HW7_prob3_tangential impulse

HW7_prob3_tangential - Problem Tangential Impulse Orbit Change(a From the result of GPS Problem 2-11(2.9 in 2nd ed we can relate the change in

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Problem - Tangential Impulse Orbit Change (a) From the result of GPS Problem 2-11 (2.9 in 2 nd ed.) we can relate the change in angular momentum incurred by the comet-star system to the strength of the tangential impulse S , ( μr 2 · θ ) f ( r 2 · θ ) i = l l 0 = S, (1) where the subscripts i and f refer to values just before and after the impulse, respectively. Since the impulse occurs at perihelion, r = r p ,where · r =0 ,wecan use the energy equation for the parabolic orbit to relate r p and l 0 . The general expression for the energy of the orbit is E = μ · r 2 2 k r + l 2 2 μr 2 . (2) For the parabolic orbit, E =0 , and we have 0= k r p + l 2 0 2 μr 2 p , (3) which yields r p = l 2 0 2 μk . (4) The new circular orbit has radius r p , and we can use the circular orbit condition to relate r p and l , f ef ( r p )=0= k r 2 p + l 2 μr 3 p , (5) which yields, r p = l 2 μk . (6) Comparing Eqs.(4) and (6), we f nd l 2 = l 2 0 2 , (7) implying two possible values for
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/19/2010 for the course PHYSICS ph 409 taught by Professor Wilemski during the Fall '10 term at Missouri S&T.

Page1 / 3

HW7_prob3_tangential - Problem Tangential Impulse Orbit Change(a From the result of GPS Problem 2-11(2.9 in 2nd ed we can relate the change in

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online