Orbitz Gum!... or maybe not! Two rockets_i S_1 and S_2 are moving in coplansr, c

Question

Orbitz Gum!... or maybe not! Two rockets_i S_1 and S_2 are moving in coplansr, circular, counterclockwise orbits of radii r_1 and r_2 = 6r_1, respectively, about the Earth. A supply rocket is to be launched from S_1 in a direction tangent to its orbit at the locatiou marked A. It is to reach S_2 with a velocity tangent to the orbit of S_2 at the location marked B. The supply rocket will orbit the earth in an elliptical orbit after launching. In terms of G, M_Earth, and r_1... N.B. The length of the semi-major axis of the elliptical orbit shown is a = 1/2(r_1 + r_2) Find the speed of the rocket S_1 in its orbit. Compute the ratio of the supply rocket's speed at B to A. That is, compute U_B/U_A. Compute the speed of the supply rocket relative to S_1 immediately after launch. Compute the angle beta (as seen in the diagram) giving the position of S_2 relative to S_1 at the time of launching the supply rocket. Your answer should be numerical.

Explanation / Answer

a) KE = GMm/2r1

0.5 m v^2 = GMm/2r1

v = sqrt [GMearth/r1]

b)Vb/Va = sqrt [r1/6r1] = 0.408

c) V =  sqrt [GMearth/6r1] -  sqrt [GMearth/r1] =   0.592   [GMearth/r1]

d) angle beta = wt = vt/(6r1) =  t sqrt[GMearth/6r1]/6r1

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