Question Detail
Question
The time period T of a satellite orbiting the Earth in a circular orbit of radius r is given by:
Correct Answer
Option D is the correct answer.
Detailed Explanation
From v = 2πr/T and v = √(GM_E/r), equating gives 2πr/T = √(GM_E/r). Squaring both sides: 4π²r²/T² = GM_E/r. Rearranging gives T² = (4π²/GM_E) r³, so T = 2π √(r³/GM_E). Option C is just the square root of that equation and is equivalent.
Hint
Combine the formulas for orbital speed and the circumference of the orbit.