Eccentricity and conical sections

What, apart from a popular way of describing English people, is eccentricity?

In astrophysics, it describes how flat orbits are. This includes orbits of planets, satellites, comets and even things that don't come back, such as Oumuamua.

Most people will tell you that planets orbit around the Sun in a circle. It's close. The Greek astronomer Ptolemy certainly thought so. But, by about the 15th Century, astronomers (mainly led by the Arabic schools) had realised there was something not quite right with circular orbits.

It fell to an observer and a mathematician to figure it out.

Tycho Brahe - the Great Dane - was the observer. He built a series of machines, some of which were enormous. These made exquisitely precise measurements of the positions of the planets in relation to the stars.

The maths genius was Johannes Kepler, who was Tycho's student. Kepler knew there was something screwy about Mars - it was never in quite the "right" position. But Tycho wouldn't allow Kepler to use his Mars data - it was too precious for Tycho to give away. There it lay for years.

But on Tycho's deathbed, Kepler finally got permission, Tycho's last words being roughly "I don't want people to think I lived in vain". From these data, Kepler realised that the orbit of Mars was not a circle, but more eccentric - it was an oval. This helped Kepler, but also Newton and eventually Einstien in their work.

Circles, ovals, parabolas and hyperbolas are all known as "conical sections". Imagine using a saw to cut through an ice cream cone. The eccentricity of the section relates to the angle of the saw.

Cut straight across, you get a circle, with an eccentricity of zero. Tilt the saw to cut on a slight angle and you get an oval, which has an eccentricity of somewhere between zero and 1 . Tilt further and cut parallel to one edge of the cone and you get a parabola, with an eccentricity of 1. Further still and the cut is a hyperbola, with an eccentricity of more than 1.