This simulation shows the asteroid 2010 TK7, which orbits the Sun with a period of approximately one year, and was the first Earth Trojan to be discovered (in 2011). The initial date of the simulation is 27th August 2011, and the time step is set to five years so that the Earth appears to be fixed in position during evolution.
The simulation also contains the Sun, together with all known planets and the Moon.
If you run the simulation (forward or backward), you can see how the asteroid moves relative to the Earth. You will see that it is a Trojan that is currently leading the Earth in its orbit. If you run the simulation far enough, you will find periods when it switches to being a Trojan that follows the Earth in its orbit, and also periods when it follows a horseshoe-shaped path relative to the Earth.
You can find out more from the following website:
Copyright © 2005-2019, AstroGrav Astronomy Software