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A satellite is placed in an orbit in the equatorial plane so that it is able to transmit signals to all points on Earth up to a latitude of 60 deg. The angular velocity of the satellite in this orbit is
- sqrt(G*M/(8*R³))
- sqrt(G*M/(2*R³))
- sqrt(G*M/(4*R³))
- sqrt(3*sqrt(3)*G*M/(8*R³))
Correct answer: sqrt(G*M/(8*R³))
Solution
For the satellite to just reach latitude 60 deg, the line of sight is tangent to Earth at that latitude. The geometry gives the orbital radius r = R/cos(60 deg) = 2R. The orbital angular velocity for a circular orbit is omega = sqrt(G*M/r³) = sqrt(G*M/(8R³)).
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