An object is released from rest when it is a height h above the surface of a pla

Question

An object is released from rest when it is a height h above the surface of a planet of mass M and radius R. What is the speed of the object just before striking the surface of the planet? Neglect any air resistance. Let h = 4.0 Times 10^6 m, R = 5.0 Times 10^6 m, and M = 4.0 Times 10^24 kg. A satellite is placed in a geosynchronous orbit. In this equatorial orbit with a period of 24 hours, the satellite hovers over one point on the earth's equator. What is the height of the satellite above the planet's surface? What is the gravitational field magnitude at the location of the satellite from the previous problem?

Explanation / Answer

potential energy = G * mass1 * mass2 / distance

let mass of object is m

potential energy = 6.676 * 10^-11 * 4 * 10^24 * m / (4 * 10^6 + 5 * 10^6)

by conervation of energy

initial energy = final energy

6.676 * 10^-11 * 4 * 10^24 * m / (4 * 10^6 + 5 * 10^6) = 0.5 * mv^2

6.676 * 10^-11 * 4 * 10^24 / (4 * 10^6 + 5 * 10^6) = 0.5 * v^2

v = 7703.39 m/s

speed of the object = 7703.39 m/s

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