# Name for 1-e and 1+e terms?

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?

• $e$ 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 $1+e$. – engineer Dec 1 '15 at 9:45
• Are you looking for names for $1-e$ and $1+e$, or $\frac{1-e}{1+e}$ and $\frac{1+e}{1-e}$? – HDE 226868 Dec 31 '15 at 18:04
• The former pair. – Russell Borogove Dec 31 '15 at 19:20

## 1 Answer

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.

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