Click the flag. Pluto makes two orbits for every three orbits of Neptune around the Sun. The ratio of their frequencies is 3 to 2, a kind of "orbital resonance." To bring out the analogy between the orbital frequencies and musical frequencies (once called the music of the spheres), when Pluto is directly below Sun we hear note E. When Neptune is directly below Sun we hear note B, a "perfect fifth" about E. B has 3/2 the frequency of E, just as the orbital ratio is 3/2. You can adjust "speed" but the ratios of the angular frequencies remains 3 to 2. Sizes and distances are not to scale.
We are focusing on orbital frequency and their ratios. The simplest way to do that is to focus on angular frequency (or "angular velocity"). We made Pluto and Neptune a separate spinning sprite, each a distance (radius) from the center of the sprite. Then the code focuses on the speed of the angle change, the frequency with which a 360 degree spin is completed. We set Neptune to orbit 1.5 times as fast as Pluto. The angular frequencies are not affected by the radius or circumference of the orbits, and so are not affected by the fact that the sizes and distances are not to scale.
