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A satellite is revolving around the Sun in a circular orbit. The orbital radius of the satellite is exactly half the orbital radius of the Earth around the Sun. If the acceleration of the Earth due to the Sun's gravity is denoted as a_E, find the acceleration of this satellite in terms of a_E. Express your answer as x * a_E and find x.
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Correct answer: 4
Solution
Gravitational acceleration at distance r from the Sun is a = GM_sun / r². For Earth: a_E = GM_sun / r_E². For the satellite at rₛ = r_E/2: aₛ = GM_sun / (r_E/2)² = 4 * GM_sun / r_E² = 4 * a_E. Therefore x = 4.
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