Elliptical orbits

An ellipse has two foci $F_1$ and $F_2$, and has the property that for any point the distance $F_1P+F_2P$ is a constant. It also has a horizontal semi-axis $a$ and a vertical $b$. It is common in astronomy to characterize an orbit by its ``eccentricity'' $e$, given by the ratio of the distance between the foci, and the length of the major axis $2a$. Since $F_1P+F_2P=2a$, it is easy to show that (consider a point $P$ at $x=0$,$y=b$)

$$e=\sqrt{1-\frac{b^2}{a^2}},$$

with $0<e<1$. A special case is $a=b$ for which the ellipse reduces to a circle and $e=0$. The earth orbit has eccentricity $e=0.0167$.