of the earth. Vis-viva equation: 2 22 v ra µ =− = The vis-viva equation can be rearranged to yield 2 v r ⎛⎞ ⎜⎟ ⎝⎠ .

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## This note was uploaded on 08/26/2008 for the course EAS 4510 taught by Professor Fitz-coy during the Spring '05 term at University of Florida.

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sln4 - EAS 4510 HW#4 Solutions Spring 2005 1) Problem 1.4...

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