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To find some of the parameters characterizing an object moving in a circular orbit. The motivation for Isaac Newton to discover his laws of motion was to explain the properties of planetary orbits that were observed by Tycho Brahe and analyzed by Johannes Kepler. A good starting point for understanding this (as well as the speed of the space shuttle and the height of geostationary satellites) is the simplest orbit: a circular one. This problem concerns the properties of circular orbits for a satellite orbiting a planet of mass M. For all parts of this problem, where appropriate, use G for the universal gravitational constant. Find the orbital speed  v  of a satellite in a circular orbit of radius  R  around a planet of mass  M . Express the orbital speed in terms of  G ,  M , and  R . Find the kinetic energy  K  of a satellite with mass  m  in a circular orbit of radius  R  around a planet of mass  M . Express your answer in terms of  m ,  M ,  G , and  R . Find the satellite's orbital period  T . Express your answer in terms of  G ,  M ,  R , and  π .

To find some of the parameters characterizing an object moving in a circular orbit. The motivation for Isaac Newton to discover his laws of motion was to explain the properties of planetary orbits that were observed by Tycho Brahe and analyzed by Johannes Kepler. A good starting point for understanding this (as well as the speed of the space shuttle and the height of geostationary satellites) is the simplest orbit: a circular one. This problem concerns the properties of circular orbits for a satellite orbiting a planet of mass M. For all parts of this problem, where appropriate, use G for the universal gravitational constant. Find the orbital speed  v  of a satellite in a circular orbit of radius  R  around a planet of mass  M . Express the orbital speed in terms of  G ,  M , and  R . Find the kinetic energy  K  of a satellite with mass  m  in a circular orbit of radius  R  around a planet of mass  M . Express your answer in terms of  m ,  M ,  G , and  R . Find the satellite's orbital period  T . Express your answer in terms of  G ,  M ,  R , and  π .

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To find some of the parameters characterizing an object moving in a circular orbit.
The motivation for Isaac Newton to discover his laws of motion was to explain the properties of planetary orbits that were observed by Tycho Brahe and analyzed by Johannes Kepler. A good starting point for understanding this (as well as the speed of the space shuttle and the height of geostationary satellites) is the simplest orbit: a circular one. This problem concerns the properties of circular orbits for a satellite orbiting a planet of mass M.

For all parts of this problem, where appropriate, use G for the universal gravitational constant.

  1. Find the orbital speed  v  of a satellite in a circular orbit of radius  R  around a planet of mass  M . Express the orbital speed in terms of  G ,  M , and  R .
  2. Find the kinetic energy  K  of a satellite with mass  m  in a circular orbit of radius  R  around a planet of mass  M . Express your answer in terms of  m ,  M ,  G , and  R .
  3. Find the satellite's orbital period  T . Express your answer in terms of  G ,  M ,  R , and  π .
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