<p>That's Wikipedia for you. The linked page demonstrates that Wikipedia is not a reliable source. Here are some of the problems:</p>
<ul>
<li>The values for aphelion, perihelion, semi-major axis, and eccentricity are inconsistent with one other.</li>
<li>The values for perihelion, semi-major axis, and eccentricity are unsourced.</li>
<li>The values for perihelion, semi-major axis, and eccentricity have far too much precision. Sedna was discovered 17 years ago, corresponding to about 0.15% of Sedna's orbital period. That's far too short of an arc length to justify five or six places of accuracy.</li>
<li>The value for semi-major axis is inconsistent with other sources.</li>
<li>The value for aphelion is poorly conducted original research. Footnote 5 (the reference for the aphelion value) states that the source is from osculating orbital elements about the solar system barycenter as retrieved from JPL Horizons.
There are two key things wrong with this. One is the use of osculating elements, which can be deceiving. The other is using orbital elements about the solar system barycenter rather than about the Sun. This is just wrong.</li>
</ul>

CC BY-SA 4.0
2020-12-31T10:57:47.360Z
Barycentric elements for ETNOs are a thing; see [Becker et al. 2018](https://ui.adsabs.harvard.edu/abs/2018AJ....156...81B/abstract) table 3.
Mike G
CC BY-SA 4.0
2020-12-28T16:39:24.297Z
2020-12-28T16:39:24.297Z
David Hammen
<p>The Wikipedia article version in question took the aphelion and period from barycentric elements generated by JPL HORIZONS, and everything else from heliocentric elements listed in the JPL Small Body Database.
Such mixing is inappropriate; as you noticed, it violates such rules as
<span class="math-container">$$ \frac{q}{1 - e} = \frac{Q}{1 + e} = a $$</span></p>
<p>Then what set of elements should be used?
Different reputable sources give different answers:</p>
<div class="s-table-container">
<table class="s-table">
<thead>
<tr>
<th style="text-align: left;">Source</th>
<th style="text-align: right;">epoch (JD)</th>
<th style="text-align: right;">a (au)</th>
<th style="text-align: right;">e</th>
<th style="text-align: right;">q (au)</th>
<th style="text-align: right;">Q (au)</th>
<th style="text-align: right;">period (yr)</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align: left;">JPL <a href="https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=90377" rel="nofollow noreferrer">SBDB</a></td>
<td style="text-align: right;">2459000.5</td>
<td style="text-align: right;">485</td>
<td style="text-align: right;">0.8426</td>
<td style="text-align: right;">76.26</td>
<td style="text-align: right;">893</td>
<td style="text-align: right;">10700</td>
</tr>
<tr>
<td style="text-align: left;">ESA <a href="https://newton.spacedys.com/astdys/index.php?pc=1.1.1&amp;n=90377" rel="nofollow noreferrer">AstDyS</a></td>
<td style="text-align: right;">2459200.5</td>
<td style="text-align: right;">492</td>
<td style="text-align: right;">0.8448</td>
<td style="text-align: right;">76.30</td>
<td style="text-align: right;">907</td>
<td style="text-align: right;">10900</td>
</tr>
</tbody>
</table>
</div>
<p>Each of these agrees with JPL <a href="https://ssd.jpl.nasa.gov/horizons.cgi?find_body=1&amp;body_group=sb&amp;sstr=90377" rel="nofollow noreferrer">HORIZONS</a> generated heliocentric elements at the same epoch:
<br/>(a=A, e=EC, q=QR, Q=AD, period=PR/365.25)</p>
<pre><code>2459000.500000000 = A.D. 2020-May-31 00:00:00.0000 TDB 
 EC= 8.426174173255342E-01 QR= 7.625935860006692E+01 IN= 1.193068539938317E+01
 OM= 1.442476602118453E+02 W = 3.113484332854660E+02 Tp=  2479370.363763529807
 N = 9.240582598736822E-05 MA= 3.581177059136809E+02 TA= 3.218455376566813E+02
 A = 4.845476373824915E+02 AD= 8.928359161649162E+02 PR= 3.895858255184166E+06
2459200.500000000 = A.D. 2020-Dec-17 00:00:00.0000 TDB 
 EC= 8.447267182563530E-01 QR= 7.630461951406060E+01 IN= 1.193098395982830E+01
 OM= 1.442229068967588E+02 W = 3.112368043377307E+02 Tp=  2479295.935655418318
 N = 9.047381952318225E-05 MA= 3.581818891812720E+02 TA= 3.223092404343984E+02
 A = 4.914214387510542E+02 AD= 9.065382579880477E+02 PR= 3.979051640543999E+06
</code></pre>
<p>The Wikipedia article editors, <a href="https://en.wikipedia.org/wiki/90377_Sedna#cite_note-footnoteG-7" rel="nofollow noreferrer">citing</a> the example of <a href="https://ui.adsabs.harvard.edu/abs/2009ApJ...695..268K/abstract" rel="nofollow noreferrer">Kaib et al. 2009</a> for <a href="https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=308933" rel="nofollow noreferrer">2006 SQ<sub>372</sub></a>, prefer the smaller fluctuations of barycentric elements for long-period objects.
JPL HORIZONS generates these:</p>
<pre><code>2459000.500000000 = A.D. 2020-May-31 00:00:00.0000 TDB 
 EC= 8.495511413376979E-01 QR= 7.619102866448806E+01 IN= 1.192852412826112E+01
 OM= 1.444015111060359E+02 W = 3.112855109740004E+02 Tp=  2479348.034461207222
 N = 8.654118662895153E-05 MA= 3.582391002227536E+02 TA= 3.217633777437514E+02
 A = 5.064247701307355E+02 AD= 9.366585115969829E+02 PR= 4.159869005997260E+06
2459200.500000000 = A.D. 2020-Dec-17 00:00:00.0000 TDB 
 EC= 8.495511411598982E-01 QR= 7.619102949417497E+01 IN= 1.192852416491278E+01
 OM= 1.444015079430050E+02 W = 3.112855120822691E+02 Tp=  2479348.033582778648
 N = 8.654118536876835E-05 MA= 3.582564085614893E+02 TA= 3.220917580263758E+02
 A = 5.064247750469919E+02 AD= 9.366585205998089E+02 PR= 4.159869066571852E+06
</code></pre>
<p>In the same tabular format as above:</p>
<div class="s-table-container">
<table class="s-table">
<thead>
<tr>
<th style="text-align: left;">Source</th>
<th style="text-align: right;">epoch (JD)</th>
<th style="text-align: right;">a (au)</th>
<th style="text-align: right;">e</th>
<th style="text-align: right;">q (au)</th>
<th style="text-align: right;">Q (au)</th>
<th style="text-align: right;">period (yr)</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align: left;">HORIZONS barycentric</td>
<td style="text-align: right;">2459000.5</td>
<td style="text-align: right;">506</td>
<td style="text-align: right;">0.8496</td>
<td style="text-align: right;">76.19</td>
<td style="text-align: right;">937</td>
<td style="text-align: right;">11400</td>
</tr>
</tbody>
</table>
</div>
<p>If you want to plot Sedna's position in planetarium software, you should use heliocentric elements because that's what the software expects.</p>

CC BY-SA 4.0
2020-12-29T19:21:03.897Z
2020-12-31T11:16:46.630Z
2020-12-31T11:16:46.630Z
Mike G
<p><a href="https://en.wikipedia.org/w/index.php?title=90377_Sedna&amp;oldid=995364491" rel="nofollow noreferrer">This article</a> on Wikipedia about Sedna states that its aphelion is 937 AU, its perihelion is 76 AU and its semi-major axis is 484 AU.</p>
<p>I would have expected the SMA to be half of the sum of the aphelion and perihelion. Is the article in error, or is there a difference that I'm not aware of?</p>
<p>I know apoapsis and periapsis are sometimes given relative the surface of the object being orbited, see <a href="https://space.stackexchange.com/questions/21363/relation-between-semi-major-axis-and-radius-of-an-orbit">this thread</a>, but the effect should be negligible in this case and would anyway work in the opposite direction. Anything else I'm not seeing?</p>

CC BY-SA 4.0
2020-12-28T13:02:34.213Z
I think this is just wikipedia being wikipedian and using a mix of sources.  The linked Horizons page https://web.archive.org/web/20121119041320/http://home.surewest.net/kheider/astro/sedna-bc.txt gives  a = 503.5  pr=76 and ar=931,  which are consistent
James K
CC BY-SA 4.0
2020-12-28T13:58:45.343Z
What James said. And maybe someone misread a hand-written 931 as 937.
PM 2Ring
<orbital-mechanics>
Semi-major axis vs. apogee and perigee of orbit
Kristoffer Sjöö
# Semi-major axis vs. apogee and perigee of orbit

(Asked by: username_0 on 2020-12-28)

[This article](https://en.wikipedia.org/w/index.php?title=90377_Sedna&oldid=995364491) on Wikipedia about Sedna states that its aphelion is 937 AU, its perihelion is 76 AU and its semi-major axis is 484 AU.

I would have expected the SMA to be half of the sum of the aphelion and perihelion. Is the article in error, or is there a difference that I'm not aware of?

I know apoapsis and periapsis are sometimes given relative the surface of the object being orbited, see [this thread](https://space.stackexchange.com/questions/21363/relation-between-semi-major-axis-and-radius-of-an-orbit), but the effect should be negligible in this case and would anyway work in the opposite direction. Anything else I'm not seeing?

**Tags:** orbital-mechanics
> **Comments:**
> **username_1**: I think this is just wikipedia being wikipedian and using a mix of sources.  The linked Horizons page https://web.archive.org/web/20121119041320/http://home.surewest.net/kheider/astro/sedna-bc.txt gives  a = 503.5  pr=76 and ar=931,  which are consistent  
> **username_2**: What James said. And maybe someone misread a hand-written 931 as 937.  

---

## 2 answers

### Answer by username_3 on 2020-12-28. Score: 3 | Accepted answer

That's Wikipedia for you. The linked page demonstrates that Wikipedia is not a reliable source. Here are some of the problems:

* The values for aphelion, perihelion, semi-major axis, and eccentricity are inconsistent with one other.
* The values for perihelion, semi-major axis, and eccentricity are unsourced.
* The values for perihelion, semi-major axis, and eccentricity have far too much precision. Sedna was discovered 17 years ago, corresponding to about 0.15% of Sedna's orbital period. That's far too short of an arc length to justify five or six places of accuracy.
* The value for semi-major axis is inconsistent with other sources.
* The value for aphelion is poorly conducted original research. Footnote 5 (the reference for the aphelion value) states that the source is from osculating orbital elements about the solar system barycenter as retrieved from JPL Horizons.
  There are two key things wrong with this. One is the use of osculating elements, which can be deceiving. The other is using orbital elements about the solar system barycenter rather than about the Sun. This is just wrong.

> **Comments:**
> **username_4**: Barycentric elements for ETNOs are a thing; see [Becker et al. 2018](https://ui.adsabs.harvard.edu/abs/2018AJ....156...81B/abstract) table 3.  

---

### Answer by username_4 on 2020-12-29. Score: 3

The Wikipedia article version in question took the aphelion and period from barycentric elements generated by JPL HORIZONS, and everything else from heliocentric elements listed in the JPL Small Body Database.
Such mixing is inappropriate; as you noticed, it violates such rules as
$$ \frac{q}{1 - e} = \frac{Q}{1 + e} = a $$
Then what set of elements should be used?
Different reputable sources give different answers:




Source
epoch (JD)
a (au)
e
q (au)
Q (au)
period (yr)




JPL SBDB
2459000.5
485
0.8426
76.26
893
10700


ESA AstDyS
2459200.5
492
0.8448
76.30
907
10900




Each of these agrees with JPL HORIZONS generated heliocentric elements at the same epoch:
(a=A, e=EC, q=QR, Q=AD, period=PR/365.25)
2459000.500000000 = A.D. 2020-May-31 00:00:00.0000 TDB 
 EC= 8.426174173255342E-01 QR= 7.625935860006692E+01 IN= 1.193068539938317E+01
 OM= 1.442476602118453E+02 W = 3.113484332854660E+02 Tp=  2479370.363763529807
 N = 9.240582598736822E-05 MA= 3.581177059136809E+02 TA= 3.218455376566813E+02
 A = 4.845476373824915E+02 AD= 8.928359161649162E+02 PR= 3.895858255184166E+06
2459200.500000000 = A.D. 2020-Dec-17 00:00:00.0000 TDB 
 EC= 8.447267182563530E-01 QR= 7.630461951406060E+01 IN= 1.193098395982830E+01
 OM= 1.442229068967588E+02 W = 3.112368043377307E+02 Tp=  2479295.935655418318
 N = 9.047381952318225E-05 MA= 3.581818891812720E+02 TA= 3.223092404343984E+02
 A = 4.914214387510542E+02 AD= 9.065382579880477E+02 PR= 3.979051640543999E+06

The Wikipedia article editors, citing the example of Kaib et al. 2009 for 2006 SQ372, prefer the smaller fluctuations of barycentric elements for long-period objects.
JPL HORIZONS generates these:
2459000.500000000 = A.D. 2020-May-31 00:00:00.0000 TDB 
 EC= 8.495511413376979E-01 QR= 7.619102866448806E+01 IN= 1.192852412826112E+01
 OM= 1.444015111060359E+02 W = 3.112855109740004E+02 Tp=  2479348.034461207222
 N = 8.654118662895153E-05 MA= 3.582391002227536E+02 TA= 3.217633777437514E+02
 A = 5.064247701307355E+02 AD= 9.366585115969829E+02 PR= 4.159869005997260E+06
2459200.500000000 = A.D. 2020-Dec-17 00:00:00.0000 TDB 
 EC= 8.495511411598982E-01 QR= 7.619102949417497E+01 IN= 1.192852416491278E+01
 OM= 1.444015079430050E+02 W = 3.112855120822691E+02 Tp=  2479348.033582778648
 N = 8.654118536876835E-05 MA= 3.582564085614893E+02 TA= 3.220917580263758E+02
 A = 5.064247750469919E+02 AD= 9.366585205998089E+02 PR= 4.159869066571852E+06

In the same tabular format as above:




Source
epoch (JD)
a (au)
e
q (au)
Q (au)
period (yr)




HORIZONS barycentric
2459000.5
506
0.8496
76.19
937
11400




If you want to plot Sedna's position in planetarium software, you should use heliocentric elements because that's what the software expects.


---

