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1. A probe of mass m is in a circular orbit of radius r around a planet (mass M). a. Draw the free body diagram showing the forces on the probe. b. Use what you know about circular motion dynamics to determine the orbital speed of the probe in terms of G, M, m and/or r as needed. Assume M » m and use Newton's Second Law. Also recall the centripetal acceleration. m c. What is the kinetic energy of the probe in this orbit in terms of G, M, m, and r? Please simplify your answer. d. What is the total energy of the probe when it is in this orbit? Please simplify your answer. e. The probe is initially at rest on the surface the planet of radius Rp. How much work must the rockets do on the probe to lift it into the orbit of radius 3R,,? Answers in terms of G, R₂, M and/or m as needed.

1. A probe of mass m is in a circular orbit of radius r around a planet (mass M). a. Draw the free body diagram showing the forces on the probe. b. Use what you know about circular motion dynamics to determine the orbital speed of the probe in terms of G, M, m and/or r as needed. Assume M » m and use Newton's Second Law. Also recall the centripetal acceleration. m c. What is the kinetic energy of the probe in this orbit in terms of G, M, m, and r? Please simplify your answer. d. What is the total energy of the probe when it is in this orbit? Please simplify your answer. e. The probe is initially at rest on the surface the planet of radius Rp. How much work must the rockets do on the probe to lift it into the orbit of radius 3R,,? Answers in terms of G, R₂, M and/or m as needed.

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1. A probe of mass m is in a circular orbit of radius r around a planet (mass M). a. Draw the free body diagram showing the forces on the probe. b. Use what you know about circular motion dynamics to determine the orbital speed of the probe in terms of G, M, m and/or r as needed. Assume M » m and use Newton's Second Law. Also recall the centripetal acceleration. m C. What is the kinetic energy of the probe in this orbit in terms of G, M, m, and r? Please simplify your answer. d. What is the total energy of the probe when it is in this orbit? Please simplify your answer. e. The probe is initially at rest on the surface of the planet of radius Rp. How much work must the rockets do on the probe to lift it into the orbit of radius 3R? Answers in terms of G, Rp, M and/or m as needed.
Transcribed Image Text:1. A probe of mass m is in a circular orbit of radius r around a planet (mass M). a. Draw the free body diagram showing the forces on the probe. b. Use what you know about circular motion dynamics to determine the orbital speed of the probe in terms of G, M, m and/or r as needed. Assume M » m and use Newton's Second Law. Also recall the centripetal acceleration. m C. What is the kinetic energy of the probe in this orbit in terms of G, M, m, and r? Please simplify your answer. d. What is the total energy of the probe when it is in this orbit? Please simplify your answer. e. The probe is initially at rest on the surface of the planet of radius Rp. How much work must the rockets do on the probe to lift it into the orbit of radius 3R? Answers in terms of G, Rp, M and/or m as needed.
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