1. By how much does the gravitational field between two objects decrease when the distance between their centers is doubled? Tripled? Increased tenfold?
2. Consider an apple at the top of a tree that is pulled by Earth’s gravity with a force of 1 N. If the tree were twice as tall, would the gravitational field be only \frac{1}{4} as strong? Defend your answer.
1. It decreases to one-fourth, one-ninth, and one-hundredth the original value.
2. No, because an apple at the top of the twiceas- tall apple tree is not twice as far from Earth’s center. The taller tree would need a height equal to the radius of Earth (6,370 km) for the apple’s weight at its top to reduce to \frac{1}{4} N. Before its weight decreases by 1%, an apple or any object must be raised 32 km—nearly four times the height of Mt. Everest. So, as a practical matter, we disregard the effects of everyday changes in elevation.