<p>This appears to be the <a href="https://en.wikipedia.org/wiki/Latitude#Geocentric_latitude" rel="nofollow noreferrer">geocentric latitude</a> ($\psi$), which is the angle between the equatorial plane and the point on the surface of the ellipse. It can be calculated from the geodetic latitude (also known as the geographic latitude) ($\phi$) and the eccentricity of the ellipse ($e$):
$$\psi(\phi)=\tan^{-1}\left(\left(1-e^2\right)\tan\phi\right)$$
If $e=0$, then the two lattitudes are the same, because the focus is at the center of the ellipse.</p>

<p><img src="https://upload.wikimedia.org/wikipedia/commons/0/06/Two-types-of-latitude.png" alt="">
<br>
<sup>Image courtesy of Wikipedia user Wmc824 under <a href="https://creativecommons.org/licenses/by/3.0/deed.en" rel="nofollow noreferrer">the Creative Commons Attribution 3.0 Unported license</a>.</sup></p>

<p>It might make more sense to use this latitude to describe the position of an orbiting object, but the vector from the focus to the object's position $(r,\theta)$ is perpendicular to the tangential component of the object's velocity vector, meaning that the geodetic latitude may be better.</p>

CC BY-SA 3.0
2017-02-03T14:39:27.633Z
Yeah, but I think it's supposed to be in degrees, but I keep getting a number like 6 million. I'm just not entirely sure what units it's in.
James Kirk
CC BY-SA 3.0
2017-02-03T15:00:08.980Z
Okay, so your saying that an answer like 6 million makes sense because it's just a point on the edge of a map?
James Kirk
CC BY-SA 3.0
2017-02-03T17:25:45.070Z
@JamesKirk No 6 million should not make sense. Since this is an angle, it should only be defined between 0 and 360 degrees. A value of 6 million just doesn't make sense. Depending on your functions and equations, you may find that you wind up with something between -90 and 90 degrees. We couldn't know how you're getting that answer though without seeing your equations and numbers.
zephyr
CC BY-SA 3.0
2017-02-03T18:47:35.817Z
@JamesKirk What zephyr said. That's way too large. Check any conversions you might have made.
HDE 226868
CC BY-SA 3.0
2017-02-03T19:11:33.623Z
Okay, I'll double check it.
James Kirk
CC BY-SA 3.0
2017-02-03T14:46:39.080Z
2017-02-03T15:00:28.830Z
2017-02-03T15:00:28.830Z
HDE 226868
<p>For the last week or so, I have been teaching myself orbital mechanics within the context of <a href="http://www.braeunig.us/space/index.htm" rel="nofollow noreferrer">Braeunig's Rocket and Space Technology</a>.</p>

<p>I noticed a symbol, $\phi '$, and was wondering what context that was used in? I think it is an angle measurement, but I know that it is almost equal to the semi-major axis on earth.</p>

<p>From the box labeled <strong>Geodetic Latitude, Geocentric Latitude, and Declination</strong>, found about half way down after selecting <strong>Orbital Mechanics</strong> <a href="http://www.braeunig.us/space/index.htm" rel="nofollow noreferrer">here</a>.</p>

<p><a href="https://i.sstatic.net/OEYWY.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/OEYWY.gif" alt="enter image description here"></a></p>

CC BY-SA 3.0
2017-02-03T14:46:00.023Z
No problem. Welcome to Astronomy Stack Exchange! By the way, questions about rockets and space technology are usually the domain of [Space Exploration Stack Exchange](http://space.stackexchange.com/), but since this one is about generic orbital mechanics it is probably ok.
called2voyage
CC BY-SA 3.0
2017-02-04T10:32:20.970Z
In mathematical notation in general, a prime could be used to indicate a different reference position, or coordinate system, or a time derivative, or something else. Can you at least do a screen shot of how it's used there, or link to the particular place where you find it - it's hard to answer without more information, and if there were an answer wouldn't be so useful for anyone else reading this later.
uhoh
CC BY-SA 3.0
2017-02-04T13:37:05.820Z
Ah, it's in the comment. Didn't see it there. I'll move it to the question. I've added the figure, adjusted the linking. This can help make questions easier to answer. In this case you can see it says "*The geocentric latitude, $\phi$' is the angle between*..." right there on the page you were looking at.
uhoh
<orbital-mechanics>
What is $\phi '$ in orbital mechanics?
James Kirk
# What is $\phi '$ in orbital mechanics?

(Asked by: username_0 on 2017-02-03)

For the last week or so, I have been teaching myself orbital mechanics within the context of [Braeunig's Rocket and Space Technology](http://www.braeunig.us/space/index.htm).

I noticed a symbol, $\phi '$, and was wondering what context that was used in? I think it is an angle measurement, but I know that it is almost equal to the semi-major axis on earth.

From the box labeled **Geodetic Latitude, Geocentric Latitude, and Declination**, found about half way down after selecting **Orbital Mechanics** [here](http://www.braeunig.us/space/index.htm).

[![enter image description here](https://i.sstatic.net/OEYWY.gif)](https://i.sstatic.net/OEYWY.gif)

**Tags:** orbital-mechanics
> **Comments:**
> **username_1**: No problem. Welcome to Astronomy Stack Exchange! By the way, questions about rockets and space technology are usually the domain of [Space Exploration Stack Exchange](http://space.stackexchange.com/), but since this one is about generic orbital mechanics it is probably ok.  
> **username_2**: In mathematical notation in general, a prime could be used to indicate a different reference position, or coordinate system, or a time derivative, or something else. Can you at least do a screen shot of how it's used there, or link to the particular place where you find it - it's hard to answer without more information, and if there were an answer wouldn't be so useful for anyone else reading this later.  
> **username_2**: Ah, it's in the comment. Didn't see it there. I'll move it to the question. I've added the figure, adjusted the linking. This can help make questions easier to answer. In this case you can see it says "*The geocentric latitude, $\phi$' is the angle between*..." right there on the page you were looking at.  

---

## 1 answers

### Answer by username_3 on 2017-02-03. Score: 5 | Accepted answer

This appears to be the [geocentric latitude](https://en.wikipedia.org/wiki/Latitude#Geocentric_latitude) ($\psi$), which is the angle between the equatorial plane and the point on the surface of the ellipse. It can be calculated from the geodetic latitude (also known as the geographic latitude) ($\phi$) and the eccentricity of the ellipse ($e$):
$$\psi(\phi)=\tan^{-1}\left(\left(1-e^2\right)\tan\phi\right)$$
If $e=0$, then the two lattitudes are the same, because the focus is at the center of the ellipse.

![](https://upload.wikimedia.org/wikipedia/commons/0/06/Two-types-of-latitude.png)
  
Image courtesy of Wikipedia user Wmc824 under [the Creative Commons Attribution 3.0 Unported license](https://creativecommons.org/licenses/by/3.0/deed.en).

It might make more sense to use this latitude to describe the position of an orbiting object, but the vector from the focus to the object's position $(r,\theta)$ is perpendicular to the tangential component of the object's velocity vector, meaning that the geodetic latitude may be better.

> **Comments:**
> **username_0**: Yeah, but I think it's supposed to be in degrees, but I keep getting a number like 6 million. I'm just not entirely sure what units it's in.  
> **username_0**: Okay, so your saying that an answer like 6 million makes sense because it's just a point on the edge of a map?  
> **username_4**: @JamesKirk No 6 million should not make sense. Since this is an angle, it should only be defined between 0 and 360 degrees. A value of 6 million just doesn't make sense. Depending on your functions and equations, you may find that you wind up with something between -90 and 90 degrees. We couldn't know how you're getting that answer though without seeing your equations and numbers.  
> **username_3**: @JamesKirk What zephyr said. That's way too large. Check any conversions you might have made.  
> **username_0**: Okay, I'll double check it.  

---

