In several equations of orbital elements (such as the determination of true anomaly from mean anomaly), the terms 1-e and 1+e appear. These are the ratios of the orbital periapsis and apoapsis to the semi-major axis, but do the ratios themselves have names?

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    $\begingroup$ $e$ is called eccentricity in that case. But that's probably not, what you were asking for. Not sure, if there are terms for $1-e$ and $ 1+e $. $\endgroup$
    – engineer
    Dec 1 '15 at 9:45
  • $\begingroup$ Are you looking for names for $1-e$ and $1+e$, or $\frac{1-e}{1+e}$ and $\frac{1+e}{1-e}$? $\endgroup$
    – HDE 226868
    Dec 31 '15 at 18:04
  • $\begingroup$ The former pair. $\endgroup$ Dec 31 '15 at 19:20

As the commenter states, $e$ is indeed called the orbital eccentricity. If you add a radial scale length (e.g., semi-major axis) to both of those values the $1-e$ describes the periapsis (closest approach of orbit) and the $1+e$ apoapsis (furthest) of an elliptical orbit. They don't have a specific special name, as they are dimensionless measures, but can be quite useful in determining the orbit of planets and other Keplerian systems.

Periapsis: $$ r_{p}=a(1-e) $$ Apoapsis: $$ r_{a}=a(1+e) $$

Perhaps the could be named the maximum radial eccentricity and minimum radial eccentricity, if you needed to describe these parameters in a report or class homework etc.

  • $\begingroup$ I was trying to choose variable names for those terms in a computer program. $\endgroup$ Dec 1 '15 at 16:48
  • $\begingroup$ e_p and e_a should be sufficient. $\endgroup$ Dec 1 '15 at 17:08
  • $\begingroup$ $1-e$ determined as $r_p/a$ would be the "semi-major axis normalized periapsis distance" but I guess this is a bit clumsy... $\endgroup$ Dec 1 '15 at 20:42

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