How to Find Gravitational Potential Energy when Gravity Changes (i.e. large heights)

We look at how to do gravitational energy the 'right way.' This is because gravity really is a non-constant force, and U = mgh is simply an approximation. While it works when the height is small compared to the radius of the earth, it does not work for space launches, orbits, and so on. Let us see what happens and how to do this, starting with Newton's law of gravity and our old gradient friend, F = -dU/dr. We will also see how this gets us escape velocity and Schwartzschild radius (for black holes).

How to Interpret Potential Wells

We have looked at potential wells, which are just graphs of potential energy as a function of position. The classic way of thinking about this is to imagine one object fixed at the origin, and have a second object moving along the x-axis. The graph tells us the potential energy between the two as you move that second object. We look at the potential energy gradient in order to determine the force function, F = -dU/dr, or in other words the force graph is found by plotting the negative slope of the potential energy graph. I outline this by using the 'Nike' problem from an old AP exam. Check it out!