Question 1 of 4 attempt 4 the acceleration due to gravity, , is constant at sea level on the earth's surface. however, the acceleration decreases as an object moves away from the earth's surface due to the increase in distance from the center of the earth. derive an expression for the acceleration due to gravity at a distance ℎ above the surface of the earth, ℎ . express the equation in terms of the radius of the earth, , and ℎ .

The acceleration of Earth's gravity at any distance ' R ' from its center is

g = G m/r²

G = the gravitational constant

m = Earth's mass

r = the distance from the Earth's center

As long as you're walking around on the Earth's surface, your distance from its center is the Earth's radius ... big 'R' ... and the acceleration of gravity is (G m/R²) no matter where on Earth you are.

But if you get into a hot-air balloon or an airplane, and raise yourself up to 'h' off of the surface, then you're farther from the center of the Earth.  Now your distance from the center is (R + h), and the acceleration of gravity up there where you are is (G m/(R+h)²) ... that's less than it is down on the surface.

So there's the equation we're looking for.

Acceleration of gravity at any altitude 'h' = G m / (R+h)²

answer and explanation;

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.