A satellite is in a circular orbit about the Earth at a distance of one Earth radius above the surface.What is the speed of the satellite? (The radius of the Earth is 6.4 x 10⁶ m,and G = 6.67 x 10^-11 N*m²/kg². ) A)2 800 m/s B)4 200 m/s C)5 600 m/s D)16 800 m/s

Question

Quizplus · Accepted Answer

The speed of a satellite in a circular orbit is given by the formula:

v = sqrt(GM/R)

Where:
G = gravitational constant = 6.67 x 10^-11 N m^2/kg^2
M = mass of the Earth = 5.97 x 10^24 kg
R = radius of the orbit = (radius of the Earth + altitude of the orbit) = (6.4 x 10^6 m + 6.4 x 10^6 m) = 1.28 x 10^7 m

Substituting the values, we get:

v = sqrt(6.67 x 10^-11 N m^2/kg^2 x 5.97 x 10^24 kg / 1.28 x 10^7 m)
v = sqrt(2.98 x 10^14 m^3/s^2)
v = 5.6 x 10^3 m/s

Therefore, the best choice is C) 5 600 m/s.

A Satellite Is in a Circular Orbit About the Earth