Plot of the planet's radial position as a function of time _p ( t) for the two planet simulations. The dashed-diamond and solid-star lines (colored red and black in the online version) indicate the curves ( ( t)), points ( a), and horizontal scales ( t) that correspond to the t = 0 and t = 10 planet runs, respectively. The symbols are the approximate semi-major axes a computed for each 0 to 2ϕ change in azimuth of the planet as explained in the text.