<p>Since the Solar system is a multi-body system (with <span class="math-container">$N&gt;2$</span> bodies of significant mass), the orbits of its constituents are not exact Keplerian orbits.</p>
<p>To lowest order, each planet orbits the Sun (or rather the centre of mass of all interior planets) on a Keplerian orbit, but the interactions with the planets as well as the fact that the centre of mass of the interior is not fixed lead to deviations of the true orbit from this simplification. These deviations can be treated either numerically or via perturbation theory, but are non-trivial functions of time.</p>
<p>The same holds for the Sun: to lowest order one can neglect all planets but Jupiter (which is more then twice as massive as all the remaining planets combined), when the Sun follows an elliptic orbit with semi-major axis of about 0.005AU (smaller than that of Jupiter by their mass ratio). This is of the same order as the radius of the Sun, i.e. the barycentre of the Solar system hardly leaves the Sun. However, as above, the pull by all other planets lead to a deviation from this simple model. Again, these deviations are non-trivial.</p>

CC BY-SA 4.0
2021-05-24T14:23:10.123Z
2021-05-24T14:23:10.123Z
Walter
<p>What are the orbital parameters of the Sun such as orbit velocity etc in it's orbit around the Solar System's center of mass? Consider the Sun pointlike or alternatively when talkin about the Sun's movement I mean it's center of mass.</p>
<p>Do not tell me that the Sun is stationary because the planets' masses can be neglected. I do no want such oversimplifications.</p>

CC BY-SA 4.0
2021-05-24T14:14:37.520Z
Welcome to astronomy SE. Your question currently sounds like a "do my homework for me" kind of question, which is off-topic here. Please edit your question to include detailed explanations of your attempts to answer your own questions, and describe specifically the concepts that confuse you. Otherwise, this question will likely be closed as off topic.
Daddy Kropotkin
CC BY-SA 4.0
2021-05-24T14:18:07.893Z
Do I really have to explain what orbital parameters are? This is a question in celestial mechanics and it's got nothing to do with formal education.
Some Student
CC BY-SA 4.0
2021-05-24T20:02:24.593Z
No, it's more about the concepts. For example see the question that your question is a duplicate of.
Daddy Kropotkin
CC BY-SA 4.0
2021-05-24T21:41:18.153Z
@DaddyKropotkin It doesn't sound like a "do my homework for me"  kind of question to me at all, and questions *related* to homework are not off-topic. We can not guess who a user is or why they ask a question. However, questions that *do not show any evidence of prior research or effort* can be addressed with "What have you tried so far?" in a kind and helpful  comment as you point out, and as a last resort, down voted of one really wants to, and are sometimes closed as "needs details or clarification".
uhoh
CC BY-SA 4.0
2021-05-24T21:45:43.743Z
@DaddyKropotkin note that neither [What topics can I ask about here?](https://astronomy.stackexchange.com/help/on-topic) nor [What types of questions should I avoid asking?](https://astronomy.stackexchange.com/help/dont-ask) mention homework.
uhoh
CC BY-SA 4.0
2021-05-24T21:47:31.397Z
@DaddyKropotkin Then have a look at [I can't find this site's “homework policy” or find out how “suspected homework question askers” should be treated](https://astronomy.meta.stackexchange.com/q/473/7982) in meta. "There is NO prohibition against homework questions here at Astronomy. StephenG's comment that he was voting to close for *suspicion* of homework was ill-advised and had no basis in site policy." Stack exchange works by applying the same basic tenants to all questions and all users evenly and equally. We work hard to avoid "this sounds like" thinking whenever possible.
uhoh
CC BY-SA 4.0
2021-05-24T21:53:03.987Z
@Pete your question is a good and interesting one, and so has been asked (and answered) before. Next time try to add a bit of "evidence of research" as it sometimes helps provide higher quality answers and (if it matters to you) sometimes more up votes as well :-) It turns out that if you hover your cursor over the up and down vote arrows for questions, the "tooltip guidelines" are related to amount of research. https://i.sstatic.net/yCFWy.png Not everybody follows those guidelines (I don't; I vote however I want) but it's a good reminder that a bit of research helps. *Enjoy!*
uhoh
CC BY-SA 4.0
2021-05-24T22:49:10.123Z
@uhoh Sorry, *homework* is an open discussion here, I'm still used to Physics SE. https://astronomy.meta.stackexchange.com/questions/87/homework-policy
Daddy Kropotkin
CC BY-SA 4.0
2021-05-24T23:15:11.160Z
@DaddyKropotkin answers to that question are really about a homework tag and it seems the opinion is that since they are both okay and infrequent (as long as they meet all the standard criteria) no special tag is necessary. Luckily Astronomy SE is a lot nicer and more welcoming than Physics SE, partly because it can afford to be with a 16x lower question rate, and partly because fewer students take Astronomy courses than Physics courses, the gamification aspects of SE haven't taken hold here. Physics SE is much better than it used to be several years ago (it was essentially "broken")...
uhoh
CC BY-SA 4.0
2021-05-24T23:16:18.100Z
@DaddyKropotkin but I still think it should be divided up so that real, healthy communities can develop. https://physics.meta.stackexchange.com/a/12734/83380
uhoh
<the-sun><solar-system><celestial-mechanics>
Orbital parameters of the Sun
Some Student
# Orbital parameters of the Sun

(Asked by: username_0 on 2021-05-24)

What are the orbital parameters of the Sun such as orbit velocity etc in it's orbit around the Solar System's center of mass? Consider the Sun pointlike or alternatively when talkin about the Sun's movement I mean it's center of mass.

Do not tell me that the Sun is stationary because the planets' masses can be neglected. I do no want such oversimplifications.

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

> **Comments:**
> **username_1**: Welcome to astronomy SE. Your question currently sounds like a "do my homework for me" kind of question, which is off-topic here. Please edit your question to include detailed explanations of your attempts to answer your own questions, and describe specifically the concepts that confuse you. Otherwise, this question will likely be closed as off topic.  
> **username_0**: Do I really have to explain what orbital parameters are? This is a question in celestial mechanics and it's got nothing to do with formal education.  
> **username_1**: No, it's more about the concepts. For example see the question that your question is a duplicate of.  
> **username_2**: @username_1 It doesn't sound like a "do my homework for me"  kind of question to me at all, and questions *related* to homework are not off-topic. We can not guess who a user is or why they ask a question. However, questions that *do not show any evidence of prior research or effort* can be addressed with "What have you tried so far?" in a kind and helpful  comment as you point out, and as a last resort, down voted of one really wants to, and are sometimes closed as "needs details or clarification".  
> **username_2**: @username_1 note that neither [What topics can I ask about here?](https://astronomy.stackexchange.com/help/on-topic) nor [What types of questions should I avoid asking?](https://astronomy.stackexchange.com/help/dont-ask) mention homework.  
> **username_2**: @username_1 Then have a look at [I can't find this site's “homework policy” or find out how “suspected homework question askers” should be treated](https://astronomy.meta.stackexchange.com/q/473/7982) in meta. "There is NO prohibition against homework questions here at Astronomy. StephenG's comment that he was voting to close for *suspicion* of homework was ill-advised and had no basis in site policy." Stack exchange works by applying the same basic tenants to all questions and all users evenly and equally. We work hard to avoid "this sounds like" thinking whenever possible.  
> **username_2**: @Pete your question is a good and interesting one, and so has been asked (and answered) before. Next time try to add a bit of "evidence of research" as it sometimes helps provide higher quality answers and (if it matters to you) sometimes more up votes as well :-) It turns out that if you hover your cursor over the up and down vote arrows for questions, the "tooltip guidelines" are related to amount of research. https://i.sstatic.net/yCFWy.png Not everybody follows those guidelines (I don't; I vote however I want) but it's a good reminder that a bit of research helps. *Enjoy!*  
> **username_1**: @username_2 Sorry, *homework* is an open discussion here, I'm still used to Physics SE. https://astronomy.meta.stackexchange.com/questions/87/homework-policy  
> **username_2**: @username_1 answers to that question are really about a homework tag and it seems the opinion is that since they are both okay and infrequent (as long as they meet all the standard criteria) no special tag is necessary. Luckily Astronomy SE is a lot nicer and more welcoming than Physics SE, partly because it can afford to be with a 16x lower question rate, and partly because fewer students take Astronomy courses than Physics courses, the gamification aspects of SE haven't taken hold here. Physics SE is much better than it used to be several years ago (it was essentially "broken")...  
> **username_2**: @username_1 but I still think it should be divided up so that real, healthy communities can develop. https://physics.meta.stackexchange.com/a/12734/83380  

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## 1 answers

### Answer by username_3 on 2021-05-24. Score: 2 | Accepted answer

Since the Solar system is a multi-body system (with $N>2$ bodies of significant mass), the orbits of its constituents are not exact Keplerian orbits.

To lowest order, each planet orbits the Sun (or rather the centre of mass of all interior planets) on a Keplerian orbit, but the interactions with the planets as well as the fact that the centre of mass of the interior is not fixed lead to deviations of the true orbit from this simplification. These deviations can be treated either numerically or via perturbation theory, but are non-trivial functions of time.

The same holds for the Sun: to lowest order one can neglect all planets but Jupiter (which is more then twice as massive as all the remaining planets combined), when the Sun follows an elliptic orbit with semi-major axis of about 0.005AU (smaller than that of Jupiter by their mass ratio). This is of the same order as the radius of the Sun, i.e. the barycentre of the Solar system hardly leaves the Sun. However, as above, the pull by all other planets lead to a deviation from this simple model. Again, these deviations are non-trivial.


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