 Let's now look at the generalized form of gravitational potential energy. Previously you would have seen gravitational potential energy as e equal to mg change in h. This equation is valid for approximately constant g, or in other words, when I'll change in height or h as much smaller than r the distance between two masses as seen in Newton's law of universal gravitation. And this is the form of gravitational potential energy that we use when we're close to the surface of the earth. If we think about moving through a gravitational field with varying gravitational field strength, speeding from the earth to the sun for example, we know that the acceleration due to gravity, g, will be different at every point and will increase rapidly as we approach the sun. If we try to apply the potential energy equation we've shown here, there is no obvious gravitational field strength we should use. For this we need the more generalized form of potential energy. This equation is e equal to big g multiplied by both of the masses times the inverse of the initial distance minus the inverse of the final distance between the masses. So what can we deduce from the general potential energy equation? Well we can see the energy is linearly dependent on the product of the masses. Finally as objects move further away from each other, in the case where the final distance is greater than the initial distance, the potential energy is increased. This makes intuitive sense when we consider the kinetic energy of the system. As two masses move further apart from one another, the gravitational force pulling them together will decelerate that movement, reducing the kinetic energy and correspondingly increasing the potential energy to conserve total energy of the system. Consider a conceptual flyby of an asteroid around the star. The asteroid speeds up, turns around and slows down as a result of forces applied by the gravitational field. At every point the gravitational field is applying a force and the asteroid is moving. This means work is being done. Remember the formula for work is equal to the applied force multiplied by the distance travelled in the direction of that force. So as the asteroid speeds up it's the field itself doing work on the asteroid. As the asteroid slows down the work done on the asteroid is negative, which means the asteroid is actually doing work back on the field. Actually calculating the work done with this formula can be really hard when the motion follows a wild path and the vector field is pointing all over the place. Luckily we can use the change in the potential energy instead. That's something we'll look at in the next video.