<p>Inspired by this excellent question,I found <a href="https://www.wikiwand.com/en/List_of_Solar_System_objects_by_greatest_aphelion" rel="nofollow noreferrer">this page</a> that describes the issue in some detail for non-specialist readers.  If I'm not botching the explanation, the reason for the difference is that near perihelion when the object has its maximum kinetic energy, its potential energy is typically lower relative to the barycenter of the solar system than to the Sun itself.  The difference is often enough that highly-eccentric closed orbits about the barycenter appear to be hyperbolic with respect to the Sun, so the difference between aphelions in heliocentric and barycentric coordinates can vary by any amount.</p>

CC BY-SA 4.0
2021-12-17T15:43:25.513Z
So which system is typically used before and after perihelion? A lot of comets are said to be hyperbolic but were long-period before perihelion.
WarpPrime
CC BY-SA 4.0
2021-12-17T15:50:20.417Z
@fasterthanlight Neither. The leading ephemerides organizations (JPL in the US, the Institute for Applied Astronomy in Russia, and the IMCCE in France) all calculate their ephemerides by propagating barycentric Cartesian position and velocity. Orbital elements aren't all they are cracked up to be.
David Hammen
CC BY-SA 4.0
2021-12-17T15:51:10.347Z
@fasterthanlight - Planetary perturbations near perihelion will change the aphelion for most highly-eccentric objects, regardless of the coordinates used.
antlersoft
CC BY-SA 4.0
2021-12-17T20:22:29.207Z
Asked https://astronomy.stackexchange.com/q/47836/31410
WarpPrime
CC BY-SA 4.0
2021-12-17T15:36:24.777Z
2021-12-21T06:04:26.593Z
2021-12-21T06:04:26.593Z
antlersoft
<p>If there were no planets, the Sun would remain at the barycenter, and a small body's orbit would be a perfect Keplerian ellipse.
A real trajectory is more complicated.
Osculating orbital elements only describe an ellipse which approximates it for the given epoch and center; they are valid for a few months, not years.
With that limitation in mind, you can use either barycentric or heliocentric elements to make a <em>short</em>-term prediction of its position.
For a long, highly eccentric orbit, elements for an epoch near perihelion are <em>not</em> valid near aphelion.</p>
<p>The Sun's wobble around the barycenter affects other objects' velocities relative to the Sun, leading to significant fluctuations in heliocentric elements when an object is moving slowly.
Far from the Sun, barycentric elements are more stable.
Close to the Sun, heliocentric elements may fit the real trajectory better.</p>
<p>Here is a plot of 2017 MB7's osculating semimajor axis vs. epoch as estimated by JPL HORIZONS.
The barycentric value increases from ~1000 au before 2010 to ~1400 au after 2025 due to a boost from Jupiter.
The short-term fluctuations don't necessarily indicate real changes in aphelion, only different parameters for ellipse segments approximating the object's path.</p>
<p><img src="https://i.sstatic.net/6qsJU.png" alt="Plot of osculating semimajor axis vs. epoch" /></p>

CC BY-SA 4.0
2021-12-24T23:31:45.860Z
Could you explain the (roughly) sinusoidal fluctuations in the barycentric model for the body before and after perihelion?
WarpPrime
CC BY-SA 4.0
2021-12-24T23:53:21.513Z
@fasterthanlight In the blue curve, 2017±2 years? You may get a better sense of that by stepping through the [JPL orbit viewer](https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html#/?sstr=K17M07B&view=VOP).
Mike G
CC BY-SA 4.0
2021-12-25T03:07:05.623Z
I meant to say the heliocentric model, sorry for the inconvenience.
WarpPrime
CC BY-SA 4.0
2021-12-25T03:24:58.940Z
@fasterthanlight The orange curve's smooth ~12-year oscillation outside 2015-2019 is due to Jupiter's effect on the Sun.
Mike G
CC BY-SA 4.0
2021-12-24T22:49:25.310Z
2021-12-24T22:49:25.310Z
Mike G
<p>When talking about celestial bodies orbiting the sun with a decently circular orbit or small aphelion, the heliocentric orbital parameters are almost identical to the barycentric parameters. However, most comet-like (highly eccentric with very large aphelion, but not hyperbolic/parabolic) orbits have vastly different parameters. For instance, according to <a href="https://en.wikipedia.org/wiki/2017_MB7" rel="nofollow noreferrer">Wikipedia,</a> the minor planet <span class="math-container">$2017\ MB_7$</span> has a heliocentric aphelion of <span class="math-container">$\sim 7000-9000 \text{ AU}$</span>, while the barycentric aphelion is only <span class="math-container">$\sim 1800 \text{ AU}$</span>. Why is this happening?</p>

CC BY-SA 4.0
2021-12-16T16:59:55.180Z
quick note: this is the last question asked before graduation (beta logo gone)
WarpPrime
CC BY-SA 4.0
2021-12-16T18:21:36.087Z
Helpful to note that the same article mentions that the barycentric model is based on the long-term change of the solar system barycenter.
WarpPrime
CC BY-SA 4.0
2021-12-17T08:27:23.177Z
This is a prime example of a bad wikipedia page. Lots of broken links, lots of personal research based on a misunderstanding of / misuse of osculating elements, it's poorly written; the list goes on and on and on.
David Hammen
CC BY-SA 4.0
2021-12-17T13:34:40.873Z
@DavidHammen Do you have a possible explanation for the difference in the barycentric and heliocentric modeling?
WarpPrime
CC BY-SA 4.0
2021-12-17T15:30:19.260Z
Using some sort of proper barycentric orbital elements makes sense for objects that always orbit well outside Netptune's orbit -- which 2017 MB7 does not. JPL's Horizon's system uses osculating elements rather than proper elements. That combined with the fact that computing osculating elements from barycentric Cartesian coordinates for objects well inside of Neptune's is more or less garbage in, garbage out. 2017 MB7 was inside Jupiter's orbit at the time of discovery.  Using osculating orbital elements based on barycentric position and velocity results in garbage for such an object.
David Hammen
CC BY-SA 4.0
2021-12-21T16:36:55.460Z
@David, JPL Horizons uses Chebyshev coefficients fitted to an n-body simulation. https://ipnpr.jpl.nasa.gov/progress_report/42-196/196C.pdf
Greg Miller
CC BY-SA 4.0
2021-12-21T16:44:46.823Z
The Wikipedia article doesn't cite a source, and I'm not going to bother actually doing the calculation.  But one likely source of confusion is that Kelperian orbital elements are just approximations.  An n-body simulation is required to account for the fact that the Sun moves relative to the barycenter.
Greg Miller
CC BY-SA 4.0
2021-12-21T17:56:30.477Z
@GregMiller Horizons calculates position and velocity from those Chebyshev coefficients, and then calculates osculating elements from the calculated position and velocity.
David Hammen
<orbit><comets><eccentric-orbit>
What is the difference between barycentric-centered and heliocentric-centered coordinates?
WarpPrime
# What is the difference between barycentric-centered and heliocentric-centered coordinates?

(Asked by: username_0 on 2021-12-16)

When talking about celestial bodies orbiting the sun with a decently circular orbit or small aphelion, the heliocentric orbital parameters are almost identical to the barycentric parameters. However, most comet-like (highly eccentric with very large aphelion, but not hyperbolic/parabolic) orbits have vastly different parameters. For instance, according to [Wikipedia,](https://en.wikipedia.org/wiki/2017_MB7) the minor planet $2017\ MB\_7$ has a heliocentric aphelion of $\sim 7000-9000 \text{ AU}$, while the barycentric aphelion is only $\sim 1800 \text{ AU}$. Why is this happening?

**Tags:** orbit, comets, eccentric-orbit

> **Comments:**
> **username_0**: quick note: this is the last question asked before graduation (beta logo gone)  
> **username_0**: Helpful to note that the same article mentions that the barycentric model is based on the long-term change of the solar system barycenter.  
> **username_1**: This is a prime example of a bad wikipedia page. Lots of broken links, lots of personal research based on a misunderstanding of / misuse of osculating elements, it's poorly written; the list goes on and on and on.  
> **username_0**: @username_1 Do you have a possible explanation for the difference in the barycentric and heliocentric modeling?  
> **username_1**: Using some sort of proper barycentric orbital elements makes sense for objects that always orbit well outside Netptune's orbit -- which 2017 MB7 does not. JPL's Horizon's system uses osculating elements rather than proper elements. That combined with the fact that computing osculating elements from barycentric Cartesian coordinates for objects well inside of Neptune's is more or less garbage in, garbage out. 2017 MB7 was inside Jupiter's orbit at the time of discovery.  Using osculating orbital elements based on barycentric position and velocity results in garbage for such an object.  
> **username_2**: @username_1, JPL Horizons uses Chebyshev coefficients fitted to an n-body simulation. https://ipnpr.jpl.nasa.gov/progress_report/42-196/196C.pdf  
> **username_2**: The Wikipedia article doesn't cite a source, and I'm not going to bother actually doing the calculation.  But one likely source of confusion is that Kelperian orbital elements are just approximations.  An n-body simulation is required to account for the fact that the Sun moves relative to the barycenter.  
> **username_1**: @username_2 Horizons calculates position and velocity from those Chebyshev coefficients, and then calculates osculating elements from the calculated position and velocity.  

---

## 2 answers

### Answer by username_3 on 2021-12-17. Score: 3

Inspired by this excellent question,I found [this page](https://www.wikiwand.com/en/List_of_Solar_System_objects_by_greatest_aphelion) that describes the issue in some detail for non-specialist readers. If I'm not botching the explanation, the reason for the difference is that near perihelion when the object has its maximum kinetic energy, its potential energy is typically lower relative to the barycenter of the solar system than to the Sun itself. The difference is often enough that highly-eccentric closed orbits about the barycenter appear to be hyperbolic with respect to the Sun, so the difference between aphelions in heliocentric and barycentric coordinates can vary by any amount.

> **Comments:**
> **username_0**: So which system is typically used before and after perihelion? A lot of comets are said to be hyperbolic but were long-period before perihelion.  
> **username_1**: @fasterthanlight Neither. The leading ephemerides organizations (JPL in the US, the Institute for Applied Astronomy in Russia, and the IMCCE in France) all calculate their ephemerides by propagating barycentric Cartesian position and velocity. Orbital elements aren't all they are cracked up to be.  
> **username_3**: @fasterthanlight - Planetary perturbations near perihelion will change the aphelion for most highly-eccentric objects, regardless of the coordinates used.  
> **username_0**: Asked https://astronomy.stackexchange.com/q/47836/31410  

---

### Answer by username_4 on 2021-12-24. Score: 1

If there were no planets, the Sun would remain at the barycenter, and a small body's orbit would be a perfect Keplerian ellipse.
A real trajectory is more complicated.
Osculating orbital elements only describe an ellipse which approximates it for the given epoch and center; they are valid for a few months, not years.
With that limitation in mind, you can use either barycentric or heliocentric elements to make a *short*-term prediction of its position.
For a long, highly eccentric orbit, elements for an epoch near perihelion are *not* valid near aphelion.

The Sun's wobble around the barycenter affects other objects' velocities relative to the Sun, leading to significant fluctuations in heliocentric elements when an object is moving slowly.
Far from the Sun, barycentric elements are more stable.
Close to the Sun, heliocentric elements may fit the real trajectory better.

Here is a plot of 2017 MB7's osculating semimajor axis vs. epoch as estimated by JPL HORIZONS.
The barycentric value increases from ~1000 au before 2010 to ~1400 au after 2025 due to a boost from Jupiter.
The short-term fluctuations don't necessarily indicate real changes in aphelion, only different parameters for ellipse segments approximating the object's path.

![Plot of osculating semimajor axis vs. epoch](https://i.sstatic.net/6qsJU.png)

> **Comments:**
> **username_0**: Could you explain the (roughly) sinusoidal fluctuations in the barycentric model for the body before and after perihelion?  
> **username_4**: @fasterthanlight In the blue curve, 2017±2 years? You may get a better sense of that by stepping through the [JPL orbit viewer](https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html#/?sstr=K17M07B&view=VOP).  
> **username_0**: I meant to say the heliocentric model, sorry for the inconvenience.  
> **username_4**: @fasterthanlight The orange curve's smooth ~12-year oscillation outside 2015-2019 is due to Jupiter's effect on the Sun.  

---

