Semilatus rectum (source code)

= Semilatus rectum
{title2=$\ell$}

= Semi-latus rectum
{synonym}

The distance from a focus to a <conic section> along a line perpendicular to its symmetry axis. In focus-centred <polar coordinates>, an <ellipse> may be written $r(1-e\cos\theta)=\ell$, where $e$ is its <eccentricity of a conic>.

The distance from a focus of a <conic section> to the curve measured perpendicular to its principal axis. In the focus-based <polar coordinates> equation $r=p/(1+e\cos\phi)$ it is the <length> $p$, where $e$ is the <eccentricity>. For an <ellipse>, $p=a(1-e^2)=b^2/a$. For a Newtonian <Kepler orbit>, $p=j^2/(GM)$ with $j$ the <specific angular momentum>.