<p>As you can see from the diagrams below of the motion of the Solar System's barycenter relative to the Sun (courtesy of Wikipedia), the Sun's motion with respect to the system's barycenter is <em>not</em> a simple closed curve, and it doesn't have a simple period.</p>
<p><a href="https://upload.wikimedia.org/wikipedia/commons/0/0c/Solar_system_barycenter.svg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/QeG73.png" alt="Solar system barycentre 1945-1995" /></a></p>
<p>(Click the above image for a SVG version).</p>
<p><a href="https://i.sstatic.net/VjyLz.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/VjyLz.png" alt="Solar System barycenter 2000-2051" /></a></p>
<p>It is primarily dominated by Jupiter's period (11.862 years) because Jupiter has most of the non-solar mass of the Solar System. (On a related note, Jupiter has most of the angular momentum of the solar system). Jupiter's mass is approximately 0.0009543 solar masses, so the Sun is almost 1048 times more massive than Jupiter.</p>
<p>According to <a href="https://en.m.wikipedia.org/wiki/Barycenter#Inside_or_outside_the_Sun?" rel="nofollow noreferrer">Wikipedia</a></p>
<blockquote>
<p>To calculate the actual motion of the Sun, you only need to consider
the motions of the four giant planets (Jupiter, Saturn, Uranus,
Neptune). The contributions of all other planets, dwarf planets, etc.
are negligible.</p>
</blockquote>
<hr />
<p>Here is a <a href="https://sagecell.sagemath.org/?z=eJyNVn9z2jgQ_d-fQud2xjYFx4bSuzLDXClxprThx4DbTo8wHgVEcM9YPkmmgUy--60kGxMy7R0Tgr3afXq7-7S2aZqodYmyhApE10hsCJrRBDM023NBtugWs_2SpIIRxEiCRbwjSFDtl6cGgs9XFgtBUnS7R5Mhak7j9A41vabvei3XbyqXz9kKC7KSkTknKjolP9AHyuIDTTlaxwlBvclAx_me67cM0zQNI95mlAnYug7ff3LCBTfWjG5RLAgTlCYcFS4xT-IlMYycJaiLzI0QGe9cXHC-cr9niZtijt07urvAWXyxKfaN5L4uWEwD_kU7wnhMUxkO5GH3W8xJtNyupAXY9MfDYW902UWW71lGPxiFwRRu2p73Du6HvU9BFEw-BEOwfQtmlhH23l8HUfhtEoDlS9APx1OwzsJgEs0Gf0mjj_aWMf4cRp9Hg3AGhk_DxqVlTIOraHLdG0mXoH89mISDvrbOvkG43OBj0_NgU4ka9cdTyWM0HgXKEl333gfXM2XShsvgOuxFYWHpz75EV-PpsBeWTMfvP0aXvbB3EqLIw33T0p1YkTVaE7HcRNBKbHOBmagjLmjmdFSPdZ3W0vm3ly9n4yvjoazfIyTdm4ZROBgGXetBxT7KSownlY1mYILIACLVjhIUmg6gZevdjHJhQ4frSJLoPlhryrZYWB1kCXIvrMe6khKHlTjNcrlgW0DAqkt6zqOjQKs-M-JygtlyYzNTyu9LMJ0NxqPODa_ZN7OaYyrZuRLbce8YzTPb1xjx-gjzWxedqEcXQ34yFqfCXptfMUvhTHSUwMugmKOH4hpI3-YCDgXY-JLFmRQzgszQwwnuo-nokmzPeNt_cufm5Q1UPLDdmroMxsEp85LwVuKOaErOOZqjMVLKDaaDmemcrT7F0V0ROUsVlLIlcUq47pPydHmWxEJZbR1V7HOTmu53Gqe2Wpu3O_6bheMYJ5jbY5nnfmdhGO8gjjC8FEqAnN9q5XVN_-3rdsPz4c_UMpSmt5UJ54JGuZo73SuccFLIVApH6vRMyi4XUHnb0Vjl3bF0KupZ9TTnU9g517nbVt2SGTT8heokjKlU-TwpzUKFvlAeMTSM_pBuJM23kLIgtgxwOkXxtEMhAr7EMDG7qE0abWUQEZwN0IocfnONK1ELSAlU0d6rkwpLc29R0AWui6rtFVJDb1RD64RiYXOnykbGQ4uqMLkXhAD6Ar0qQY6rR4IwbzOSrmyVjCodbCUJ6sxEvIWjTjKAar1pu8021GeF91ynLVXmF1HQlZW9u6-j3R6-B6dKcCfdwLdWoV2g1rl8d_fgsOMyvrw4qIuCSLYDFP1YsY_s68irKxWAULjmDwnXEQIeQOMAVxUliE_hONgAVaQKSytYWsmlp-z1DM3ZTp2k-dwuAEGR9j3UU4bu5a80yt-DA7U_NvoXJKBXQKCqzn-RqIjMQb4uJCDbBYRQo2DRKFg0JAvJr6C6OAcoe_2_sqnUUO2uE4TH9V0s57Xtqfp72pXnKcNSym_etn_3PBDK31u9IDPziX73mMB1BjNHtFa2BoLWxQfSbXk1DqWiGV7GYt_13DY8JWhCWdekDKd3pJiEE_QK1JRtCCMVgDwWNU3gFMI_QrxYr71yZCuEksNcH5zXi9MDetTXoq4zkATbil-Bd5vkpMQ7CfyFPtvOkyNfL9VRnH1gcFxWBOXkBn7gOm_CYtVX6I_nepKN85yA7lW104snyeohUxT8j5_We7nH6clz5zmGmqRl345hW3wHr6b4WaQcr0Vgp7k4ujOy-pVrs_MzV-V5Sw4xYUUDzz11m12-oT_sNcNb0g1ZDj3A9_Ayoh8__wIJY0Ui&amp;lang=sage" rel="nofollow noreferrer">Sage / Python script which displays an interactive 3D plot</a> of the above diagrams, using data from
the <a href="https://ssd.jpl.nasa.gov/?horizons" rel="nofollow noreferrer">JPL Horizons</a> on-line solar system data and ephemeris computation service. Horizons can produce data covering a wide range of dates, please see the Horizons documentation for details.</p>
<p>FWIW, here's a plot of the Sun's speed relative to the barycentre.</p>
<p><a href="https://i.sstatic.net/w0ZXB.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/w0ZXB.png" alt="Sun speed relative to barycentre" /></a></p>

CC BY-SA 4.0
2018-10-16T01:08:20.117Z
In years (see OP)
sunSis
CC BY-SA 4.0
2018-10-16T01:16:40.470Z
@sunSis It varies quite a bit, but it's roughly 12 years.
PM 2Ring
CC BY-SA 4.0
2018-10-16T10:30:25.463Z
@SunSis - The correct answer is in this answer: "*the Sun's motion with respect to the system's barycenter is not a simple closed curve, and it doesn't have a simple period.*" By insisting on a simple period, you are demanding an answer that doesn't exist.
David Hammen
CC BY-SA 4.0
2018-11-02T11:09:32.387Z
Thank you for your edit [here](https://astronomy.stackexchange.com/q/28240/7982)! Seeing my mistakes that you fixed made me laugh out loud in a library :o
uhoh
CC BY-SA 4.0
2021-05-03T15:53:11.307Z
Could the motion of the sun w.r.t. the solar system barycenter be considered as quasiperiodic, e.g., if we consider the orbital timescale to be much smaller than the timescale over which the orbital angular momentum changes appreciably?
Daddy Kropotkin
CC BY-SA 4.0
2021-05-03T16:19:34.597Z
@DaddyKropotkin Sure. Although the Sun's motion wrt the barycentre doesn't form a simple closed loop, it's actually fairly well-behaved, because the periods of Saturn, and Uranus are roughly 2.5× and 7× the period of Jupiter. My Sage script uses cubic Bezier curves to plot the path. The parameter `ss` controls the step size (in years) used for the Bezier curves. Currently, `ss=1` so every year point is used in the curve calculation. If you set `ss=3`, only every 3rd year point will be used, but the curve will still go fairly close to the in-between year points.
PM 2Ring
CC BY-SA 4.0
2021-05-03T18:25:31.317Z
Very neat! Are you using cubic Bezier curves because you are considering four points in the plane, i.e., Saturn, Uranus, Jupiter, and the Sun? Or is there another reason? Do the gravitational dynamics reduce to the Bernstein polynomials? Like, this isn't just computer graphics, right? You're implementing Newtonian gravity?
Daddy Kropotkin
CC BY-SA 4.0
2021-05-03T19:56:47.783Z
@DaddyKropotkin I'm not calculating the data, I'm pulling it directly from the [JPL Development Ephemeris](https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory_Development_Ephemeris) via their Horizons interface. I'm using that 3D position & velocity data (of the Sun, relative to the Solar System barycentre) to calculate the Bezier control points, which Sage then uses to plot the curves. Although the curves are in 3D, at this scale it's not easy to see that the curves aren't perfectly planar. The Z coordinate variation is ~1% of the X & Y variation.
PM 2Ring
CC BY-SA 4.0
2021-05-03T21:44:10.870Z
That's awesome! Thanks for explaining.
Daddy Kropotkin
CC BY-SA 4.0
2022-12-20T13:45:21.480Z
Also see https://astronomy.stackexchange.com/a/44903/16685
PM 2Ring
CC BY-SA 4.0
2018-10-16T00:56:14.093Z
2022-09-18T03:26:29.040Z
2022-09-18T03:26:29.040Z
PM 2Ring
<p>In years, what is the time it takes our sun to orbit around our solar system's barycenter?</p>

CC BY-SA 4.0
2018-10-16T17:29:49.870Z
There isn't a stable location of the barycenter, so....
Carl Witthoft
<the-sun><solar-system>
What is the orbital period of our sun around its barycenter?
sunSis
# What is the orbital period of our sun around its barycenter?

(Asked by: username_0 on 2018-10-16)

In years, what is the time it takes our sun to orbit around our solar system's barycenter?

**Tags:** the-sun, solar-system

> **Comments:**
> **username_1**: There isn't a stable location of the barycenter, so....  

---

## 1 answers

### Answer by username_2 on 2018-10-16. Score: 18

As you can see from the diagrams below of the motion of the Solar System's barycenter relative to the Sun (courtesy of Wikipedia), the Sun's motion with respect to the system's barycenter is *not* a simple closed curve, and it doesn't have a simple period.

[![Solar system barycentre 1945-1995](https://i.sstatic.net/QeG73.png)](https://upload.wikimedia.org/wikipedia/commons/0/0c/Solar_system_barycenter.svg)

(Click the above image for a SVG version).

[![Solar System barycenter 2000-2051](https://i.sstatic.net/VjyLz.png)](https://i.sstatic.net/VjyLz.png)

It is primarily dominated by Jupiter's period (11.862 years) because Jupiter has most of the non-solar mass of the Solar System. (On a related note, Jupiter has most of the angular momentum of the solar system). Jupiter's mass is approximately 0.0009543 solar masses, so the Sun is almost 1048 times more massive than Jupiter.

According to [Wikipedia](https://en.m.wikipedia.org/wiki/Barycenter#Inside_or_outside_the_Sun?)

> To calculate the actual motion of the Sun, you only need to consider
> the motions of the four giant planets (Jupiter, Saturn, Uranus,
> Neptune). The contributions of all other planets, dwarf planets, etc.
> are negligible.

---

Here is a [Sage / Python script which displays an interactive 3D plot](https://sagecell.sagemath.org/?z=eJyNVn9z2jgQ_d-fQud2xjYFx4bSuzLDXClxprThx4DbTo8wHgVEcM9YPkmmgUy--60kGxMy7R0Tgr3afXq7-7S2aZqodYmyhApE10hsCJrRBDM023NBtugWs_2SpIIRxEiCRbwjSFDtl6cGgs9XFgtBUnS7R5Mhak7j9A41vabvei3XbyqXz9kKC7KSkTknKjolP9AHyuIDTTlaxwlBvclAx_me67cM0zQNI95mlAnYug7ff3LCBTfWjG5RLAgTlCYcFS4xT-IlMYycJaiLzI0QGe9cXHC-cr9niZtijt07urvAWXyxKfaN5L4uWEwD_kU7wnhMUxkO5GH3W8xJtNyupAXY9MfDYW902UWW71lGPxiFwRRu2p73Du6HvU9BFEw-BEOwfQtmlhH23l8HUfhtEoDlS9APx1OwzsJgEs0Gf0mjj_aWMf4cRp9Hg3AGhk_DxqVlTIOraHLdG0mXoH89mISDvrbOvkG43OBj0_NgU4ka9cdTyWM0HgXKEl333gfXM2XShsvgOuxFYWHpz75EV-PpsBeWTMfvP0aXvbB3EqLIw33T0p1YkTVaE7HcRNBKbHOBmagjLmjmdFSPdZ3W0vm3ly9n4yvjoazfIyTdm4ZROBgGXetBxT7KSownlY1mYILIACLVjhIUmg6gZevdjHJhQ4frSJLoPlhryrZYWB1kCXIvrMe6khKHlTjNcrlgW0DAqkt6zqOjQKs-M-JygtlyYzNTyu9LMJ0NxqPODa_ZN7OaYyrZuRLbce8YzTPb1xjx-gjzWxedqEcXQ34yFqfCXptfMUvhTHSUwMugmKOH4hpI3-YCDgXY-JLFmRQzgszQwwnuo-nokmzPeNt_cufm5Q1UPLDdmroMxsEp85LwVuKOaErOOZqjMVLKDaaDmemcrT7F0V0ROUsVlLIlcUq47pPydHmWxEJZbR1V7HOTmu53Gqe2Wpu3O_6bheMYJ5jbY5nnfmdhGO8gjjC8FEqAnN9q5XVN_-3rdsPz4c_UMpSmt5UJ54JGuZo73SuccFLIVApH6vRMyi4XUHnb0Vjl3bF0KupZ9TTnU9g517nbVt2SGTT8heokjKlU-TwpzUKFvlAeMTSM_pBuJM23kLIgtgxwOkXxtEMhAr7EMDG7qE0abWUQEZwN0IocfnONK1ELSAlU0d6rkwpLc29R0AWui6rtFVJDb1RD64RiYXOnykbGQ4uqMLkXhAD6Ar0qQY6rR4IwbzOSrmyVjCodbCUJ6sxEvIWjTjKAar1pu8021GeF91ynLVXmF1HQlZW9u6-j3R6-B6dKcCfdwLdWoV2g1rl8d_fgsOMyvrw4qIuCSLYDFP1YsY_s68irKxWAULjmDwnXEQIeQOMAVxUliE_hONgAVaQKSytYWsmlp-z1DM3ZTp2k-dwuAEGR9j3UU4bu5a80yt-DA7U_NvoXJKBXQKCqzn-RqIjMQb4uJCDbBYRQo2DRKFg0JAvJr6C6OAcoe_2_sqnUUO2uE4TH9V0s57Xtqfp72pXnKcNSym_etn_3PBDK31u9IDPziX73mMB1BjNHtFa2BoLWxQfSbXk1DqWiGV7GYt_13DY8JWhCWdekDKd3pJiEE_QK1JRtCCMVgDwWNU3gFMI_QrxYr71yZCuEksNcH5zXi9MDetTXoq4zkATbil-Bd5vkpMQ7CfyFPtvOkyNfL9VRnH1gcFxWBOXkBn7gOm_CYtVX6I_nepKN85yA7lW104snyeohUxT8j5_We7nH6clz5zmGmqRl345hW3wHr6b4WaQcr0Vgp7k4ujOy-pVrs_MzV-V5Sw4xYUUDzz11m12-oT_sNcNb0g1ZDj3A9_Ayoh8__wIJY0Ui&lang=sage) of the above diagrams, using data from
the [JPL Horizons](https://ssd.jpl.nasa.gov/?horizons) on-line solar system data and ephemeris computation service. Horizons can produce data covering a wide range of dates, please see the Horizons documentation for details.

FWIW, here's a plot of the Sun's speed relative to the barycentre.

[![Sun speed relative to barycentre](https://i.sstatic.net/w0ZXB.png)](https://i.sstatic.net/w0ZXB.png)

> **Comments:**
> **username_0**: In years (see OP)  
> **username_2**: @username_0 It varies quite a bit, but it's roughly 12 years.  
> **username_3**: @SunSis - The correct answer is in this answer: "*the Sun's motion with respect to the system's barycenter is not a simple closed curve, and it doesn't have a simple period.*" By insisting on a simple period, you are demanding an answer that doesn't exist.  
> **username_4**: Thank you for your edit [here](https://astronomy.stackexchange.com/q/28240/7982)! Seeing my mistakes that you fixed made me laugh out loud in a library :o  
> **username_5**: Could the motion of the sun w.r.t. the solar system barycenter be considered as quasiperiodic, e.g., if we consider the orbital timescale to be much smaller than the timescale over which the orbital angular momentum changes appreciably?  
> **username_2**: @DaddyKropotkin Sure. Although the Sun's motion wrt the barycentre doesn't form a simple closed loop, it's actually fairly well-behaved, because the periods of Saturn, and Uranus are roughly 2.5× and 7× the period of Jupiter. My Sage script uses cubic Bezier curves to plot the path. The parameter `ss` controls the step size (in years) used for the Bezier curves. Currently, `ss=1` so every year point is used in the curve calculation. If you set `ss=3`, only every 3rd year point will be used, but the curve will still go fairly close to the in-between year points.  
> **username_5**: Very neat! Are you using cubic Bezier curves because you are considering four points in the plane, i.e., Saturn, Uranus, Jupiter, and the Sun? Or is there another reason? Do the gravitational dynamics reduce to the Bernstein polynomials? Like, this isn't just computer graphics, right? You're implementing Newtonian gravity?  
> **username_2**: @DaddyKropotkin I'm not calculating the data, I'm pulling it directly from the [JPL Development Ephemeris](https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory_Development_Ephemeris) via their Horizons interface. I'm using that 3D position & velocity data (of the Sun, relative to the Solar System barycentre) to calculate the Bezier control points, which Sage then uses to plot the curves. Although the curves are in 3D, at this scale it's not easy to see that the curves aren't perfectly planar. The Z coordinate variation is ~1% of the X & Y variation.  
> **username_5**: That's awesome! Thanks for explaining.  
> **username_2**: Also see https://astronomy.stackexchange.com/a/44903/16685  

---

