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Semilatus Rectum

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

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

where $r_+=a(1+e)$ and $r_-=a(1-e)$ are the Apoapsis and Periapsis, and $e$ is the Ellipse's Eccentricity. Plugging in for $r_+$ and $r_-$ 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)

\end{displaymath} (3)

See also Eccentricity, Ellipse, Focus, Latus Rectum, Semimajor Axis, Semiminor Axis

© 1996-9 Eric W. Weisstein