Learning Goal: To find some of the parameters characterizing an object moving in a circular orbit. The motivation for Isaac Newton 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. Part A Find the orbital speed 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. ▸ View Available Hint(s) V = Submit Part B D IVE| ΑΣΦ K = 3 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. Π| ΑΣΦ Submit ? Request Answer
Gravitational force
In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.
Acceleration Due to Gravity
In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.

![Part C Complete previous part(s)
Part D
Find the satellite's orbital period T.
Express your answer in terms of G, M, R, and T.
► View Available Hint(s)
T =
Submit
Π ΑΣΦ
Part E Complete previous part(s)
C
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