Semilatus Rectum

Given an Ellipse, the semilatus rectum is defined as the distance measured from a Focus such that

$\begin{displaymath} {1\over L}\equiv {1\over 2}\left({{1\over r_+}+{1\over r_-}}\right), \end{displaymath}$

(1)

where

and

are the Apoapsis and Periapsis, and

is the Ellipse's Eccentricity. Plugging in for

and

then gives

$\displaystyle {1\over L}$	$\textstyle =$	$\displaystyle {1\over 2a}\left({{1\over 1-e}+{1\over 1+e}}\right)= {1\over 2a} {(1+e)+(1-e)\over 1-e^2}$
	$\textstyle =$	$\displaystyle {1\over a} {1\over 1-e^2},$	(2)

$\begin{displaymath} L=a(1-e^2). \end{displaymath}$

(3)