<p>JPL Solar System Dynamics has produced the variations.  The original page is not available that I can find but the <a href="https://web.archive.org/web/20210807130733/https://ssd.jpl.nasa.gov/txt/p_elem_t1.txt" rel="nofollow noreferrer">Wayback Machine</a> has it archived, and I have included a copy below.  The first line for each are the orbital elements, and the second line are the variations per century.  They are valid from 1800-2050AD.</p>
<p>A <a href="https://web.archive.org/web/20210420020242/https://ssd.jpl.nasa.gov/txt/p_elem_t2.txt" rel="nofollow noreferrer">second set of elements and variations</a>, valid from 3000BC to 3000AD is also available, but have some extra terms beyond linear variations.</p>
<p>These elements also appear in the Explanatory Supplement to the Astronomical Almanac with steps on how to use them to create a simple, low accuracy ephemeris.  I have  <a href="https://www.celestialprogramming.com/planets_with_keplers_equation.html" rel="nofollow noreferrer">implemented this ephemeris here</a>.</p>
<pre><code>                a              e               I                L            long.peri.      long.node.
          AU, AU/Cy     rad, rad/Cy     deg, deg/Cy      deg, deg/Cy      deg, deg/Cy     deg, deg/Cy
-----------------------------------------------------------------------------------------------------------
Mercury   0.38709927      0.20563593      7.00497902      252.25032350     77.45779628     48.33076593
          0.00000037      0.00001906     -0.00594749   149472.67411175      0.16047689     -0.12534081
Venus     0.72333566      0.00677672      3.39467605      181.97909950    131.60246718     76.67984255
          0.00000390     -0.00004107     -0.00078890    58517.81538729      0.00268329     -0.27769418
EM Bary   1.00000261      0.01671123     -0.00001531      100.46457166    102.93768193      0.0
          0.00000562     -0.00004392     -0.01294668    35999.37244981      0.32327364      0.0
Mars      1.52371034      0.09339410      1.84969142       -4.55343205    -23.94362959     49.55953891
          0.00001847      0.00007882     -0.00813131    19140.30268499      0.44441088     -0.29257343
Jupiter   5.20288700      0.04838624      1.30439695       34.39644051     14.72847983    100.47390909
         -0.00011607     -0.00013253     -0.00183714     3034.74612775      0.21252668      0.20469106
Saturn    9.53667594      0.05386179      2.48599187       49.95424423     92.59887831    113.66242448
         -0.00125060     -0.00050991      0.00193609     1222.49362201     -0.41897216     -0.28867794
Uranus   19.18916464      0.04725744      0.77263783      313.23810451    170.95427630     74.01692503
         -0.00196176     -0.00004397     -0.00242939      428.48202785      0.40805281      0.04240589
Neptune  30.06992276      0.00859048      1.77004347      -55.12002969     44.96476227    131.78422574
          0.00026291      0.00005105      0.00035372      218.45945325     -0.32241464     -0.00508664
Pluto    39.48211675      0.24882730     17.14001206      238.92903833    224.06891629    110.30393684
         -0.00031596      0.00005170      0.00004818      145.20780515     -0.04062942     -0.01183482
</code></pre>

CC BY-SA 4.0
2022-08-02T19:16:11.473Z
Those elements tables are on https://ssd.jpl.nasa.gov/planets/approx_pos.html There's all sorts of goodies on the SSD FTP browser, which has an HTML portal: https://ssd.jpl.nasa.gov/ftp/
PM 2Ring
CC BY-SA 4.0
2022-08-02T18:37:30.137Z
2022-08-02T18:37:30.137Z
Greg Miller
<p>Which one of the gas and ice giants of our solar system has the least varying orbital characteristics (obliquity, eccentricity etc.)?</p>

CC BY-SA 4.0
2022-08-01T12:38:43.913Z
You might be interested in checking [this](https://www.cambridge.org/core/books/solar-system-dynamics/108745217E4A18190CBA340ED5E477A2) textbook: "Solar System Dynamics" by Murray & Dermott.
nuwe
CC BY-SA 4.0
2022-08-01T15:15:39.987Z
Anything you researched on your question yourself, any sources you checked already?
planetmaker
CC BY-SA 4.0
2022-08-01T15:21:41.670Z
You could probably get all this from Wikipedia E.g https://en.wikipedia.org/wiki/Orbital_eccentricity
user438383
CC BY-SA 4.0
2022-08-01T16:03:59.560Z
@planetmaker I did research but could not find the minimum and maximums of Saturn and Jupiter
איתי מרלוב
CC BY-SA 4.0
2022-08-01T16:41:21.950Z
There's a big difference between "a brief look at one wikipedia page did not give me any results", "this article in scientific american stated varying values of the ascending node, but not obliquity and eccentricity - where can I find those?" and "I searched ADS, arxiv, etc. and the papers X,Y and Z don't agree, what is the actual variance of the planets' obliquity and eccentricity?" What level of research did you do and what level of answer do you need? Please phrase your question accordingly. Please also see https://stackoverflow.com/help/how-to-ask
planetmaker
CC BY-SA 4.0
2022-08-02T18:39:51.283Z
I edited the title to better reflect the question being asked.
Greg Miller
<gas-giants><eccentricity><obliquity>
Which one of the gas and ice giants has the least varying orbital characteristics?
איתי מרלוב
# Which one of the gas and ice giants has the least varying orbital characteristics?

(Asked by: username_0 on 2022-08-01)

Which one of the gas and ice giants of our solar system has the least varying orbital characteristics (obliquity, eccentricity etc.)?

**Tags:** gas-giants, eccentricity, obliquity
> **Comments:**
> **username_1**: You might be interested in checking [this](https://www.cambridge.org/core/books/solar-system-dynamics/108745217E4A18190CBA340ED5E477A2) textbook: "Solar System Dynamics" by Murray & Dermott.  
> **username_2**: Anything you researched on your question yourself, any sources you checked already?  
> **username_3**: You could probably get all this from Wikipedia E.g https://en.wikipedia.org/wiki/Orbital_eccentricity  
> **username_0**: @planetmaker I did research but could not find the minimum and maximums of Saturn and Jupiter  
> **username_2**: There's a big difference between "a brief look at one wikipedia page did not give me any results", "this article in scientific american stated varying values of the ascending node, but not obliquity and eccentricity - where can I find those?" and "I searched ADS, arxiv, etc. and the papers X,Y and Z don't agree, what is the actual variance of the planets' obliquity and eccentricity?" What level of research did you do and what level of answer do you need? Please phrase your question accordingly. Please also see https://stackoverflow.com/help/how-to-ask  
> **username_4**: I edited the title to better reflect the question being asked.  

---

## 1 answers

### Answer by username_4 on 2022-08-02. Score: 1

JPL Solar System Dynamics has produced the variations.  The original page is not available that I can find but the Wayback Machine has it archived, and I have included a copy below.  The first line for each are the orbital elements, and the second line are the variations per century.  They are valid from 1800-2050AD.
A second set of elements and variations, valid from 3000BC to 3000AD is also available, but have some extra terms beyond linear variations.
These elements also appear in the Explanatory Supplement to the Astronomical Almanac with steps on how to use them to create a simple, low accuracy ephemeris.  I have  implemented this ephemeris here.
                a              e               I                L            long.peri.      long.node.
          AU, AU/Cy     rad, rad/Cy     deg, deg/Cy      deg, deg/Cy      deg, deg/Cy     deg, deg/Cy
-----------------------------------------------------------------------------------------------------------
Mercury   0.38709927      0.20563593      7.00497902      252.25032350     77.45779628     48.33076593
          0.00000037      0.00001906     -0.00594749   149472.67411175      0.16047689     -0.12534081
Venus     0.72333566      0.00677672      3.39467605      181.97909950    131.60246718     76.67984255
          0.00000390     -0.00004107     -0.00078890    58517.81538729      0.00268329     -0.27769418
EM Bary   1.00000261      0.01671123     -0.00001531      100.46457166    102.93768193      0.0
          0.00000562     -0.00004392     -0.01294668    35999.37244981      0.32327364      0.0
Mars      1.52371034      0.09339410      1.84969142       -4.55343205    -23.94362959     49.55953891
          0.00001847      0.00007882     -0.00813131    19140.30268499      0.44441088     -0.29257343
Jupiter   5.20288700      0.04838624      1.30439695       34.39644051     14.72847983    100.47390909
         -0.00011607     -0.00013253     -0.00183714     3034.74612775      0.21252668      0.20469106
Saturn    9.53667594      0.05386179      2.48599187       49.95424423     92.59887831    113.66242448
         -0.00125060     -0.00050991      0.00193609     1222.49362201     -0.41897216     -0.28867794
Uranus   19.18916464      0.04725744      0.77263783      313.23810451    170.95427630     74.01692503
         -0.00196176     -0.00004397     -0.00242939      428.48202785      0.40805281      0.04240589
Neptune  30.06992276      0.00859048      1.77004347      -55.12002969     44.96476227    131.78422574
          0.00026291      0.00005105      0.00035372      218.45945325     -0.32241464     -0.00508664
Pluto    39.48211675      0.24882730     17.14001206      238.92903833    224.06891629    110.30393684
         -0.00031596      0.00005170      0.00004818      145.20780515     -0.04062942     -0.01183482

> **Comments:**
> **username_5**: Those elements tables are on https://ssd.jpl.nasa.gov/planets/approx_pos.html There's all sorts of goodies on the SSD FTP browser, which has an HTML portal: https://ssd.jpl.nasa.gov/ftp/  

---

