<p>I'm using Skyfield to calculate some ecliptic longitudes for various dates. I understand that the 0° point of ecliptic longitude changes based on precession due to being the intersection between the ecliptic and the celestial equator, but as far as I can tell this should only lead to a rotation of the ecliptic, and shouldn't change the difference between ecliptic longitudes themselves, only offset them equally.</p>
<p>However, what I find when calculating this difference for older dates is that it actually does change, so clearly something is going on that I don't quite understand. The difference is larger the further back or forward in time from today I check. Here are some example values:</p>
<pre><code>date and time: 2000-01-01 00:00:00 UTC
ecliptic longitude of Pluto as seen from Earth, with precession: 251.4423867598416
ecliptic longitude of Juno as seen from Earth, with precession: 278.0447519268405
difference: -26.60236516699888
ecliptic longitude of Pluto as seen from Earth, without precession: 251.4462722291623
ecliptic longitude of Juno as seen from Earth, without precession: 278.0486383062446
difference -26.60236607708228
difference between the differences: -9.100834006403602e-07

date and time: 1800-01-01 00:00:00 UTC
ecliptic longitude of Pluto as seen from Earth, with precession: 331.41515410502547
ecliptic longitude of Juno as seen from Earth, with precession: 310.66231298714155
difference: 20.752841117883918
ecliptic longitude of Pluto as seen from Earth, without precession: 334.21524492213473
ecliptic longitude of Juno as seen from Earth, without precession: 313.4557265008473
difference 20.759518421287453
difference between the differences: 0.0066773034035350065

date and time: 2200-01-01 00:00:00 UTC
ecliptic longitude of Pluto as seen from Earth, with precession: 144.74720464480612
ecliptic longitude of Juno as seen from Earth, with precession: 252.19120370149466
difference: -107.44399905668854
ecliptic longitude of Pluto as seen from Earth, without precession: 141.94565398823505
ecliptic longitude of Juno as seen from Earth, without precession: 249.3919999574794
difference -107.44634596924436
difference between the differences: -0.0023469125558222004

date and time: 1000-01-01 00:00:00 UTC
ecliptic longitude of Pluto as seen from Earth, with precession: 215.88352515432385
ecliptic longitude of Juno as seen from Earth, with precession: 222.06486481268652
difference: -6.181339658362674
ecliptic longitude of Pluto as seen from Earth, without precession: 229.8449049370316
ecliptic longitude of Juno as seen from Earth, without precession: 236.01560254922802
difference -6.17069761219642
difference between the differences: 0.010642046166253749

date and time: 3000-01-01 00:00:00 UTC
ecliptic longitude of Pluto as seen from Earth, with precession: 281.25959800237814
ecliptic longitude of Juno as seen from Earth, with precession: 352.8312616380944
difference: -71.57166363571628
ecliptic longitude of Pluto as seen from Earth, without precession: 267.25800738956053
ecliptic longitude of Juno as seen from Earth, without precession: 338.8213324904173
difference -71.56332510085679
difference between the differences: 0.00833853485949021

date and time: -1000-01-01 00:00:00 UTC
ecliptic longitude of Pluto as seen from Earth, with precession: 130.5063312531234
ecliptic longitude of Juno as seen from Earth, with precession: 323.32094562295737
difference: -192.81461436983398
ecliptic longitude of Pluto as seen from Earth, without precession: 172.2490220604472
ecliptic longitude of Juno as seen from Earth, without precession: 4.995252624931857
difference 167.25376943551535
difference between the differences: 0.06838380534929911
</code></pre>
<p>Does anyone have a good explanation for what is causing these differences? As we can see the ecliptic longitudes themselves are quite offset, by more than 10° for the furthest dates (over 40° for year -1000), but from my understanding the differences should in principle remain the same. Skyfield lists in its documentation that it's using the IAU 2000A model to account for precession, and I tried reading a bit about it, but I couldn't find anything that would explain this. I know that there's something called ecliptic precession as well, but from what I could tell this is not something that is being considered (or is it?).</p>

CC BY-SA 4.0
2024-07-20T19:25:37.990Z
Maybe it has to do with the adjustment (or lack, thereof) of orbital elements for each body?
Pierre Paquette
CC BY-SA 4.0
2024-07-20T19:31:09.393Z
@PierrePaquette: I'm not sure I understand what you mean. As far as I understand the same orbital elements are being used in both cases, the only difference being Earth's precession being accounted for by passing `'date'` to `ecliptic_latlon`. This changes the celestial equator, and thus the starting point of the ecliptic, but I don't see how the plane of the ecliptic itself would somehow be different in the two cases.
Outis Nemo
CC BY-SA 4.0
2024-07-20T19:40:12.527Z
What I meant was that maybe the orbital elements are not adjusted the same way for both bodies to account for time-induced changes like precession and such.
Pierre Paquette
CC BY-SA 4.0
2024-07-20T20:38:02.057Z
@PierrePaquette: I'm afraid I still don't understand quite what you mean. As mentioned above I don't see how there would be any difference in the orbital elements themselves. As you might tell from the examples provided it's clear that the bodies are being observed at quite different ecliptic longitudes due to the shift itself, with a difference of over 40° for the year -1000, but they're still being observed at almost the exact same longitudes relative to one another. I don't see what the orbital elements themselves would account for in this case, but please enlighten me.
Outis Nemo
CC BY-SA 4.0
2024-07-20T20:45:47.907Z
Sorry, it makes sense in my head but I can’t find the words to explain it. Just forget about that for now. If I figure out a way to explain it, I’ll come back.
Pierre Paquette
CC BY-SA 4.0
2024-07-20T21:07:18.873Z
@OutisNemo The effect of precession on ecliptic longitude is approximately linear for a small amount of precession, but not over a longer time span, and it also affects ecliptic latitude. This diagram may help: https://i.sstatic.net/dx7WX.gif from this answer by robjohn https://astronomy.stackexchange.com/a/47674/16685 That answer's about lunar nodal precession, but it's the same principal. You can ignore precession of the ecliptic plane (relative to the ICRF), since it's small, and has a huge period.
PM 2Ring
CC BY-SA 4.0
2024-07-20T21:15:23.453Z
@PM2Ring: Thanks for reassuring me that ecliptic precession can be safely ignored. I'm trying to look at that answer and illustration, but I still struggle to see how it would somehow affect the difference between two other planets in terms of ecliptic longitude. It seems to me like the ecliptic plane itself remains the exact same, and that only the starting point (where it intersects with the celestial equator) changes. Even if the change isn't linear over long periods, it should still be the same for all the observed bodies based on this, at least as far as I can tell.
Outis Nemo
<coordinate><software><ecliptic><precession><skyfield>
Why is there a discrepancy between the difference in ecliptic longitudes as found with Skyfield when accounting or not accounting for precession?
Outis Nemo
# Why is there a discrepancy between the difference in ecliptic longitudes as found with Skyfield when accounting or not accounting for precession?

(Asked by: username_0 on 2024-07-20)

I'm using Skyfield to calculate some ecliptic longitudes for various dates. I understand that the 0° point of ecliptic longitude changes based on precession due to being the intersection between the ecliptic and the celestial equator, but as far as I can tell this should only lead to a rotation of the ecliptic, and shouldn't change the difference between ecliptic longitudes themselves, only offset them equally.
However, what I find when calculating this difference for older dates is that it actually does change, so clearly something is going on that I don't quite understand. The difference is larger the further back or forward in time from today I check. Here are some example values:
date and time: 2000-01-01 00:00:00 UTC
ecliptic longitude of Pluto as seen from Earth, with precession: 251.4423867598416
ecliptic longitude of Juno as seen from Earth, with precession: 278.0447519268405
difference: -26.60236516699888
ecliptic longitude of Pluto as seen from Earth, without precession: 251.4462722291623
ecliptic longitude of Juno as seen from Earth, without precession: 278.0486383062446
difference -26.60236607708228
difference between the differences: -9.100834006403602e-07

date and time: 1800-01-01 00:00:00 UTC
ecliptic longitude of Pluto as seen from Earth, with precession: 331.41515410502547
ecliptic longitude of Juno as seen from Earth, with precession: 310.66231298714155
difference: 20.752841117883918
ecliptic longitude of Pluto as seen from Earth, without precession: 334.21524492213473
ecliptic longitude of Juno as seen from Earth, without precession: 313.4557265008473
difference 20.759518421287453
difference between the differences: 0.0066773034035350065

date and time: 2200-01-01 00:00:00 UTC
ecliptic longitude of Pluto as seen from Earth, with precession: 144.74720464480612
ecliptic longitude of Juno as seen from Earth, with precession: 252.19120370149466
difference: -107.44399905668854
ecliptic longitude of Pluto as seen from Earth, without precession: 141.94565398823505
ecliptic longitude of Juno as seen from Earth, without precession: 249.3919999574794
difference -107.44634596924436
difference between the differences: -0.0023469125558222004

date and time: 1000-01-01 00:00:00 UTC
ecliptic longitude of Pluto as seen from Earth, with precession: 215.88352515432385
ecliptic longitude of Juno as seen from Earth, with precession: 222.06486481268652
difference: -6.181339658362674
ecliptic longitude of Pluto as seen from Earth, without precession: 229.8449049370316
ecliptic longitude of Juno as seen from Earth, without precession: 236.01560254922802
difference -6.17069761219642
difference between the differences: 0.010642046166253749

date and time: 3000-01-01 00:00:00 UTC
ecliptic longitude of Pluto as seen from Earth, with precession: 281.25959800237814
ecliptic longitude of Juno as seen from Earth, with precession: 352.8312616380944
difference: -71.57166363571628
ecliptic longitude of Pluto as seen from Earth, without precession: 267.25800738956053
ecliptic longitude of Juno as seen from Earth, without precession: 338.8213324904173
difference -71.56332510085679
difference between the differences: 0.00833853485949021

date and time: -1000-01-01 00:00:00 UTC
ecliptic longitude of Pluto as seen from Earth, with precession: 130.5063312531234
ecliptic longitude of Juno as seen from Earth, with precession: 323.32094562295737
difference: -192.81461436983398
ecliptic longitude of Pluto as seen from Earth, without precession: 172.2490220604472
ecliptic longitude of Juno as seen from Earth, without precession: 4.995252624931857
difference 167.25376943551535
difference between the differences: 0.06838380534929911

Does anyone have a good explanation for what is causing these differences? As we can see the ecliptic longitudes themselves are quite offset, by more than 10° for the furthest dates (over 40° for year -1000), but from my understanding the differences should in principle remain the same. Skyfield lists in its documentation that it's using the IAU 2000A model to account for precession, and I tried reading a bit about it, but I couldn't find anything that would explain this. I know that there's something called ecliptic precession as well, but from what I could tell this is not something that is being considered (or is it?).

**Tags:** coordinate, software, ecliptic, precession, skyfield
> **Comments:**
> **username_1**: Maybe it has to do with the adjustment (or lack, thereof) of orbital elements for each body?  
> **username_0**: @PierrePaquette: I'm not sure I understand what you mean. As far as I understand the same orbital elements are being used in both cases, the only difference being Earth's precession being accounted for by passing `'date'` to `ecliptic_latlon`. This changes the celestial equator, and thus the starting point of the ecliptic, but I don't see how the plane of the ecliptic itself would somehow be different in the two cases.  
> **username_1**: What I meant was that maybe the orbital elements are not adjusted the same way for both bodies to account for time-induced changes like precession and such.  
> **username_0**: @PierrePaquette: I'm afraid I still don't understand quite what you mean. As mentioned above I don't see how there would be any difference in the orbital elements themselves. As you might tell from the examples provided it's clear that the bodies are being observed at quite different ecliptic longitudes due to the shift itself, with a difference of over 40° for the year -1000, but they're still being observed at almost the exact same longitudes relative to one another. I don't see what the orbital elements themselves would account for in this case, but please enlighten me.  
> **username_1**: Sorry, it makes sense in my head but I can’t find the words to explain it. Just forget about that for now. If I figure out a way to explain it, I’ll come back.  
> **username_2**: @OutisNemo The effect of precession on ecliptic longitude is approximately linear for a small amount of precession, but not over a longer time span, and it also affects ecliptic latitude. This diagram may help: https://i.sstatic.net/dx7WX.gif from this answer by robjohn https://astronomy.stackexchange.com/a/47674/16685 That answer's about lunar nodal precession, but it's the same principal. You can ignore precession of the ecliptic plane (relative to the ICRF), since it's small, and has a huge period.  
> **username_0**: @PM2Ring: Thanks for reassuring me that ecliptic precession can be safely ignored. I'm trying to look at that answer and illustration, but I still struggle to see how it would somehow affect the difference between two other planets in terms of ecliptic longitude. It seems to me like the ecliptic plane itself remains the exact same, and that only the starting point (where it intersects with the celestial equator) changes. Even if the change isn't linear over long periods, it should still be the same for all the observed bodies based on this, at least as far as I can tell.  

---

## 0 answers

