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An **ellipse** is one of four possible types of **conic section**. The others are the **circle**, the **parabola**, and the **hyperbola**.

A **conic section** is a shape obtained from cutting a cone.

Types of conic sections (from wikipedia, modified)

There are two parameters controlling the shape of these guys. Let’s focus on the **ellipse**, which is the one interesting regarding planetary motion.

Ellipse

The two parameters that control the shape of the elipse are *a* (**semimajor axis**, which can have any positive value) and *e* (**eccentricity**, which for an ellipse 0 < *e* < 1). So we can calculate the other stuff as a function of *a* and *e*. For example:

Kepler suggested that the planets orbit in ellipses, with the Sun in one of the focus, the **principal focus**, while the other focus is empty.

Elliptic trajectory of planet around the Sun according to the Kepler model

It is useful to express the position of a planet as a function of *θ* and *r* (instead of cartesian coordinates).

The point where the planet is closest to the Sun is for *θ* = 0º (**perihelion**). The point where the planet is farthest from the Sun is for *θ* = 180º (**aphelion**).

The other *conic sections* have different ranges for *e *(*a* simply indicates the size):

Circle: *e* = 0

Ellipse: 0 < *e* < 1

Parabola: *e* = 1

Hyperbola: *e* > 1

Next: Kepler’s Laws Revisited

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