A satellite is in a circular orbit around Earth at an altitude of 400 km above the surface. If the radius of Earth is 6,400 km, what is the approximate ratio of the gravitational acceleration at this altitude to the gravitational acceleration at Earth's surface?

Core Concept

Gravitational acceleration follows the inverse square law: g ∝ 1/r². The distance from Earth's center at the satellite's orbit is 6,400 km + 400 km = 6,800 km. The ratio is (6,400/6,800)² ≈ 0.88. Option A is incorrect because it doesn't account for the inverse square relationship. Option C is incorrect as it's too low, possibly using the altitude instead of the total radius. Option D is incorrect as it's much too low, possibly using the cube of the radius ratio instead of the square.