Epicycles are almost as good as trigonometric series: general system-based analysis

To adequately describe the planets’ motion, ancient astronomers used epicycles, when a planet makes a circular motion not around the Earth, but around a special auxiliary point which, in turn, performs a circular motion around the Earth – or around a second auxiliary point which, in turns, rotates around the Earth, etc. Standard textbooks malign this approach by calling it bad science, but in reality, this is, in effect, trigonometric (Fourier) series – an extremely useful tool in science and engineering. It should be mentioned, however, that the epicycles are almost as good as trigonometric series – in the sense that in some cases, they need twice as many parameters to achieve the same accuracy. 1 Epicycles: Bad Science or Genius Idea Epicycles: what they are. For purposes of navigation, since the ancient times, astronomers have studied the visible motion of the planets and the stars. In the first crude approximation, their trajectories form a circle. To provide a more accurate description, astronomers proposed the following idea – called epicycles. First step is to assume that while a point corresponding to a planet follows a circular motion around the Earth, the planet itself performs a circular motion around this point. To get an even more accurate description, we assume that it is not the planet itself, but rather the second point associated