Finally, a special case of the three-body problem was investigated. This was found by C. Moore in 1993 which dealt with a three-body figure-eight orbit. In this, three bodies of equal mass follow one another along a figure-eight loop. In this, the masses were set to equal 1, so \(m_1=m_2=m_3=1\), and gravity was set to equal 1, so \(g=1\). The same 12 equations from the previous part were used, and the resulting videos can be seen below.
Below we can see that the trajectories are indeed sensitive to small changes in initial conditions, as shown by changing \(v_{x_3}\) by \(10^{-k}\) for \(1\le k\le 5\). With all k's it results in an animation, where the figure-eight pattern seems to persist while shifting towards the right until it runs off the screen but it only noticeable with when k is small.