A company sends a satellite up to 4.0 Earth radii from the center of the Earth a

Question

A company sends a satellite up to 4.0 Earth radii from the center of the Earth and then launches it at a speed of 7423 m/s. Their hope is that it will go into a circular orbit at that distance. (Earth data: Mass = 5.98×1024kg, Radius = 6.38×106m)

a) Can a satellite be in circular orbit at that distance and speed without using any kind of propulsion?

b) How fast should the satellite go in order to orbit at this distance?

c) From Earth it is very hard to judge the speed of a satellite, but we can definitely see its angular motion. What average angular acceleration do we see as the satellite changes its speed?

Explanation / Answer

M = 5.98×1024kg ; R = 6.38×106 ; distance of satellite from centre of earth r = 4R

a) The required speed v = (GM/r)1/2 = (6.67* 10-11 * 5.98×1024 / 4 * 6.38×106 )1/2 = 3953 m/s

As the speed is different from required speed satellite cannot be in circular orbit at that distance and speed without using any kind of propulsion.

b) The required speed v = (GM/r)1/2 = (6.67* 10-11 * 5.98×1024 / 4 * 6.38×106 )1/2 = 3953 m/s

c) Please provide in the question how and by what value is speed changing. Till then I can't answer

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