<p><strong>So, my ultimate objective is to map solar longitude values onto a pseudo-Gregorian calendar.</strong> I <em>thought</em> this would be simple, but it has turned out to be anything but.</p>
<p>I have asked several questions on Reddit about aspects of how to do this:</p>
<ol>
<li><p><a href="https://www.reddit.com/r/askastronomy/comments/mg7qgz/how_do_you_convert_solar_longitude_to_time_and/" rel="nofollow noreferrer">How do you convert solar longitude to time and map that time on a Gregorian-proportioned year, in the case of an eccentric orbit?</a></p>
</li>
<li><p><a href="https://www.reddit.com/r/Mars/comments/sxjjwp/how_would_you_convert_martian_solar_longitude/" rel="nofollow noreferrer">How would you convert Martian solar longitude into time, for example, in order to plot certain Martian events on a pseudo-Gregorian calendar?</a></p>
</li>
<li><p><a href="https://www.reddit.com/r/askastronomy/comments/tj4rjq/how_would_you_convert_solar_longitude_inclination/" rel="nofollow noreferrer">How would you convert solar longitude, inclination, and any other required quantities to true anomaly, and vice versa?</a></p>
</li>
</ol>
<p>The first received no answers, while the second (effectively a repeat of the first) was answered. The answerer <a href="https://www.reddit.com/r/Mars/comments/sxjjwp/comment/hxw762o/?utm_source=reddit&amp;utm_medium=web2x&amp;context=3" rel="nofollow noreferrer">told me</a> effectively what I wanted to find was the mean anomaly, or the elapsed fraction of time of the tropical year that has passed since perihelion, which is true. They provided me links to formulae to calculate the mean anomaly from the true anomaly, which they described as distinct from solar longitude but that converting between the two should be &quot;fairly straightforward.&quot; (They did describe their orbital mechanics as &quot;embarrassingly rusty&quot;, however.)</p>
<p>Now, I <em>couldn't</em> figure out how to convert between the two, and with me figuring whatever difference existed (in their derivative, not their offset) should be down to inclination, asked the third question. The sole answerer so far, unlike the answerer to the former question, <a href="https://www.reddit.com/r/askastronomy/comments/tj4rjq/comment/i1i5x0f/?utm_source=reddit&amp;utm_medium=web2x&amp;context=3" rel="nofollow noreferrer">says</a> that they are in fact the same thing (again derivative-wise), though they admit they <em>hadn't even heard of</em> solar longitude before my question.</p>
<p>I figure people here are more likely to be knowledgeable about the mathematics of orbits, hence I'm seeking clarification on the relationship between these quantities—that is, solar longitude (L<sub>s</sub>) and true anomaly (ν)—in order to fulfill my objective.</p>

CC BY-SA 4.0
2022-03-22T03:13:39.757Z
They are quite similar when referring to the Earth, but measured from different starting points, which makes converting between the two a bit non-trivial.  If you want a deeper understanding, look up "Kepler's Equation" to learn about True Anomaly, and "Ecliptic Coordinates" to learn about Solar Longitude.
Greg Miller
CC BY-SA 4.0
2022-03-22T03:14:00.387Z
A more direct answer to your overall question about converting solar longitude to a date.  See the link below.  At step 5, xecl, yecl, zelc are the ecliptic XYZ coordinates.  Plugging those into a "rectagular to polar coordinate" algorithm will give you the solar lat, lon, and distance.
https://www.celestialprogramming.com/planets_with_keplers_equation.html
Greg Miller
CC BY-SA 4.0
2022-03-22T08:57:01.747Z
Although it doesn't directly answer your question, https://en.wikipedia.org/wiki/Timekeeping_on_Mars has good info. However, the diagram at the top of the article is faulty, see the [SVG version](https://upload.wikimedia.org/wikipedia/commons/4/4b/Mars_earth_orbit.svg)
PM 2Ring
CC BY-SA 4.0
2022-03-22T09:12:02.960Z
It's a Good Idea to find out exactly how these Martian solar longitudes are defined. I *expect* solar longitudes to be measured from the (south to north) equinox point, along the Martian "ecliptic". But even that's slightly ambiguous, due to the precession of the equinoxes: "The precession cycle is 93,000 Martian years (175,000 Earth years), much longer than on Earth".
PM 2Ring
CC BY-SA 4.0
2022-03-22T23:42:02.467Z
About converting Ls into a date… By operating under the rebuttable presumption that Ls = ν but offset at least in Earth's case, I was able to do that, and create a calculator (https://docs.google.com/spreadsheets/d/1Mo6L7dpD8s8ZC3EP8pQTIcoyPEnyTq4PEFVCOokJXik/edit) for determining the solar energy received per day at a given Earth latitude that seems perfectly accurate. I really worry I'm wrong though, and also worry that finding Ls → ν for other bodies is super involved or inexact, as getting to this point has been 13 months of pain.
Grant Hartlage
CC BY-SA 4.0
2022-03-23T11:38:26.757Z
@GrantHartlage, probably it is just me. but I don't quite understands what you are trying to do. Are you talking of Mars only? If this the case your calendar should include 687 days. The way of doing this is very much like Earth which you have already made if I understand your comment correctly.
d_e
<orbit><orbital-mechanics><coordinate><orbital-elements><mathematics>
What is the relationship between true anomaly and solar longitude?
Grant Hartlage
# What is the relationship between true anomaly and solar longitude?

(Asked by: username_0 on 2022-03-21)

**So, my ultimate objective is to map solar longitude values onto a pseudo-Gregorian calendar.** I *thought* this would be simple, but it has turned out to be anything but.

I have asked several questions on Reddit about aspects of how to do this:

1. [How do you convert solar longitude to time and map that time on a Gregorian-proportioned year, in the case of an eccentric orbit?](https://www.reddit.com/r/askastronomy/comments/mg7qgz/how_do_you_convert_solar_longitude_to_time_and/)
2. [How would you convert Martian solar longitude into time, for example, in order to plot certain Martian events on a pseudo-Gregorian calendar?](https://www.reddit.com/r/Mars/comments/sxjjwp/how_would_you_convert_martian_solar_longitude/)
3. [How would you convert solar longitude, inclination, and any other required quantities to true anomaly, and vice versa?](https://www.reddit.com/r/askastronomy/comments/tj4rjq/how_would_you_convert_solar_longitude_inclination/)

The first received no answers, while the second (effectively a repeat of the first) was answered. The answerer [told me](https://www.reddit.com/r/Mars/comments/sxjjwp/comment/hxw762o/?utm_source=reddit&utm_medium=web2x&context=3) effectively what I wanted to find was the mean anomaly, or the elapsed fraction of time of the tropical year that has passed since perihelion, which is true. They provided me links to formulae to calculate the mean anomaly from the true anomaly, which they described as distinct from solar longitude but that converting between the two should be "fairly straightforward." (They did describe their orbital mechanics as "embarrassingly rusty", however.)

Now, I *couldn't* figure out how to convert between the two, and with me figuring whatever difference existed (in their derivative, not their offset) should be down to inclination, asked the third question. The sole answerer so far, unlike the answerer to the former question, [says](https://www.reddit.com/r/askastronomy/comments/tj4rjq/comment/i1i5x0f/?utm_source=reddit&utm_medium=web2x&context=3) that they are in fact the same thing (again derivative-wise), though they admit they *hadn't even heard of* solar longitude before my question.

I figure people here are more likely to be knowledgeable about the mathematics of orbits, hence I'm seeking clarification on the relationship between these quantities—that is, solar longitude (Ls) and true anomaly (ν)—in order to fulfill my objective.

**Tags:** orbit, orbital-mechanics, coordinate, orbital-elements, mathematics

> **Comments:**
> **username_1**: They are quite similar when referring to the Earth, but measured from different starting points, which makes converting between the two a bit non-trivial.  If you want a deeper understanding, look up "Kepler's Equation" to learn about True Anomaly, and "Ecliptic Coordinates" to learn about Solar Longitude.  
> **username_1**: A more direct answer to your overall question about converting solar longitude to a date.  See the link below.  At step 5, xecl, yecl, zelc are the ecliptic XYZ coordinates.  Plugging those into a "rectagular to polar coordinate" algorithm will give you the solar lat, lon, and distance. https://www.celestialprogramming.com/planets_with_keplers_equation.html  
> **username_2**: Although it doesn't directly answer your question, https://en.wikipedia.org/wiki/Timekeeping_on_Mars has good info. However, the diagram at the top of the article is faulty, see the [SVG version](https://upload.wikimedia.org/wikipedia/commons/4/4b/Mars_earth_orbit.svg)  
> **username_2**: It's a Good Idea to find out exactly how these Martian solar longitudes are defined. I *expect* solar longitudes to be measured from the (south to north) equinox point, along the Martian "ecliptic". But even that's slightly ambiguous, due to the precession of the equinoxes: "The precession cycle is 93,000 Martian years (175,000 Earth years), much longer than on Earth".  
> **username_0**: About converting Ls into a date… By operating under the rebuttable presumption that Ls = ν but offset at least in Earth's case, I was able to do that, and create a calculator (https://docs.google.com/spreadsheets/d/1Mo6L7dpD8s8ZC3EP8pQTIcoyPEnyTq4PEFVCOokJXik/edit) for determining the solar energy received per day at a given Earth latitude that seems perfectly accurate. I really worry I'm wrong though, and also worry that finding Ls → ν for other bodies is super involved or inexact, as getting to this point has been 13 months of pain.  
> **username_3**: @username_0, probably it is just me. but I don't quite understands what you are trying to do. Are you talking of Mars only? If this the case your calendar should include 687 days. The way of doing this is very much like Earth which you have already made if I understand your comment correctly.  

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## 0 answers

