The value of acceleration due gravity at mountain?

Answer 1

Technically, the acceleration due to gravity is inversely proportional to the square of the distance from the center of the earth. That means that the farther from the earth's center you are, the smaller the acceleration due to gravity is. So gravitational acceleration is smaller on a mountain-top or in an airplane. Let's do a little calculation to get an idea of how much it changes. Let's figure out the acceleration of gravity inside an airplane at 35,000 ft above sea level: -- We know what it is at sea level on the equator: 9.78 meters per second2. That's when our distance from the center of the earth is equal to the earth's radius = 3,963 miles. -- When we're at 35,000 ft, we're farther from the center of the earth. 35,000 ft = (35,000 / 5280) = 6.63 miles. So our total distance from the center of the earth is (3,963 + 6.63) = 3,969.63 miles. -- The acceleration (and force) of gravity is inversely proportional to the square of this distance, so the new number is 9.78 times (3963 / 3969.63)2 = 9.78 x (0.9983298)2 = 9.78 x (0.996662) = 9.74736 m/s2 We have discovered that the acceleration due to gravity ... and the weight of every passenger in the airplane ... has become 0.33 percent smaller since they left the ground, because the distance from the center of the earth has increased. If you normally weigh 250 pounds on your bathroom scale, then at 35,000 ft, you weigh only 249.17 pounds.