00:01
The problem wants us to find at what altitude above the earth's surface is the acceleration due to gravity equal to g over 4, where g is equal to the gravitational acceleration at the surface of the earth.
00:14
So let's go ahead and draw a test mass at the surface of the earth with mass m.
00:20
And since earth is a sphere, we can condense all of earth's mass to the center of the earth and treat the system as two -point objects.
00:29
Here, let's go ahead and write out the force equation.
00:34
F little g, which is the gravitational force, equals f big g, which is newton's gravitational force, and f little g at the surface of the earth is mg, and newton's gravitational force is g, m, e, divided by r .e, which is the radius of the earth, squared.
00:58
Notice how the test mask cancels and we're left with g equal big g m e over r e squared...