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A satellite is placed in an orbit as close to the Earth's surface as possible (a grazing orbit). Which of the following statements are correct? (A) Its orbital speed is maximum. (B) The time period of its revolution is minimum. (C) The total mechanical energy of the Earth-satellite system is minimum (most negative). (D) The total mechanical energy of the Earth-satellite system is maximum.
- its speed is maximum.
- time period of its rotation is minimum.
- the total energy of the earth plus satellite' system is minimum.
- the total energy of the earth plus satellite' system is maximum.
Correct answer: its speed is maximum.
Solution
For a satellite at orbital radius r: speed v = sqrt(GM/r) is largest when r is smallest. Period T = 2*pi*r/v = 2*pi*sqrt(r³/(GM)) is smallest when r is smallest. Total energy E = -GMm/(2r) is most negative (minimum) when r is smallest. So options A, B, and C are all correct. Option D is wrong (energy is minimum, not maximum).
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