An artificial satellite travels in an elliptical orbit around the earth, at a la

Question

An artificial satellite travels in an elliptical orbit around the earth, at a large distance from it. When the satellite is at its closest distance R0 from the center of the earth, the velocity of the satellite is observed to have a magnitude v0, and a direction perpendicular to the line of sight from the earth to the satellite. a) What is the speed of the satellite when it is at a distance 3R0 from the center of the earth? Express your answer in terms of v0, R0, and the radius Re of the earth, and the magnitude g of the gravitational acceleration at the surface of the earth. b) At the instant when the satellite is at this distance 3 R0, from the earth, what is the direction between the satellite’s velocity and the line of sight from the earth to
the satellite? Express your answer in terms of the satellite`s speed v at this instant and its speed v0 when it was closest to the earth. Hint: Total angular momentum and total energy should be conserved

Explanation / Answer

a) voRo = v x 3Ro

v = vo/3

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