The planet Uranus has a radius of 25,360 km and a surface acceleration due to gravity of 9.0 m/s 2 at its poles. Its moon Miranda (discovered by Kuiper in 1948) is in a circular orbit about Uranus at an altitude of 104,000 km above the planet’s surface. Miranda has a mass of 6.6 × 10 19 kg and a radius of 236 km. (a) Calculate the mass of Uranus from the given data. (b) Calculate the magnitude of Miranda’s acceleration due to its orbital motion about Uranus. (c) Calculate the acceleration due to Miranda’s gravity at the surface of Miranda. (d) Do the answers to parts (b) and (c) mean that an object released 1 m above Miranda’s surface on the side toward Uranus will fall up relative to Miranda? Explain.
The planet Uranus has a radius of 25,360 km and a surface acceleration due to gravity of 9.0 m/s 2 at its poles. Its moon Miranda (discovered by Kuiper in 1948) is in a circular orbit about Uranus at an altitude of 104,000 km above the planet’s surface. Miranda has a mass of 6.6 × 10 19 kg and a radius of 236 km. (a) Calculate the mass of Uranus from the given data. (b) Calculate the magnitude of Miranda’s acceleration due to its orbital motion about Uranus. (c) Calculate the acceleration due to Miranda’s gravity at the surface of Miranda. (d) Do the answers to parts (b) and (c) mean that an object released 1 m above Miranda’s surface on the side toward Uranus will fall up relative to Miranda? Explain.
The planet Uranus has a radius of 25,360 km and a surface acceleration due to gravity of 9.0 m/s2 at its poles. Its moon Miranda (discovered by Kuiper in 1948) is in a circular orbit about Uranus at an altitude of 104,000 km above the planet’s surface. Miranda has a mass of 6.6 × 1019 kg and a radius of 236 km. (a) Calculate the mass of Uranus from the given data. (b) Calculate the magnitude of Miranda’s acceleration due to its orbital motion about Uranus. (c) Calculate the acceleration due to Miranda’s gravity at the surface of Miranda. (d) Do the answers to parts (b) and (c) mean that an object released 1 m above Miranda’s surface on the side toward Uranus will fall up relative to Miranda? Explain.
You are working at a summer internship for
NASA, working to study exoplanets (planets we
have detected around other stars). Calculate the
orbital radius (distance of the planet to the star)
of the newly detected planet Beta Sirius, if its'
orbital period around its star is 5.51 x 107 s.
You know from the data that the star has a
mass of 2.21 x 1029 kg, and a radius of 2.70 x
106 and the planet has a mass of 3.00 x 1022
kg.
Your Answer:
Answer
The Magellan orbiter orbits Venus with a period of 3.26 hours. How far (in km) above the surface of the planet is it? (The mass of Venus is 4.87 ✕ 1024 kg, and the radius of Venus is 6.05 ✕ 103 km.)
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