Be glad for this little dance step, too. This rock is half the size of the asteroid that wiped out the dinosaurs.
Cruithne, discovered in 1986, is a small solar system body. It would fill the space between my house and my church, about three miles across.
No chance of it hitting the Earth, at least not anytime soon. It orbits the sun at a twenty degree angle from our planet. Plus, the Earth has engaged it in a complex little dance that ensures a safe distance.
The left diagram from wikipedia commons shows the orbital comparisons from a view to the “north” of the sun.
Much more interesting is the depiction of Cruithne’s orbit as seen from Earth. The asteroid would appear to move in a variable bean-shaped orbit around a point somewhat ahead of Earth’s path around the sun. In a cycle of 774 years, that orbit approaches our planet till Cruithne has a series of passes just inside eight million miles. That’s just close enough for the Earth to “push” this asteroid away for a cycle where the “yellow bean” recedes from the neighborhood. After those 774 years, Cruithne’s “bean” approaches from the other side of Earth’s orbit and gets pushed away again.
Cruithne does its own share of pushing back. At closest approach every 774 years, it nudges the Earth’s orbit a little more than half an inch. Then 774 years later, it nudges us back in place when it comes from the other direction.
A third applet would be useful now. Look at the right illustration. Imagine, if you can, that yellow bean shape moving slowly ahead of the Earth, circling the sun, and catching up to the Earth on the other side. Once it gets there, it will slow down and pause for a bit, then start moving again around the sun the way it came. After 774 years, that yellow shape will slow as it approaches Earth, stop, and move back again.
If you can’t visualize it, take my word for it. It’s not going to hit us.
Cruithne is sometimes described as “Earth’s second moon.” Not true really. Cruithne definitely orbits the sun. Even an Earth-stationary reference would show Cruithne circling a point of empty space, not the third planet.
Can we see it from Earth? Not easily. Cruithne is fainter than Pluto. Duncan Waldron discovered it while examining photographic plates in Australia. You would need a fairly powerful telescope to view it directly, much more that what you can buy from a discount store. A 12-inch reflector at least. Then you have to pick it out against all the background stars of the 15th magnitude or fainter.
Catholic Sensibility 
I was doing some reading on Saturn’s moons when I came across the similar phenomenon of the Epimetheus-Janus co-orbit. It was difficult to visualize at first, especially with an Earth-stationary diagram. But the relational depiction makes it much more sensible. “Of course,” I thought, “naturally the gravity of the approaching body would shove aside the other one.” The wiki page for “horseshoe orbit” was the initial cause of my confusion.
Now, when you say “pause” and “stop,” you don’t really mean “cease all motion,” do you? More like, “creep along?” Or does it merely appear to be stationary, relative to the Earth?
Of course, when I say “it” in that first sentence, I’m talking about the Cruithne orbit.
I mean the path of Cruithne’s orbit (the yellow bean) slows, stops, and reverses itself.