This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Problem Goldstein 312 (3 rd ed. 3.18) From the result of Problem 29 (2.11 in 3 rd ed.) we can relate the change in r incurred by the particle of reduced mass to the strength of the radial impulse S , ( r ) 2 ( r ) 1 = S , (1) where the subscripts 1 and 2 refer to values just before and after the impulse, respectively. Since the impulse occurs at perigee, ( r ) 1 = 0 , and we f nd r 2 = S/ . (2) The general expression for the energy of the orbit is E = r 2 2 k r + l 2 2 r 2 . (3) We can evaluate the initial energy at the perigee, r = r p : E 1 = k r p + l 2 2 r 2 p . (4) Although r p is no longer the perigee of the new orbit after the impulse, we can still evaluate the f nal energy at r = r p , because the two orbits share this point in common. We have the result, E 2 = S 2 2 k r p + l 2 2 r 2 p = E 1 + S 2 2 . (5) Note that the two orbits have the same angular momentum, l . Because the radial impulse was applied at the perigee, it is parallel to the radius vector at this point and does not generate a torque.at this point and does not generate a torque....
View
Full
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.
 Fall '10
 Wilemski
 mechanics, Mass

Click to edit the document details