of ascending node ($\Omega$). Along with the period ($P$) and an arbitrary zero of time, these are the so-called Keplerian elements of an orbit. Figure 4 diagrams and defines these orientational and orbital parameters. In the plane of the orbit, the angle between the planet and the periastron/periapse (distance of closest approach to the star) at the star is $\theta$. In the jargon of celestial mechanics, $\theta$ is the so-called “true anomaly." For an edge-on orbit ($i = 90^{\circ}$), and one for which the line of nodes is perpendicular to the line of sight ($\Omega = 90^{\circ}$) and parallel to the star-periapse line ($\omega = 0^{\circ}$), $\theta$ is complementary to $\alpha$ ($\alpha = 90^{\circ} - \theta$). As a result, $\theta = 0^{\circ}$ at $\alpha = 90^{\circ}$ (greatest elongation) and increases with time. Also, for such an edge-on orbit, $\alpha = 0^{\circ}$ at superior conjunction. In general, $$\cos(\alpha) = \sin(\theta + \omega)\sin(i)\sin(\Omega) - \cos(\Omega)\cos(\theta + \omega) \, .
\label{cosinef}$$ This is merely an application of the law of cosines.

For a circular orbit, $R$ is equal to the semi-major axis ($a$). However, a planet in an eccentric orbit can experience significant variation in $R$, and, therefore, stellar insolation (by a factor 