This simulation shows four asteroids which orbit the Sun with periods of approximately one year, whilst occasionally spending periods circling the Earth. The initial date of the simulation is 27th August 2011, and the evolution time step is set to one year so that the Earth appears to be fixed in position during evolution. The four asteroids that are included are Cruithne, 2002 AA29, 2003 YN107, and 2010 SO16.
If you run the simulation forward or backward, you can see how the asteroids move relative to the Earth. You will see that 2002 AA29, 2003 YN107, and 2010 SO16 alternately move ahead of and behind the Earth, so that they seem to follow a horseshoe-shaped path relative to the Earth. Since different computers run at different speeds, you may need to edit the evolution time step to get the simulation to run at an acceptable rate.
You can find out more about asteroid 2010 SO16 from the following website:
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