Help in finding the distance from the center of the Earth

Question

show the solution : a satellite is moving about the Earth in a circular orbit with a velocity of 7.8 x10^3 m/s. what is the distance from the center of the earth?

Answer 1

speed of an object in circular orbit is given by:

v = SQRT(GM/r)

G = gravitational constant = 6.67x10^(-11) Nm^2/kg^2

M = mass of the Earth = 5.98x10^24 kg

r = distance from the center of the Earth

You want to find r when v = 7.8x10^3 m/s:

r = GM/v^2

r = (6.67x10^(-11))(5.98x10^24)/(7.8x10^3)^2 meters

r = 0.6556x10^7

r = 6.556x10^6 meters  = 6.556x10^3 km = 6556 km

Answer 2

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