<p>The fact is, Sun can't exert any moment about the barycenter unless Sun and its planets may be resting on some solid object which may be physically resting on some fulcrum type of thing. Of course Sun wobbles about SSB but not due to balancing of moments. It wobbles due to a different reason. It occupies a place where the gravitational forces exerted by it on all planets get balanced which gives us an impression that it is revolving about SSB.</p>

CC BY-SA 4.0
2023-02-17T15:19:33.160Z
2023-02-17T15:42:19.347Z
2023-02-17T15:42:19.347Z
S C Sawhney
<p>The solar system barycenter (SSB) is sometimes inside the Sun and sometimes outside.
As an observer outside the solar system could detect with <a href="https://en.wikipedia.org/wiki/Doppler_spectroscopy" rel="noreferrer">Doppler spectroscopy</a>, the Sun is what's wobbling around.</p>
<p>The Sun's offset from the SSB is a vector sum of roughly:</p>
<ul>
<li>0.00496 au ±5% away from Jupiter</li>
<li>0.00272 au ±6% away from Saturn</li>
<li>0.00083 au ±5% away from Uranus</li>
<li>0.00155 au ±1% away from Neptune</li>
</ul>
<p>The other planets contribute much smaller amounts to the total.
Each planet's contribution is proportional to the product of its mass and its orbital distance.</p>
<p>When these components add constructively as in 2020-2023, the center of the Sun can be as far as 2 R<sub>☉</sub> away from the SSB.
When they cancel as in 2029-2030, the center of the Sun is within 0.5 R<sub>☉</sub> of the SSB.
The solar radius R<sub>☉</sub> is 0.00465 au, shown here with a dashed line.</p>
<p><img src="https://i.sstatic.net/M1FEA.png" alt="Plot of Sun-SSB distance vs. time" /></p>

CC BY-SA 4.0
2021-01-18T19:17:37.793Z
Nice graph! Did you create it using JPL *Horizons* data? You can clearly see the ~20 year period of the [Jupiter-Saturn conjunction](https://en.wikipedia.org/wiki/Great_conjunction) cycle. It'd also be interesting to see the corresponding graph of the SSB's (heliocentric) ecliptic latitude. Of course, the 20 year period would be less obvious in the direction graph, but I assume there'd be a ~60 year period (60 ~= 5 Jupiter periods ~= 2 Saturn periods).
PM 2Ring
CC BY-SA 4.0
2021-01-18T19:22:47.727Z
@PM2Ring Almost: I used Skyfield to read JPL DE430.
Mike G
CC BY-SA 4.0
2023-07-05T09:56:51.697Z
@PM2Ring: What there is is rather a 179-year period, which I believe is due to what is called the great inequality of Jupiter and Saturn (which Laplace originally calculated to ~877 years, then to ~924 years, but now would be estimated to around ~895 years if I'm not mistaken (someone correct me if I'm wrong). Here I've used a JPL ephemeris to plot out the Sol-SSB distance in terms of Solar radii from year -2999 to 3000, demonstrating the cyclical nature of it: https://i.postimg.cc/k7sN5n4Z/Figure-1.png
Outis Nemo
CC BY-SA 4.0
2023-07-05T19:15:46.753Z
@Outis The ~179 year period relates to the synodic periods of (Saturn, Uranus, Neptune), relative to Jupiter, which are (19.863261, 13.812176, 12.782075) Julian years, respectively. Multiply those periods by (9, 13, 14) & we get 
(178.769349, 179.558288, 178.949050). We can find longer period solutions using the [LLL algorithm](https://en.wikipedia.org/wiki/Lenstra%E2%80%93Lenstra%E2%80%93Lov%C3%A1sz_lattice_basis_reduction_algorithm). Here's a demo in Sage. Try larger numbers for the `scale`. You can put numeric expressions in the `data` list, and comment out data lines with leading `#`.
PM 2Ring
CC BY-SA 4.0
2023-07-05T19:16:43.353Z
https://sagecell.sagemath.org/?z=eJxlUsFq4zAUvBv8Dw_3UCl1he12k3RBsPRQKKS33tKsEbaSitqSkWS55Ov75JhuYXUa6c3M0-jpCna7HVjZjo1XRqfJGThkWfaWJuUD267vqnWJ8I5ty6rcrBFWbLOtis2vNEFamqTJH6W9tKLxadLKI9Sk5-TaNaKT1zmURUFzaIUX_FkPo380nwRZYuw8P-fwLtXp3fN75IjRm3ockCr5k-icpL_TBHBFMV5qb83EnLdqIBSOxgLuQem5zNzQKd8pLR2hh4ssBBQF2Xhjyd6Jk6xlEB1B1X9yUMd5K3QL2viI98WB8-wqO9CL22AxJVmFkIOTA8_edJaD1O2MVhWNDzF37XOYYuMAK0DcSU1CWExesNALjPBJQo_10GMbiqFE80EuBXaW1pDptkQb-i274fDCXuFmUbNWiZPRmCb09G-F5-XC3Bd5cYj02RpLKyAT3ML99wUdRC8cen2yoieUvf4M6HKIgZbGP57JLcP4R43jGISyk3KyHqyJPyhGpV992qaX&lang=sage
PM 2Ring
CC BY-SA 4.0
2023-07-06T18:31:15.307Z
@PM2Ring: Ah, I see; that's very interesting, thanks. Perhaps I'm misunderstanding what the great inequality is and how it ties into this, then.
Outis Nemo
CC BY-SA 4.0
2023-07-06T20:14:45.180Z
@Outis Laplace's Great Inequality relates to the gravitational interaction between Jupiter & Saturn (and the other planets, especially Uranus & Neptune), so it includes effects due to mass, eccentricity, and inclination. In contrast, my LLL calculation is rather crude, since it's only based on the mean motions. FWIW, there's some info on the great inequality here:  https://astronomy.stackexchange.com/q/48972/16685
PM 2Ring
CC BY-SA 4.0
2021-01-17T03:01:30.003Z
2021-01-17T03:24:34.293Z
2021-01-17T03:24:34.293Z
Mike G
<p>Where is the Solar system's barycenter located?
The solar system as a whole, Where is the center of the mass for the combined mass of the Sun, inner planets, and gas giants, is it inside the Sun? Is there an AU measured distance of it?</p>

CC BY-SA 4.0
2021-01-08T03:51:18.057Z
Not an answer because I don’t have a reference at hand, but I remember a drawing in an astronomical encyclopedia I had as a kid that showed how the barycenter moved from inside to just outside the surface (photosphere?) of the sun in the span of just a few years as the different planets orbited around.
Euro Micelli
CC BY-SA 4.0
2021-01-08T03:58:21.467Z
Bingo! *This* diagram: https://cloud10.todocoleccion.online/libros-segunda-mano-astronomia/tc/2019/03/15/18/155282782_129458382.webp
Euro Micelli
CC BY-SA 4.0
2021-01-08T05:06:18.630Z
My answer here has two diagrams of the Solar System barycentre relative to the Sun, covering the period from 1945 to 2051. https://astronomy.stackexchange.com/a/28036/16685
PM 2Ring
CC BY-SA 4.0
2021-01-08T23:02:01.807Z
Thanks for the response guys. Yes, those diagrams are very good. but they lost me even more, I was looking for a fixed point with AU distance that I can use for calculations. Seems like the center of mass moves very quickly. Unexpected. I was thinking that it must be a very stable point to use as a reference.
Majoris
CC BY-SA 4.0
2021-01-09T11:54:00.390Z
@KapishM Well, we *do* use the Solar System barycentre as a fixed origin, with the Sun moving around it in those funky looking curves. FWIW, the Sun's radius is a little under 1/215 au, so its position deviates from the barycentre by around 1/100 au. Historically, we considered the Sun's position to be fixed, which is kind of equivalent, except that it treats the Sun's rest frame as an inertial frame.
PM 2Ring
CC BY-SA 4.0
2021-01-09T11:58:18.983Z
(cont) The modern approach uses the [ICRF](https://en.wikipedia.org/wiki/International_Celestial_Reference_Frame), which defines the barycenter location via a network of several thousand extragalactic radio sources (mostly quasars). Also check out the [BCRS](https://en.wikipedia.org/wiki/Barycentric_celestial_reference_system), and there's some relevant info at the JPL [Horizons](https://ssd.jpl.nasa.gov/?horizons_doc#frames) site.
PM 2Ring
CC BY-SA 4.0
2021-01-09T21:34:54.990Z
Voting to reopen. OP is asking for quantities, not just a picture.
Mike G
CC BY-SA 4.0
2021-01-13T22:28:05.203Z
Related: [Can the paper narrowing Solar System's barycentre to within 100m help find Planet Nine?](https://astronomy.stackexchange.com/q/36894/34443)
ksousa
CC BY-SA 4.0
2023-02-17T16:29:54.747Z
Also see my later answer, which has graphs (and scripts) which show the Sun - barycentre distance. https://astronomy.stackexchange.com/a/44903/16685
PM 2Ring
<planet><solar-system>
Where is the Solar system's barycenter located?
Majoris
# Where is the Solar system's barycenter located?

(Asked by: username_0 on 2021-01-08)

Where is the Solar system's barycenter located?
The solar system as a whole, Where is the center of the mass for the combined mass of the Sun, inner planets, and gas giants, is it inside the Sun? Is there an AU measured distance of it?

**Tags:** planet, solar-system

> **Comments:**
> **username_1**: Not an answer because I don’t have a reference at hand, but I remember a drawing in an astronomical encyclopedia I had as a kid that showed how the barycenter moved from inside to just outside the surface (photosphere?) of the sun in the span of just a few years as the different planets orbited around.  
> **username_1**: Bingo! *This* diagram: https://cloud10.todocoleccion.online/libros-segunda-mano-astronomia/tc/2019/03/15/18/155282782_129458382.webp  
> **username_2**: My answer here has two diagrams of the Solar System barycentre relative to the Sun, covering the period from 1945 to 2051. https://astronomy.stackexchange.com/a/28036/16685  
> **username_0**: Thanks for the response guys. Yes, those diagrams are very good. but they lost me even more, I was looking for a fixed point with AU distance that I can use for calculations. Seems like the center of mass moves very quickly. Unexpected. I was thinking that it must be a very stable point to use as a reference.  
> **username_2**: @KapishM Well, we *do* use the Solar System barycentre as a fixed origin, with the Sun moving around it in those funky looking curves. FWIW, the Sun's radius is a little under 1/215 au, so its position deviates from the barycentre by around 1/100 au. Historically, we considered the Sun's position to be fixed, which is kind of equivalent, except that it treats the Sun's rest frame as an inertial frame.  
> **username_2**: (cont) The modern approach uses the [ICRF](https://en.wikipedia.org/wiki/International_Celestial_Reference_Frame), which defines the barycenter location via a network of several thousand extragalactic radio sources (mostly quasars). Also check out the [BCRS](https://en.wikipedia.org/wiki/Barycentric_celestial_reference_system), and there's some relevant info at the JPL [Horizons](https://ssd.jpl.nasa.gov/?horizons_doc#frames) site.  
> **username_3**: Voting to reopen. OP is asking for quantities, not just a picture.  
> **username_4**: Related: [Can the paper narrowing Solar System's barycentre to within 100m help find Planet Nine?](https://astronomy.stackexchange.com/q/36894/34443)  
> **username_2**: Also see my later answer, which has graphs (and scripts) which show the Sun - barycentre distance. https://astronomy.stackexchange.com/a/44903/16685  

---

## 2 answers

### Answer by username_3 on 2021-01-17. Score: 8 | Accepted answer

The solar system barycenter (SSB) is sometimes inside the Sun and sometimes outside.
As an observer outside the solar system could detect with [Doppler spectroscopy](https://en.wikipedia.org/wiki/Doppler_spectroscopy), the Sun is what's wobbling around.

The Sun's offset from the SSB is a vector sum of roughly:

* 0.00496 au ±5% away from Jupiter
* 0.00272 au ±6% away from Saturn
* 0.00083 au ±5% away from Uranus
* 0.00155 au ±1% away from Neptune

The other planets contribute much smaller amounts to the total.
Each planet's contribution is proportional to the product of its mass and its orbital distance.

When these components add constructively as in 2020-2023, the center of the Sun can be as far as 2 R☉ away from the SSB.
When they cancel as in 2029-2030, the center of the Sun is within 0.5 R☉ of the SSB.
The solar radius R☉ is 0.00465 au, shown here with a dashed line.

![Plot of Sun-SSB distance vs. time](https://i.sstatic.net/M1FEA.png)

> **Comments:**
> **username_2**: Nice graph! Did you create it using JPL *Horizons* data? You can clearly see the ~20 year period of the [Jupiter-Saturn conjunction](https://en.wikipedia.org/wiki/Great_conjunction) cycle. It'd also be interesting to see the corresponding graph of the SSB's (heliocentric) ecliptic latitude. Of course, the 20 year period would be less obvious in the direction graph, but I assume there'd be a ~60 year period (60 ~= 5 Jupiter periods ~= 2 Saturn periods).  
> **username_3**: @username_2 Almost: I used Skyfield to read JPL DE430.  
> **username_6**: @username_2: What there is is rather a 179-year period, which I believe is due to what is called the great inequality of Jupiter and Saturn (which Laplace originally calculated to ~877 years, then to ~924 years, but now would be estimated to around ~895 years if I'm not mistaken (someone correct me if I'm wrong). Here I've used a JPL ephemeris to plot out the Sol-SSB distance in terms of Solar radii from year -2999 to 3000, demonstrating the cyclical nature of it: https://i.postimg.cc/k7sN5n4Z/Figure-1.png  
> **username_2**: @username_6 The ~179 year period relates to the synodic periods of (Saturn, Uranus, Neptune), relative to Jupiter, which are (19.863261, 13.812176, 12.782075) Julian years, respectively. Multiply those periods by (9, 13, 14) & we get  (178.769349, 179.558288, 178.949050). We can find longer period solutions using the [LLL algorithm](https://en.wikipedia.org/wiki/Lenstra%E2%80%93Lenstra%E2%80%93Lov%C3%A1sz_lattice_basis_reduction_algorithm). Here's a demo in Sage. Try larger numbers for the `scale`. You can put numeric expressions in the `data` list, and comment out data lines with leading `#`.  
> **username_2**: https://sagecell.sagemath.org/?z=eJxlUsFq4zAUvBv8Dw_3UCl1he12k3RBsPRQKKS33tKsEbaSitqSkWS55Ov75JhuYXUa6c3M0-jpCna7HVjZjo1XRqfJGThkWfaWJuUD267vqnWJ8I5ty6rcrBFWbLOtis2vNEFamqTJH6W9tKLxadLKI9Sk5-TaNaKT1zmURUFzaIUX_FkPo380nwRZYuw8P-fwLtXp3fN75IjRm3ockCr5k-icpL_TBHBFMV5qb83EnLdqIBSOxgLuQem5zNzQKd8pLR2hh4ssBBQF2Xhjyd6Jk6xlEB1B1X9yUMd5K3QL2viI98WB8-wqO9CL22AxJVmFkIOTA8_edJaD1O2MVhWNDzF37XOYYuMAK0DcSU1CWExesNALjPBJQo_10GMbiqFE80EuBXaW1pDptkQb-i274fDCXuFmUbNWiZPRmCb09G-F5-XC3Bd5cYj02RpLKyAT3ML99wUdRC8cen2yoieUvf4M6HKIgZbGP57JLcP4R43jGISyk3KyHqyJPyhGpV992qaX&lang=sage  
> **username_6**: @username_2: Ah, I see; that's very interesting, thanks. Perhaps I'm misunderstanding what the great inequality is and how it ties into this, then.  
> **username_2**: @username_6 Laplace's Great Inequality relates to the gravitational interaction between Jupiter & Saturn (and the other planets, especially Uranus & Neptune), so it includes effects due to mass, eccentricity, and inclination. In contrast, my LLL calculation is rather crude, since it's only based on the mean motions. FWIW, there's some info on the great inequality here:  https://astronomy.stackexchange.com/q/48972/16685  

---

### Answer by username_5 on 2023-02-17. Score: 0

The fact is, Sun can't exert any moment about the barycenter unless Sun and its planets may be resting on some solid object which may be physically resting on some fulcrum type of thing. Of course Sun wobbles about SSB but not due to balancing of moments. It wobbles due to a different reason. It occupies a place where the gravitational forces exerted by it on all planets get balanced which gives us an impression that it is revolving about SSB.


---

