<p>The last perihelion passage of the Neptune system barycentre relative to the Solar System barycentre (SSB) was at 1881-Feb-02 10:00 TDB.</p>
<p>Here's a plot (courtesy of JPL <a href="https://ssd.jpl.nasa.gov/horizons/" rel="nofollow noreferrer">Horizons</a>) of the distance from the Neptune barycentre to the Sun and to Solar System barycentre for a couple of decades around that date. The vertical axis is the distance in billions of kilometres.</p>
<p>From: 2405159.5 A.D. 1873-Jan-01 00:00:00.0<br />
To: 2411368.5 A.D. 1890-Jan-01 00:00:00.0
<a href="https://i.sstatic.net/wjSXY.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/wjSXY.png" alt="Neptune distance to Sun &amp; SSB" /></a></p>
<p>As you can see, relative to the Sun, there was actually a local <em>maximum</em> distance near that date, around 6 years after Neptune's closest distance to the Sun, and another local minimum around 5 years after that. The distance to the SSB behaves more like we expect from a nice elliptical orbit.</p>
<p>I created that plot using my script <a href="https://space.stackexchange.com/a/58339/38535">here</a>.</p>
<p>Zooming in,<br />
From: 2408113.5 A.D. 1881-Feb-02 00:00:00.0<br />
To: 2408114.5 A.D. 1881-Feb-03 00:00:00.0</p>
<p><a href="https://i.sstatic.net/ZOlw3.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ZOlw3.png" alt="Neptune periapsis" /></a></p>
<p>That's a plot for the distance from the Neptune barycentre to the SSB. If you want to search for the closest distance for the Neptune body centre, you can use <a href="https://sagecell.sagemath.org/?z=eJyVWHtv4kgS_59P0ePMHXbGcYDsrGY5oVuSONrsJgEBM6s5wlkNNODEr3O3CUyU735V1baxmdmTDonYXV1dXY9fPYhhGGwkVOqLrWApj9aCLbnibJXGIfstTv1vcSTZKk4ZZ4qna6HYPF7uGww-PFrCl8VzKdKtH63ZQkRKpERPglgxXzkN4vwz9ZUSEZvv2fCedUbI3Gl12k7rF6f9C7F8TuBesURyx2l9dFo_NQzDaDT8MIlTxVJhw_c_mZBKNki5VRYtVBwHkuUsQZp5C77YCL0fcoVKBP7cUf7iGfTK-cYLHvD0Jk6BA9RtNFbFK-sdb5qZFIPVSgrVu-GBFFajkaUB8BkbpRLZPT-Xcuk8JYETccmddbw954l_vskd5638QDhAMRrwx9uKVPpxhMfBdDBuzqXwFuESKWDsff8P13OHv7n3QGh-dcfNBq28ydehi6Qv7tVkMALy4PPE-_xwOxkj9Y_7s-tmY-TeeMO7_gMxuld3t8PJ7ZUmj7-OJ1rm7dXoptkAMd7VYDRCysPgwdWUu_6lezfWNE25du8mfW9SkK7GX7ybwei-PynVG1z-7l33J_3qqUn_8o6U-LmpQ_hrGRkz5DvpfxM9P1LmhWU1lmLFVkItNh6iztQIs3Mg2UwCQeEjTvCvSKwugUW7bIXS371_Px7cNF4LV741rgb39_2Ha9TgVQt8A93dh4lLBr9q4UAbT_qjiTe5vSdtX-kyIg-GVWqcENEdeuPbfxVEgUS424W7UQ3U6iRJ0S5QwqI14BW4C9Q6SSyVCeixKcN6r02Nu2aXNZXYqeabzRAuEnb8KMlww2yCsKaN9lpvWugBQ6lwpODpYmOmRn94y764o_Ht4KH7KE_Nx_GpZVDGOCjbctZpnCVmW8vwV6WYdz1WQab2Ln60KSvjT55GkK1dhjcUh3zJXvN3UHqeKaY2QJOL1E8U7mK9eK3IfTMsXQjCI73Nf0rr8f0jhNA1nVN6dQduVfNC4RDlPsSRONbReBgwyhJ3dDs2rKPduhwdFZWlEYkiWuBHQuo4Eacjk8BXRDX1qfyex8hwnmI_Mmlv-rHb_nlm5XZRzeyxsPTztN2d0U5eNI_NDq1_Tw7llEU8FBQ45_TR-h-RyyvsD6Rd6Z3_S1ruClTeZvXcg6z18ckXipI05GC4ZukZn4yCrWf82jJsEEbJ0zPanz61z27E_Kxj6LStkC4MncNA2tAZLPhE-Alu90NA_iTNoM4vY1W8LrJ0K4r3OIjhwnUqRKTvxEryyWYv_lJtem2Qvl3rMm0znqnYy6in5JW7WyApgs5k4h0MUEoXWN9haiwCsVCMQ1cRXCoGYGHxitVOGceYauROlVmAAf-urjkS-mxiWoXzynUuh3x4YEL3VVeiXJVJkd_1l5kRM5FsRChS4NBtPc6i5bu_0LyKAw8xVChKCwIdXlcFPD6-T5h8cyr1ltm0m9a0e9aeUWGAhq0xpxPkhIhp_FKQu0Xqxi_WP2oKnrAh7mhHsb-Th9jvWeBzPLmXQCJMVbP2BmaBLiDvFEVPW7NptzOrpfUk7jJWMoCSmkMnrwdFG4oYdvzprLCNykW-RN19u1BfRBk4GzhMFFaB1QlzdwqTicF8IaIlT0lQuQ9UXKOP4xfoFJSiPzh9MNaGwrXeqDNMHFtPbvnjLK1KflrazIMdSCusG9NVEHNlSusQCrhxVrKXFsPUkoCipokC6LRV0-iePwudtYqHiSx3AJU--1uZ26zXY62DH_CzD0HiJkQn5mbnMMGieTGr89oshLuBFU7lbMZZBb-kM4pasg_QIz6w_bTTrcsAjUjPuhb5wQ8weUFhh4OgUXGBA3CAEt6qyyGTam5Rsqz_ABEMeYHTy8wPluxSfPNFXi20h1SyBV19nCxLT2tjVMtme_huW8AQQa02gTcv-nT-gDkEGyxMfcTSRJ4KzLlWiUoo5eC9LUYYJB2MX2JtUuwMbjzQduhBxc7ZxYGG2kAz6aFKp8CCwuhZwyWiMrcTVSj3SB_wrrlvYVTga4JEuHa5t-CejoWy8MZOFTpkaj1QmBDgDnQ6mgyCUBWSCgKhMppoDNG0dKTAwprVUaK9WMQPi8vxNQcPfxeQ3JlFeO8FJqEP0I8Wgs2FeoGeBEOQwP7rF7EOYjxZhBlrT44omJZqO1h08q0QJfe0987BEOA8Q0nVkrUy6vf32Cse6zoXqzf2HBaz1gkbU51EtdYpTzbQKNWGlmHtPJZuOjEEUbhARwexTWzkzo2fL2ZFG6a_th6e1D4QPaObZ-UQo47DhklqGrXzR8fz30mKBx6HchaF0G56RiBWqjDi-QXaEeW3v1BmHhwF7Ub0VsZ1YQH94HutNKs3pmL2Wmllb496ZsDPOvWXpHhvOs3A8ZQuWd5-hAQbjZA_xakxw7lk8eyVPxB7ndNpuZgV8vhOSC_gcxGARONQosF04zlkKKbC4tHY0nbaH3HeX9MK_-TeczyBtd57fllKRw8wpnZC7hFfjyGHJCGHJzCYKmmCPdC9DgaVGAMd6KaPtQiUg8RR3pHIOWW1l3C1MXXyHJ3NUdZfLittdx_6ESQL_NCDoA0dXOL4gm98V8w6eyrowAJVgZ5ndA5rQgt-_Jc1DIssFP4yNEcaEsqonVA5xtRfAZrIUEOGPAgMu5Lk-QA5D_jiGWIDv00gunXoaQgZFdueMhj_uExwHITG6se0syMrd6C6fWzxrrR4py3-gRd0xdZCoUTutAt25ILzuktyVEjAsT7gkRZmy_kE3splnOsZOFdbbuIXc1jGFqbiit8cybfCbBb_oXBgt2n9F8h6RoU=&amp;lang=sage" rel="nofollow noreferrer">this script</a>, setting <code>899</code> as the target. If you want the distance to the Sun, use <code>@10</code> as the  centre. There are brief instructions on using the script <a href="https://space.stackexchange.com/a/55061/38535">here</a>.</p>
<hr />
<p>Here's a <a href="https://ssd.jpl.nasa.gov/api/horizons.api?format=text&amp;MAKE_EPHEM=YES&amp;EPHEM_TYPE=VECTORS&amp;OUT_UNITS=KM-D&amp;REF_PLANE=ECLIPTIC&amp;REF_SYSTEM=ICRF&amp;VEC_CORR=NONE&amp;VEC_LABELS=NO&amp;VEC_DELTA_T=NO&amp;CSV_FORMAT=YES&amp;OBJ_DATA=NO&amp;VEC_TABLE=6&amp;COMMAND=8&amp;CENTER=%400&amp;START_TIME=1881-Feb-2&amp;STOP_TIME=1881-Feb-3&amp;STEP_SIZE=1h" rel="nofollow noreferrer">link</a> for the Horizons data used for the last plot. And here's the raw data:</p>
<pre><code>*******************************************************************************
Ephemeris / API_USER Tue May  3 10:47:05 2022 Pasadena, USA      / Horizons
*******************************************************************************
Target body name: Neptune Barycenter (8)          {source: DE441}
Center body name: Solar System Barycenter (0)     {source: DE441}
Center-site name: BODY CENTER
*******************************************************************************
Start time      : A.D. 1881-Feb-02 00:00:00.0000 TDB
Stop  time      : A.D. 1881-Feb-03 00:00:00.0000 TDB
Step-size       : 60 minutes
*******************************************************************************
Center geodetic : 0.00000000,0.00000000,0.0000000 {E-lon(deg),Lat(deg),Alt(km)}
Center cylindric: 0.00000000,0.00000000,0.0000000 {E-lon(deg),Dxy(km),Dz(km)}
Center radii    : (undefined)
Output units    : KM-D
Output type     : GEOMETRIC cartesian states
Output format   : 6 (LT, range, and range-rate)
Reference frame : Ecliptic of J2000.0
*******************************************************************************
            JDTDB,            Calendar Date (TDB),                     LT,                     RG,                     RR,
**************************************************************************************************************************
<span class="math-container">$$SOE
2408113.500000000, A.D. 1881-Feb-02 00:00:00.0000,  1.721841396032804E-01,  4.459925356440414E+09, -1.775610666244478E-01,
2408113.541666667, A.D. 1881-Feb-02 01:00:00.0000,  1.721841396030089E-01,  4.459925356433380E+09, -1.600932159790273E-01,
2408113.583333333, A.D. 1881-Feb-02 02:00:00.0000,  1.721841396027653E-01,  4.459925356427073E+09, -1.426253883932667E-01,
2408113.625000000, A.D. 1881-Feb-02 03:00:00.0000,  1.721841396025500E-01,  4.459925356421494E+09, -1.251575835878349E-01,
2408113.666666667, A.D. 1881-Feb-02 04:00:00.0000,  1.721841396023627E-01,  4.459925356416644E+09, -1.076898016158184E-01,
2408113.708333333, A.D. 1881-Feb-02 05:00:00.0000,  1.721841396022035E-01,  4.459925356412521E+09, -9.022204256409987E-02,
2408113.750000000, A.D. 1881-Feb-02 06:00:00.0000,  1.721841396020724E-01,  4.459925356409125E+09, -7.275430640336375E-02,
2408113.791666667, A.D. 1881-Feb-02 07:00:00.0000,  1.721841396019694E-01,  4.459925356406457E+09, -5.528659310734295E-02,
2408113.833333333, A.D. 1881-Feb-02 08:00:00.0000,  1.721841396018945E-01,  4.459925356404518E+09, -3.781890258825515E-02,
2408113.875000000, A.D. 1881-Feb-02 09:00:00.0000,  1.721841396018478E-01,  4.459925356403306E+09, -2.035123490434648E-02,
2408113.916666667, A.D. 1881-Feb-02 10:00:00.0000,  1.721841396018291E-01,  4.459925356402822E+09, -2.883590222513597E-03,
2408113.958333333, A.D. 1881-Feb-02 11:00:00.0000,  1.721841396018385E-01,  4.459925356403066E+09,  1.458403165229071E-02,
2408114.000000000, A.D. 1881-Feb-02 12:00:00.0000,  1.721841396018760E-01,  4.459925356404037E+09,  3.205163069338877E-02,
2408114.041666667, A.D. 1881-Feb-02 13:00:00.0000,  1.721841396019416E-01,  4.459925356405737E+09,  4.951920692708190E-02,
2408114.083333333, A.D. 1881-Feb-02 14:00:00.0000,  1.721841396020353E-01,  4.459925356408164E+09,  6.698676024561424E-02,
2408114.125000000, A.D. 1881-Feb-02 15:00:00.0000,  1.721841396021571E-01,  4.459925356411319E+09,  8.445429075517470E-02,
2408114.166666667, A.D. 1881-Feb-02 16:00:00.0000,  1.721841396023070E-01,  4.459925356415202E+09,  1.019217984320074E-01,
2408114.208333333, A.D. 1881-Feb-02 17:00:00.0000,  1.721841396024850E-01,  4.459925356419812E+09,  1.193892832482304E-01,
2408114.250000000, A.D. 1881-Feb-02 18:00:00.0000,  1.721841396026911E-01,  4.459925356425151E+09,  1.368567452307574E-01,
2408114.291666667, A.D. 1881-Feb-02 19:00:00.0000,  1.721841396029253E-01,  4.459925356431218E+09,  1.543241844351693E-01,
2408114.333333333, A.D. 1881-Feb-02 20:00:00.0000,  1.721841396031876E-01,  4.459925356438011E+09,  1.717916007232026E-01,
2408114.375000000, A.D. 1881-Feb-02 21:00:00.0000,  1.721841396034780E-01,  4.459925356445534E+09,  1.892589943495820E-01,
2408114.416666667, A.D. 1881-Feb-02 22:00:00.0000,  1.721841396037965E-01,  4.459925356453783E+09,  2.067263649984577E-01,
2408114.458333333, A.D. 1881-Feb-02 23:00:00.0000,  1.721841396041431E-01,  4.459925356462761E+09,  2.241937128177309E-01,
2408114.500000000, A.D. 1881-Feb-03 00:00:00.0000,  1.721841396045178E-01,  4.459925356472466E+09,  2.416610378027369E-01,
$$</span>EOE
**************************************************************************************************************************

TIME

  Barycentric Dynamical Time (&quot;TDB&quot; or T_eph) output was requested. This
continuous relativistic coordinate time is equivalent to the relativistic
proper time of a clock at rest in a reference frame comoving with the
solar system barycenter but outside the system's gravity well. It is the
independent variable in the solar system relativistic equations of motion.

  TDB runs at a uniform rate of one SI second per second and is independent
of irregularities in Earth's rotation.

  Calendar dates prior to 1582-Oct-15 are in the Julian calendar system.
Later calendar dates are in the Gregorian system.

REFERENCE FRAME AND COORDINATES

  Ecliptic at the standard reference epoch

    Reference epoch: J2000.0
    X-Y plane: adopted Earth orbital plane at the reference epoch
               Note: IAU76 obliquity of 84381.448 arcseconds wrt ICRF X-Y plane
    X-axis   : ICRF
    Z-axis   : perpendicular to the X-Y plane in the directional (+ or -) sense
               of Earth's north pole at the reference epoch.

  Symbol meaning [1 day=86400.0 s]:

    JDTDB    Julian Day Number, Barycentric Dynamical Time
      LT     One-way down-leg Newtonian light-time (day)
      RG     Range; distance from coordinate center (km)
      RR     Range-rate; radial velocity wrt coord. center (km/day)

ABERRATIONS AND CORRECTIONS

 Geometric state vectors have NO corrections or aberrations applied.

Computations by ...

    Solar System Dynamics Group, Horizons On-Line Ephemeris System
    4800 Oak Grove Drive, Jet Propulsion Laboratory
    Pasadena, CA  91109   USA

    General site: https://ssd.jpl.nasa.gov/
    Mailing list: https://ssd.jpl.nasa.gov/email_list.html
    System news : https://ssd.jpl.nasa.gov/horizons/news.html
    User Guide  : https://ssd.jpl.nasa.gov/horizons/manual.html
    Connect     : browser        https://ssd.jpl.nasa.gov/horizons/app.html#/x
                  API            https://ssd-api.jpl.nasa.gov/doc/horizons.html
                  command-line   telnet ssd.jpl.nasa.gov 6775
                  e-mail/batch   https://ssd.jpl.nasa.gov/ftp/ssd/hrzn_batch.txt
                  scripts        https://ssd.jpl.nasa.gov/ftp/ssd/SCRIPTS
    Author      : Jon.D.Giorgini@jpl.nasa.gov
*******************************************************************************
</code></pre>
<hr />
<p>As Barry Carter mentions in a comment, the orbit of Neptune is nearly circular. Its mean eccentricity is ~0.009, a little over half that of Earth's orbit. So perturbations by the other giant planets (on Neptune and on the Sun) can have a significant effect on the time and position of perihelion and aphelion. And that can have <a href="https://astronomy.stackexchange.com/questions/28691/why-is-neptune-true-anomaly-decreasing/28704#28704">interesting effects on Neptune's mean and true anomaly</a> (which are measured from the perihelion).</p>
<p>Although real orbits aren't perfect ellipses, it can be useful to treat orbital motion as an ideal Keplerian orbit that changes over time. This is known as the <a href="https://en.wikipedia.org/wiki/Osculating_orbit" rel="nofollow noreferrer">osculating orbit</a></p>
<blockquote>
<p>the osculating orbit of an object in space at a given moment in time is the gravitational Kepler orbit (i.e. an elliptic or other conic one) that it would have around its central body if perturbations were absent. That is, it is the orbit that coincides with the current orbital state vectors (position and velocity).</p>
</blockquote>
<p>Horizons can produce ephemerides of osculating orbit elements. Here's a plot of the eccentricity of the Neptune barycentre, relative to the Sun, for (roughly) one orbital period, with a step size of 2 calendar months. As you can see, it varies quite a bit, and gets extremely low at times.</p>
<p>From: 2397854.5 A.D. 1853-Jan-01 00:00:00.0<br />
To: 2458849.5 A.D. 2020-Jan-01 00:00:00.0</p>
<p><a href="https://i.sstatic.net/DjAJH.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/DjAJH.png" alt="Neptune eccentricity" /></a></p>

CC BY-SA 4.0
2022-05-03T20:12:55.353Z
Thanks you so much ! Your work is awesome. I'm grateful to you that you have spend time on my question. This was exactly the answer I was needing.
LittleCoder
CC BY-SA 4.0
2022-05-04T18:49:17.343Z
@LittleCoder No worries. With a bit more zooming in, it looks like the perihelion is around 1881-Feb-02 10:10 TDB. But the data starts to get "blocky", and my plotting script behaves oddly if I zoom in too much.
PM 2Ring
CC BY-SA 4.0
2022-05-05T13:47:42.177Z
Just to add a reference, Neptune's orbit is nearly circular: https://astronomy.stackexchange.com/questions/28691/why-is-neptune-true-anomaly-decreasing/28704#28704 -- upvote for using the HTTP GET protocol with HORIZONS, a cool sneaky backdoor trick :) And, just to beat this to death, you can use https://wgc.jpl.nasa.gov:8443/webgeocalc/#NewCalculation to find the "exact" times of periapsis and apoapsis
Barry Carter
CC BY-SA 4.0
2022-05-05T18:14:35.930Z
Thanks, @barry I should mention the difficulties associated with Neptune's low eccentricity to my answer. WebGeoCalc looks interesting! Using GET with Horizons is well-documented: https://ssd-api.jpl.nasa.gov/doc/horizons.html but annoyingly, some of the query parameters that work in batch files (and which the Horizons Web interface prints) *don't* work in GET query strings, you have to use the newer synonyms.
PM 2Ring
CC BY-SA 4.0
2022-05-05T20:17:18.700Z
@LittleCoder I've updated my answer with some info you may find useful.
PM 2Ring
CC BY-SA 4.0
2022-05-05T21:29:44.780Z
Yes, thanks you so much for your details. And thanks you also for editing my question, on my French keyboard I didn't saw my typo.
LittleCoder
CC BY-SA 4.0
2022-05-07T01:26:09.327Z
@LittleCoder Using WebGeocalc, the time of perihelion (of the Neptune barycentre) is 1881-02-02 10:09:54.295 TDB = 10:09:13.110 UTC. Good luck with your simulator! It's probably a good idea to learn a bit about Horizons (or WebGeocalc), so you can use it to check the accuracy of your sim's calculations. FWIW, Jean Chapront, Michelle Chapront-Touzé, et al, used the JPL DE to develop the [Éphéméride Lunaire Parisienne](https://en.wikipedia.org/wiki/Ephemeride_Lunaire_Parisienne).
PM 2Ring
CC BY-SA 4.0
2022-05-03T17:09:04.547Z
2022-05-05T20:16:27.367Z
2022-05-05T20:16:27.367Z
PM 2Ring
<p>I'm working with a group of colleagues on a <a href="https://github.com/PaulJeFi/solar-system" rel="nofollow noreferrer">Solar System simulator</a>. We need two items of data that are missing to us:
the nearest dates of passage of Neptune at Aphelion and Perihelion.</p>

CC BY-SA 4.0
2022-05-03T14:51:07.597Z
You can get that from JPL [Horizons](https://ssd.jpl.nasa.gov/horizons/). Also see [Approximate Positions of the Planets](https://ssd.jpl.nasa.gov/planets/approx_pos.html) & [Frequently Asked Questions (FAQs)](https://ssd.jpl.nasa.gov/faq.html)
PM 2Ring
CC BY-SA 4.0
2022-05-03T14:55:49.467Z
Thanks, but where can I find the right information on the website ?
LittleCoder
<neptune>
Dates of Passage of Neptune at Aphelion and Perihelion
LittleCoder
# Dates of Passage of Neptune at Aphelion and Perihelion

(Asked by: username_0 on 2022-05-03)

I'm working with a group of colleagues on a [Solar System simulator](https://github.com/PaulJeFi/solar-system). We need two items of data that are missing to us:
the nearest dates of passage of Neptune at Aphelion and Perihelion.

**Tags:** neptune
> **Comments:**
> **username_1**: You can get that from JPL [Horizons](https://ssd.jpl.nasa.gov/horizons/). Also see [Approximate Positions of the Planets](https://ssd.jpl.nasa.gov/planets/approx_pos.html) & [Frequently Asked Questions (FAQs)](https://ssd.jpl.nasa.gov/faq.html)  
> **username_0**: Thanks, but where can I find the right information on the website ?  

---

## 1 answers

### Answer by username_1 on 2022-05-03. Score: 5 | Accepted answer

The last perihelion passage of the Neptune system barycentre relative to the Solar System barycentre (SSB) was at 1881-Feb-02 10:00 TDB.
Here's a plot (courtesy of JPL Horizons) of the distance from the Neptune barycentre to the Sun and to Solar System barycentre for a couple of decades around that date. The vertical axis is the distance in billions of kilometres.
From: 2405159.5 A.D. 1873-Jan-01 00:00:00.0
To: 2411368.5 A.D. 1890-Jan-01 00:00:00.0

As you can see, relative to the Sun, there was actually a local maximum distance near that date, around 6 years after Neptune's closest distance to the Sun, and another local minimum around 5 years after that. The distance to the SSB behaves more like we expect from a nice elliptical orbit.
I created that plot using my script here.
Zooming in,
From: 2408113.5 A.D. 1881-Feb-02 00:00:00.0
To: 2408114.5 A.D. 1881-Feb-03 00:00:00.0

That's a plot for the distance from the Neptune barycentre to the SSB. If you want to search for the closest distance for the Neptune body centre, you can use this script, setting 899 as the target. If you want the distance to the Sun, use @10 as the  centre. There are brief instructions on using the script here.

Here's a link for the Horizons data used for the last plot. And here's the raw data:
*******************************************************************************
Ephemeris / API_USER Tue May  3 10:47:05 2022 Pasadena, USA      / Horizons
*******************************************************************************
Target body name: Neptune Barycenter (8)          {source: DE441}
Center body name: Solar System Barycenter (0)     {source: DE441}
Center-site name: BODY CENTER
*******************************************************************************
Start time      : A.D. 1881-Feb-02 00:00:00.0000 TDB
Stop  time      : A.D. 1881-Feb-03 00:00:00.0000 TDB
Step-size       : 60 minutes
*******************************************************************************
Center geodetic : 0.00000000,0.00000000,0.0000000 {E-lon(deg),Lat(deg),Alt(km)}
Center cylindric: 0.00000000,0.00000000,0.0000000 {E-lon(deg),Dxy(km),Dz(km)}
Center radii    : (undefined)
Output units    : KM-D
Output type     : GEOMETRIC cartesian states
Output format   : 6 (LT, range, and range-rate)
Reference frame : Ecliptic of J2000.0
*******************************************************************************
            JDTDB,            Calendar Date (TDB),                     LT,                     RG,                     RR,
**************************************************************************************************************************
$$SOE
2408113.500000000, A.D. 1881-Feb-02 00:00:00.0000,  1.721841396032804E-01,  4.459925356440414E+09, -1.775610666244478E-01,
2408113.541666667, A.D. 1881-Feb-02 01:00:00.0000,  1.721841396030089E-01,  4.459925356433380E+09, -1.600932159790273E-01,
2408113.583333333, A.D. 1881-Feb-02 02:00:00.0000,  1.721841396027653E-01,  4.459925356427073E+09, -1.426253883932667E-01,
2408113.625000000, A.D. 1881-Feb-02 03:00:00.0000,  1.721841396025500E-01,  4.459925356421494E+09, -1.251575835878349E-01,
2408113.666666667, A.D. 1881-Feb-02 04:00:00.0000,  1.721841396023627E-01,  4.459925356416644E+09, -1.076898016158184E-01,
2408113.708333333, A.D. 1881-Feb-02 05:00:00.0000,  1.721841396022035E-01,  4.459925356412521E+09, -9.022204256409987E-02,
2408113.750000000, A.D. 1881-Feb-02 06:00:00.0000,  1.721841396020724E-01,  4.459925356409125E+09, -7.275430640336375E-02,
2408113.791666667, A.D. 1881-Feb-02 07:00:00.0000,  1.721841396019694E-01,  4.459925356406457E+09, -5.528659310734295E-02,
2408113.833333333, A.D. 1881-Feb-02 08:00:00.0000,  1.721841396018945E-01,  4.459925356404518E+09, -3.781890258825515E-02,
2408113.875000000, A.D. 1881-Feb-02 09:00:00.0000,  1.721841396018478E-01,  4.459925356403306E+09, -2.035123490434648E-02,
2408113.916666667, A.D. 1881-Feb-02 10:00:00.0000,  1.721841396018291E-01,  4.459925356402822E+09, -2.883590222513597E-03,
2408113.958333333, A.D. 1881-Feb-02 11:00:00.0000,  1.721841396018385E-01,  4.459925356403066E+09,  1.458403165229071E-02,
2408114.000000000, A.D. 1881-Feb-02 12:00:00.0000,  1.721841396018760E-01,  4.459925356404037E+09,  3.205163069338877E-02,
2408114.041666667, A.D. 1881-Feb-02 13:00:00.0000,  1.721841396019416E-01,  4.459925356405737E+09,  4.951920692708190E-02,
2408114.083333333, A.D. 1881-Feb-02 14:00:00.0000,  1.721841396020353E-01,  4.459925356408164E+09,  6.698676024561424E-02,
2408114.125000000, A.D. 1881-Feb-02 15:00:00.0000,  1.721841396021571E-01,  4.459925356411319E+09,  8.445429075517470E-02,
2408114.166666667, A.D. 1881-Feb-02 16:00:00.0000,  1.721841396023070E-01,  4.459925356415202E+09,  1.019217984320074E-01,
2408114.208333333, A.D. 1881-Feb-02 17:00:00.0000,  1.721841396024850E-01,  4.459925356419812E+09,  1.193892832482304E-01,
2408114.250000000, A.D. 1881-Feb-02 18:00:00.0000,  1.721841396026911E-01,  4.459925356425151E+09,  1.368567452307574E-01,
2408114.291666667, A.D. 1881-Feb-02 19:00:00.0000,  1.721841396029253E-01,  4.459925356431218E+09,  1.543241844351693E-01,
2408114.333333333, A.D. 1881-Feb-02 20:00:00.0000,  1.721841396031876E-01,  4.459925356438011E+09,  1.717916007232026E-01,
2408114.375000000, A.D. 1881-Feb-02 21:00:00.0000,  1.721841396034780E-01,  4.459925356445534E+09,  1.892589943495820E-01,
2408114.416666667, A.D. 1881-Feb-02 22:00:00.0000,  1.721841396037965E-01,  4.459925356453783E+09,  2.067263649984577E-01,
2408114.458333333, A.D. 1881-Feb-02 23:00:00.0000,  1.721841396041431E-01,  4.459925356462761E+09,  2.241937128177309E-01,
2408114.500000000, A.D. 1881-Feb-03 00:00:00.0000,  1.721841396045178E-01,  4.459925356472466E+09,  2.416610378027369E-01,
$$EOE
**************************************************************************************************************************

TIME

  Barycentric Dynamical Time ("TDB" or T_eph) output was requested. This
continuous relativistic coordinate time is equivalent to the relativistic
proper time of a clock at rest in a reference frame comoving with the
solar system barycenter but outside the system's gravity well. It is the
independent variable in the solar system relativistic equations of motion.

  TDB runs at a uniform rate of one SI second per second and is independent
of irregularities in Earth's rotation.

  Calendar dates prior to 1582-Oct-15 are in the Julian calendar system.
Later calendar dates are in the Gregorian system.

REFERENCE FRAME AND COORDINATES

  Ecliptic at the standard reference epoch

    Reference epoch: J2000.0
    X-Y plane: adopted Earth orbital plane at the reference epoch
               Note: IAU76 obliquity of 84381.448 arcseconds wrt ICRF X-Y plane
    X-axis   : ICRF
    Z-axis   : perpendicular to the X-Y plane in the directional (+ or -) sense
               of Earth's north pole at the reference epoch.

  Symbol meaning [1 day=86400.0 s]:

    JDTDB    Julian Day Number, Barycentric Dynamical Time
      LT     One-way down-leg Newtonian light-time (day)
      RG     Range; distance from coordinate center (km)
      RR     Range-rate; radial velocity wrt coord. center (km/day)

ABERRATIONS AND CORRECTIONS

 Geometric state vectors have NO corrections or aberrations applied.

Computations by ...

    Solar System Dynamics Group, Horizons On-Line Ephemeris System
    4800 Oak Grove Drive, Jet Propulsion Laboratory
    Pasadena, CA  91109   USA

    General site: https://ssd.jpl.nasa.gov/
    Mailing list: https://ssd.jpl.nasa.gov/email_list.html
    System news : https://ssd.jpl.nasa.gov/horizons/news.html
    User Guide  : https://ssd.jpl.nasa.gov/horizons/manual.html
    Connect     : browser        https://ssd.jpl.nasa.gov/horizons/app.html#/x
                  API            https://ssd-api.jpl.nasa.gov/doc/horizons.html
                  command-line   telnet ssd.jpl.nasa.gov 6775
                  e-mail/batch   https://ssd.jpl.nasa.gov/ftp/ssd/hrzn_batch.txt
                  scripts        https://ssd.jpl.nasa.gov/ftp/ssd/SCRIPTS
    Author      : Jon.D.Giorgini@jpl.nasa.gov
*******************************************************************************


As Barry Carter mentions in a comment, the orbit of Neptune is nearly circular. Its mean eccentricity is ~0.009, a little over half that of Earth's orbit. So perturbations by the other giant planets (on Neptune and on the Sun) can have a significant effect on the time and position of perihelion and aphelion. And that can have interesting effects on Neptune's mean and true anomaly (which are measured from the perihelion).
Although real orbits aren't perfect ellipses, it can be useful to treat orbital motion as an ideal Keplerian orbit that changes over time. This is known as the osculating orbit

the osculating orbit of an object in space at a given moment in time is the gravitational Kepler orbit (i.e. an elliptic or other conic one) that it would have around its central body if perturbations were absent. That is, it is the orbit that coincides with the current orbital state vectors (position and velocity).

Horizons can produce ephemerides of osculating orbit elements. Here's a plot of the eccentricity of the Neptune barycentre, relative to the Sun, for (roughly) one orbital period, with a step size of 2 calendar months. As you can see, it varies quite a bit, and gets extremely low at times.
From: 2397854.5 A.D. 1853-Jan-01 00:00:00.0
To: 2458849.5 A.D. 2020-Jan-01 00:00:00.0

> **Comments:**
> **username_0**: Thanks you so much ! Your work is awesome. I'm grateful to you that you have spend time on my question. This was exactly the answer I was needing.  
> **username_1**: @LittleCoder No worries. With a bit more zooming in, it looks like the perihelion is around 1881-Feb-02 10:10 TDB. But the data starts to get "blocky", and my plotting script behaves oddly if I zoom in too much.  
> **username_2**: Just to add a reference, Neptune's orbit is nearly circular: https://astronomy.stackexchange.com/questions/28691/why-is-neptune-true-anomaly-decreasing/28704#28704 -- upvote for using the HTTP GET protocol with HORIZONS, a cool sneaky backdoor trick :) And, just to beat this to death, you can use https://wgc.jpl.nasa.gov:8443/webgeocalc/#NewCalculation to find the "exact" times of periapsis and apoapsis  
> **username_1**: Thanks, @barry I should mention the difficulties associated with Neptune's low eccentricity to my answer. WebGeoCalc looks interesting! Using GET with Horizons is well-documented: https://ssd-api.jpl.nasa.gov/doc/horizons.html but annoyingly, some of the query parameters that work in batch files (and which the Horizons Web interface prints) *don't* work in GET query strings, you have to use the newer synonyms.  
> **username_1**: @LittleCoder I've updated my answer with some info you may find useful.  
> **username_0**: Yes, thanks you so much for your details. And thanks you also for editing my question, on my French keyboard I didn't saw my typo.  
> **username_1**: @LittleCoder Using WebGeocalc, the time of perihelion (of the Neptune barycentre) is 1881-02-02 10:09:54.295 TDB = 10:09:13.110 UTC. Good luck with your simulator! It's probably a good idea to learn a bit about Horizons (or WebGeocalc), so you can use it to check the accuracy of your sim's calculations. FWIW, Jean Chapront, Michelle Chapront-Touzé, et al, used the JPL DE to develop the [Éphéméride Lunaire Parisienne](https://en.wikipedia.org/wiki/Ephemeride_Lunaire_Parisienne).  

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