<p>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.</p>

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

<p>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.</p>

CC BY-SA 3.0
2015-12-01T16:48:20.020Z
I was trying to choose variable names for those terms in a computer program.
Russell Borogove
CC BY-SA 3.0
2015-12-01T17:08:46.253Z
e_p and e_a should be sufficient.
MichaelJRoberts
CC BY-SA 3.0
2015-12-01T20:42:19.217Z
$1-e$ determined as $r_p/a$ would be the "semi-major axis normalized periapsis distance" but I guess this is a bit clumsy...
AtmosphericPrisonEscape
CC BY-SA 3.0
2015-12-01T10:14:32.263Z
2015-12-01T17:08:06.520Z
2015-12-01T17:08:06.520Z
MichaelJRoberts
<p>In several equations of orbital elements (such as the determination of true anomaly from mean anomaly), the terms 1-<em>e</em> and 1+<em>e</em> appear. These are the ratios of the orbital periapsis and apoapsis to the semi-major axis, but do the ratios themselves have names?</p>

CC BY-SA 3.0
2015-12-31T18:04:24.993Z
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
CC BY-SA 3.0
2015-12-31T19:20:20.370Z
The former pair.
Russell Borogove
CC BY-SA 3.0
2015-12-01T09:45:08.700Z
$e$ 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
<orbital-elements>
Name for 1-e and 1+e terms?
Russell Borogove
# Name for 1-e and 1+e terms?

(Asked by: username_0 on 2015-12-01)

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?

**Tags:** orbital-elements
> **Comments:**
> **username_2**: $e$ 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 $.  
> **username_1**: Are you looking for names for $1-e$ and $1+e$, or $\frac{1-e}{1+e}$ and $\frac{1+e}{1-e}$?  
> **username_0**: The former pair.  

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## 1 answers

### Answer by username_3 on 2015-12-01. Score: 4

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.

> **Comments:**
> **username_0**: I was trying to choose variable names for those terms in a computer program.  
> **username_3**: e_p and e_a should be sufficient.  
> **username_4**: $1-e$ determined as $r_p/a$ would be the "semi-major axis normalized periapsis distance" but I guess this is a bit clumsy...  

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