## Section14.1Graphs in polar coordinates

Functions expressed in polar coordinates can be graphed. For the function $$r(\phi)\text{,}$$ for each value of $$\phi\text{,}$$ an angle measured counterclockwise from the $$x$$-axis, plot the distance $$r(\phi)\text{,}$$ measured outward from the origin.

For example, Keplerian orbits can be described in the form

\begin{equation*} r(\phi) = \frac{\alpha}{1+\varepsilon\cos(\phi-\delta)} \end{equation*}

as shown in Figure 14.1.1.

### Activity14.1.1.

Use the applet above to explore how the shape of a Keplerian orbit is influenced by the parameters $$\alpha\text{,}$$ $$\epsilon\text{,}$$ and $$\delta\text{.}$$