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

Gravitational acceleration decreases with height. The formula for the gravitational field at a height h above the surface of the planet is:

g' = G*M/(R+h)^2

where G is the universal gravitational constant, M is the mass of the planet, R is the radius of the planet, and h is the height above the surface.

Since we are interested in the gravitational acceleration at a height equal to one planet diameter above the surface, h = 2R.

Substituting the given values, we get:

g' = G*M/(R+2R)^2

g' = G*M/(9R^2)

g' = (1/9)*G*M/R^2

g' = (1/9)*16 m/s^2

g' = 1.78 m/s^2

Therefore, the gravitational acceleration at an altitude of one planet diameter above the surface of the planet is 1.78 m/s^2, which corresponds to choice B.

The Gravitational Acceleration on a Planet's Surface Is 16