Lesson: Gravitational Potential Energy in a Radial Field Physics
In this lesson, we will learn how to calculate the gravitational potential energy between two massive objects, and how this potential energy changes as the objects change position.
Two astronauts are trying to land a spacecraft on the Moon. The spacecraft is initially at rest at a position 4 km above the surface of the Moon, and the mass of the spacecraft and the two astronauts is 2,900 kg. The spacecraft is allowed to fall under the effect of gravity until it is 500 m above the surface of the Moon, when its thrusters are engaged. What is the speed of the spacecraft just before the thrusters are engaged? Use a value of 1,740 km for the radius of the Moon and a value of kg for the mass of the Moon. Give your answer to the nearest meter per second.
An asteroid with a mass of 3,500 kg moves from a position 40,000 km away from the center of mass of Earth to a position 22,000 km away. What is the change in the gravitational potential energy between the asteroid and Earth? Use a value of kg for the mass of Earth. Give your answer in scientific notation to two decimal places.
The distance between the centers of mass of two massive objects is . If this distance is increased to , by what factor does the gravitational potential energy between the two objects change?