Explanation Given information: From problem 13.108 : v = v 0 s = r 0 θ = α Formula used: 1 r = G M h 2 + C cos θ Calculation: Suppose the point of intersection P 0 of the elliptical and circular orbits is at the end of the minor axis, then v 0 would be parallel to the major axis. This will happen only if α + 90 o = θ 0 , that is if cos θ 0 = − sin α . So we must therefore prove that cos θ 0 = − sin α (i) We know that, 1 r = G M h 2 + C cos θ (from equation ( 12.39 ) ) (ii) At, θ = 0 . ⇒ r = r min and. ⇒ r min = r 0 ( 1 − sin α ) ⇒ 1 r 0 ( 1 − sin α ) = G M h 2 + C (iii) At, θ = 180 O . ⇒ r = r max = r 0 ( 1 + sin α ) ⇒ 1 r 0 ( 1 + sin α ) = G M h 2 − C (iv) Now adding equation (iii) and (iv) and dividing by 2

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ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

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Chapter 13.2, Problem 13.117P

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The intended circular orbit and the resulting elliptical orbit.

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Chapter 13.2, Problem 13.116P

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The intended circular orbit and the resulting elliptical orbit.

Solution Summary: The author explains that the intended circular orbit and the resulting elliptical orbit intersect at the given condition.

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