The second plot fixes Earth and Sun in place, and so you see the position of the asteroid relative to Earth. What is happening is that the asteroid is in an orb

The second plot fixes Earth and Sun in place, and so you see the position of the asteroid relative to Earth. What is happening is that the asteroid is in an orbit so similar to Earth that they do not usually pass each other, and alternatively speeds up and slows down very slightly related to us. (When it approaches Earth from "behind" on it's orbit, earth's gravity accelerates it forwards, which makes it's orbit slightly longer, which makes it take a longer time to go around it, causing it to start lagging us. When Earth catches up to it, Earth's gravity will accelerate it backwards, as in slow it down, which will shrink it's orbit, meaning it will go around faster than us.) The tight loops are caused by orbital inclination: As the asteroid is not orbiting in the same plane as Earth, each orbit around the Sun it will travel slightly above us and slightly below, this causes the loop.