<p>If the Earth was a sphere, then the curve in the last picture of tfb's answer is the <a href="https://en.wikipedia.org/wiki/Viviani%27s_curve#Parametric_representation" rel="noreferrer">curve of Viviani</a>; otherwise, if you make the oblate spheroid assumption, you get a slightly distorted version of this curve.</p>

<p>More generally, a <a href="https://en.wikipedia.org/wiki/Cl%C3%A9lie" rel="noreferrer"><em>clélie</em></a> is the name given to any spherical curve where the longitude <span class="math-container">$\varphi$</span> and colatitude <span class="math-container">$\theta$</span> have the relationship <span class="math-container">$\varphi=c\theta,\quad c&gt;0$</span>, and the curve of Viviani corresponds to the locus of a geosynchronous orbit, <span class="math-container">$c=1$</span>.</p>

CC BY-SA 4.0
2020-03-25T22:25:26.937Z
[here are some](https://space.stackexchange.com/a/37454/121020) geosynchronous orbits and they do look similar, If [Viviani's curve](https://en.wikipedia.org/wiki/Viviani%27s_curve) were a geosynchronous orbit then it would have to correspond to inclination of 90 degrees. Is it possible to add a link (or some math) that supports the curve is in fact a synchronous orbit in a rotating frame? *Thanks!*
uhoh
CC BY-SA 4.0
2020-03-25T22:47:10.393Z
also (just fyi) [Is an Earth synchronous (?) polar orbit possible?](https://space.stackexchange.com/q/40809/12102)
uhoh
CC BY-SA 4.0
2020-03-26T00:53:15.977Z
@uhoh, I think that deserves to be a question on its own. ;)
joe khool
CC BY-SA 4.0
2020-03-26T01:13:16.537Z
what a remarkable coincidence! :-) [Is a polar geosynchronous orbit described by Viviani's curve?](https://space.stackexchange.com/q/42097/12102)
uhoh
CC BY-SA 4.0
2020-03-24T07:16:00.810Z
2020-03-24T07:22:38.587Z
2020-03-24T07:22:38.587Z
joe khool
<p>Is there a name for the great circle where latitude and longitude are equal? I have attempted a google search but only the equator and the prime meridian are defined in the sources I can find. ( It is of relevance in developing a map application which keeps track of latitude and longitude ).</p>

CC BY-SA 4.0
2020-03-22T14:39:12.837Z
I think the answer is probably not, but maybe others have some idea. I doubt if it would be useful for anything (maybe some satellites might fly on such an orbit).
peterh
CC BY-SA 4.0
2020-03-23T14:42:27.083Z
Your question seems to be missing vital info .. if latitude and longitude are equal = non-changing .. how can there be a circle .. that defines only a point
eagle275
CC BY-SA 4.0
2020-03-23T15:19:07.867Z
@eagle275 as latitude $\phi\in[-\pi/2,\pi/2]$, and longitude $\lambda\in[-\pi,\pi]$, there should be a curve formed by the points where $\phi = \lambda$. I hade made the (erroneous, as pointed out by tfb) assumption that this curve would be a great circle.
Toivo Säwén
CC BY-SA 4.0
2020-03-23T16:15:55.250Z
There's a good answer. But it's also worth mentioning that this line doesn't mean anything - because longitude is arbitrary. There's no good reason for any particular meridian to be defined as zero.
Semidiurnal Simon
CC BY-SA 4.0
2020-03-23T20:07:12.030Z
@SemidiurnalSimon the 'Prime meridian' or 'Greenwich meridian' is the name of a great circle (or at least half a circle). That longitude it is arbitrary doesn't mean you can't have a great circle with a name defined by it.
Pete Kirkham
<geodesy>
Is there a name for the great circle where latitude and longitude are equal?
Toivo Säwén
# Is there a name for the great circle where latitude and longitude are equal?

(Asked by: username_0 on 2020-03-22)

Is there a name for the great circle where latitude and longitude are equal? I have attempted a google search but only the equator and the prime meridian are defined in the sources I can find. ( It is of relevance in developing a map application which keeps track of latitude and longitude ).

**Tags:** geodesy

> **Comments:**
> **username_1**: I think the answer is probably not, but maybe others have some idea. I doubt if it would be useful for anything (maybe some satellites might fly on such an orbit).  
> **username_2**: Your question seems to be missing vital info .. if latitude and longitude are equal = non-changing .. how can there be a circle .. that defines only a point  
> **username_0**: @username_2 as latitude $\phi\in[-\pi/2,\pi/2]$, and longitude $\lambda\in[-\pi,\pi]$, there should be a curve formed by the points where $\phi = \lambda$. I hade made the (erroneous, as pointed out by tfb) assumption that this curve would be a great circle.  
> **username_3**: There's a good answer. But it's also worth mentioning that this line doesn't mean anything - because longitude is arbitrary. There's no good reason for any particular meridian to be defined as zero.  
> **username_4**: @username_3 the 'Prime meridian' or 'Greenwich meridian' is the name of a great circle (or at least half a circle). That longitude it is arbitrary doesn't mean you can't have a great circle with a name defined by it.  

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## 1 answers

### Answer by username_5 on 2020-03-24. Score: 19

If the Earth was a sphere, then the curve in the last picture of tfb's answer is the [curve of Viviani](https://en.wikipedia.org/wiki/Viviani%27s_curve#Parametric_representation); otherwise, if you make the oblate spheroid assumption, you get a slightly distorted version of this curve.

More generally, a [*clélie*](https://en.wikipedia.org/wiki/Cl%C3%A9lie) is the name given to any spherical curve where the longitude $\varphi$ and colatitude $\theta$ have the relationship $\varphi=c\theta,\quad c>0$, and the curve of Viviani corresponds to the locus of a geosynchronous orbit, $c=1$.

> **Comments:**
> **username_6**: [here are some](https://space.stackexchange.com/a/37454/121020) geosynchronous orbits and they do look similar, If [Viviani's curve](https://en.wikipedia.org/wiki/Viviani%27s_curve) were a geosynchronous orbit then it would have to correspond to inclination of 90 degrees. Is it possible to add a link (or some math) that supports the curve is in fact a synchronous orbit in a rotating frame? *Thanks!*  
> **username_6**: also (just fyi) [Is an Earth synchronous (?) polar orbit possible?](https://space.stackexchange.com/q/40809/12102)  
> **username_5**: @username_6, I think that deserves to be a question on its own. ;)  
> **username_6**: what a remarkable coincidence! :-) [Is a polar geosynchronous orbit described by Viviani's curve?](https://space.stackexchange.com/q/42097/12102)  

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