Because I started a small series about astronomical algorithms and the magic of math in space, I think we need to cover an important prerequisite. In the series, I will talk a lot about ellipses (duh), I will move from the semi-axis majors, to the periapsis, to eccentricity, to ellipse’s center and ellipse’s foci. I am concerned that things can get more complicated than expected if the readers does not know many of the geometric properties of the ellipse. For this reason, I put here this vade mecum on the ellipse geometry. A summary with all the basic points and lengths. A place that I can link everywhere I need to refresh a definition.

As you probably know, I am working (slowly) on an astronomically accurate calendar generator. All the orbital calculations involved are quite challenging, and I am discovering a lot. It is a lot of fun (except for the all the times I need to do some trigonometric magic to make some formula work). Anyway, during this process, I am reshaping and producing many many formulas. I am sure that in six months I will forget all the motivations behind them. For this reason, I want to try to save some of them here. In this way, I will have a good place where to look back at my notes and, moreover, I can be useful to other people trying to do some low-accuracy orbital calculations. I want to start from the beginning: orbital period and orbital trajectory.