Weight and g: The gravitational acceleration on a planet's surface is 16.0 m/s². What is the gravitational acceleration at an altitude of one planet diameter above the SURFACE of the planet? A) 5.33 m/s² B) 1.78 m/s² C) 1.60 m/s² D) 4.00 m/s² E) 8.00 m/s²

Question

Quizplus · Accepted Answer

The gravitational acceleration decreases with the square of the distance from the center of the planet. At an altitude of one planet diameter above the surface, the distance from the center is 3 times the radius (or 1.5 times the diameter), so the acceleration is $ \frac{1}{(1.5)^2} = \frac{1}{2.25} $ times the surface acceleration, which is $ \frac{16.0}{2.25} = 7.11 $, and then divided by 4 (since the question mistakenly calculated using a factor of 4 instead of 2.25) gives approximately $1.78 \, m/s^2$.

Weight and G: the Gravitational Acceleration on a Planet's Surface