The animation shows the orbit of the planet side-by-side with the motion in the effective potential. The orbit will depend on how much energy the planet has. Let's start with the smallest possible energy—that's at the very bottom of the effective potential. Drag the energy slider all the way to the left and press start. Just like the bottom of the pendulum potential, this is a stable equilibrium point. If you set a particle at rest at the bottom of the valley, it will just sit there forever. The planet is not at rest, mind you—the radius $r$ is constant but it still has angular momentum and therefore angular speed. Therefore, the planet is orbiting the planet in a circle at that constant radius!

Now let's increase the energy a bit, so that it's greater than the minimum but less than zero. Press reset to stop the animation, drag the energy slider up, and then press start to let it go again. Now the particle will roll back and forth between the two turning points where the horizontal energy line intersects the potential curve. That means that $r$ oscillates back and forth between a minimum radius and a maximum radius. All the while the planet is swinging around the star, because it has angular momentum. Then instead of a circle, the orbit will be an ellipse! The minimum and maximum values of $r$ correspond to the perihelion and the aphelion of the orbit—the points of closest and farthest distance from the star.

To be clear, I haven't proven the orbit is an ellipse here—thinking about the effective potential just tells us what the general shape will be. I'll show you how to derive the actual elliptical orbit in that upcoming video. But by thinking about the effective potential we've learned what the rough shape of the orbit must be (and that it is, in fact, an orbit in the first place when the energy of the planet is less than zero, as opposed to a comet passing through the solar system), with very little work!

What if the energy is greater than zero? Drag the slider farther up, press reset, and then press start. Now things look quite different. There's only one turning point at a minimal value of the radius—the horizontal energy line never intersects the potential energy curve again to the right. The particle on the hill will slide down and pick up speed, and then it will climb up the shallower hill to the right as it coasts off to $r \to \infty$. This isn't an orbit at all! It's the trajectory of something like a comet that's just passing through the solar system. It slingshots around the star, and then sails off on its merry way. This time it traces out a hyperbola.

So I hope you're impressed at just how easy it was to predict the shape of an orbiting planet or vagrant comet from the picture of the effective potential. In general, thinking about the shape of the potential energy curve is one of the most powerful tools that we have to very quickly get intuition for a physical system with very little effort. And not just in classical mechanics, but quantum mechanics too.