## How can two moons of Saturn share the same orbit? (Intermediate)

I knew that the Saturn contains two sub-satellites... (I can't remember the names of them) which moves around Saturn along the same orbit and along the same path! And their circular velocity isn't the same... But they still haven't collided yet!!! Do you know about that? Is it true? How come it is possible????

Can you please explain it?

Two satellites of Saturn, Janus and Epimetheus, share the same orbit. They are about the same distance from the planet and orbit at about the same speed. However, they never overtake each other or collide. Technically, we astronomers say that they are in a "1:1 orbital resonance," or "horseshoe orbit."

This is what happens. First, the speed of a moon in its orbit is determined only by its distance from the planet. J & E share a common average distance from the planet, which has a certain orbital velocity associated with it. The two moons orbit at about this velocity. So if you imagine looking down on Saturn from above its north pole, you would see two moons circling the planet at about this velocity.

Now imagine that not only are we looking down at the planet, but we are slowly spinning in our spaceship at the same rate and in the same direction as these moons orbit the planet. In this "rotating frame," if the moons were both orbiting at exactly this rate, they would appear fixed in our windshield. Instead, what we actually see is that while one moon always stays on one side of the windshield and the other stays on the other, they appear to travel in horseshoe shapes around the planet, oscillating back and forth. This is why we call the orbit a "horseshoe orbit."

So what's going on? Well, at any one time, one moon will be slightly farther away from the planet than the other. This moon will orbit slightly more slowly. The other moon will be slightly closer to the planet and slightly faster. Eventually, the faster moon will catch up to the slower moon, but before they can collide, energy is exchanged between the moons and they switch orbits. The previously more distant and slower moon is now closer to Saturn and faster, and the previously closer faster moon is now further and slower. So as the fast moon catches up to the slow moon, the slow moon accelerates away from it to become the faster moon. So they never collide.

This continuous exhange of orbits between the two moons is a very stable configuration. Any orbit is a balance between two competing forces: gravity, which pulls things together, and the speed of the bodies, which (if it is in the right direction) tends to make them move away from each other. Think of a satellite in orbit: if it was not moving, it would fall down onto the planet, but its speed keeps it in orbit. However, gravity and speed are not completely independent of each other: gravity makes things go faster as they fall, and a moving object traveling in the wrong direction will not stay in orbit. It is an interplay between these two which allows Janus and Epimetheus to avoid each other. As the moons approach each other their speeds to begn to change due to gravity, but because of the trajectory of the moons, their gravity makes their speeds change in such a way that the orbits move away from each other again. Gravity never repels the moons in the strict sense but the result is the same: the moons reverse direction (in our rotating frame) and begin to move away from each other.

The only other known example of a horsehoe orbit is the asteroid 3753 Cruithne, which is in a horsehoe orbit with the Earth. In the frame rotating with the Earth's orbit, the Earth doesn't move much at all, because it is much larger, but the asteroid is seen to move in a horseshoe. You can learn about 3753 Cruithne here. Cruithne's orbit is much more complicated than Janus's and Epimetheus's, which look more like figure 1 on that page. The animations on this page are also helpful in understanding how a horseshoe orbit looks.

### About the Author

#### Dave Kornreich

Dave was the founder of Ask an Astronomer. He got his PhD from Cornell in 2001 and is now an assistant professor in the Department of Physics and Physical Science at Humboldt State University in California. There he runs his own version of Ask the Astronomer. He also helps us out with the odd cosmology question.

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