Physics 20: Gravitational Field Strength 'g'

Question

At what height above Earth in kilometers is the gravitational field strength 90.0% of what it is on Earth's surface?

Answer 1

On surface of Earth g = GM/R²; on height h g_h = GM/(R + h)².

GM/(R + h)² = 0.9GM/R²; (R + h)² = 10/9R²; h = R(√10/3 - 1) = 0.0541R = 0.0541·6371km = 344.25 km