Is Jupiter Responsible for the Majority of the Solar System's Angular Momentum?

[fizzy]

Hi, I found some back of envelop calculations which show that Jupiter accounts for over 60% of the solar system's angular momentum.

http://www.zipcon.net/~swhite/docs/astronomy/Angular_Momentum.html

Is that correct?

A previous thread here on the subject ( now locked for some reason ) claimed that "the vast majority" of ang. momentum would reside in the star.

Which is it? Is this a problem for simplistic accretion models ?

 

[Chronos]

Since the sun is not orbiting anything else in the solar system it effectively has zero orbital angular momentum wrt the solar system. The sun, however, does have a substantial amount of rotational angular momentum - much more than any of the planets. With respect to the galactic center, which the sun does orbit, the sun is the 800 pound gorilla in the solar system and does have the lions share of orbital angular momentum wrt the galactic center

 

[fizzy]

Thanks but that does not really answer the question.

If we put galactic rotation to one side and consider that the SS barycentre is moving in a linear fashion through space ( a reasonable approximation in view of the speed of the galactic rotation ) ; it still seems that Jupiter accounts for >60% of TOTAL ang. momentum ( orbital + rotational ).

That does not seem consistent with the idea that SS was formed by accretion of a gaseous disc. How could one of the planets end up with such a proportion of the total ang. momentum? It would seem necessary to implicate at least one interaction with a very significant mass not in the current body count.

BTW While the sun can not be said to be orbiting the SSBC since it is a hypothetical centre of mass an not a centre of gravitational attraction, it does move around it in an irregular but repetitive way and this must allow some mean a.m. value relative to the inertial reference point of the SS. The centre of the sun is not a valid reference point for inertial calculations so the orbital ang. momentum is not zero.

 

[Chronos]

Agreed, but, permit me to point out the source you cite for angular momentum does not attempt to derive angular momentum wrt the solar system barycenter [SSBC]. If it did, it would offer some haphazard figure for solar angular momentum in addition to the planets. The fact is each body in the solar system has its own barcenter wrt the sun and each other, This would be a nightmare to derive any meaningful nuimbers for and would only be valid for the particular configuration assumed for the calculation. For the sake of convenience an approximation was made - obviously using the sun's barycenter as a reference point. The solar mass is so enormous compared to the rest of the solar system that the SSBC ranges from near the center of the sum to a point just beyond its 'surface', so, the numbers given are a pretty good approximation and, of course, forces the solar orbital angular momentum to zero. While the solar orbital angular momentum would be significant, the sun is never far enough nor moving fast enough wrt ihe SSBC to rack up an eye popping value for 'L'.

 

[fizzy]

OK, it may be that solar "orbital" a.m. is not that large and can be ignored in this kind of ball-park discussion. But the question remains: why does J account for > 60% of the total a.m. of SS and doesn't that imply some other major interactions than simply explaining the SS as the result of accretion?

 

[russ_watters]

it still seems that Jupiter accounts for >60% of TOTAL ang. momentum ( orbital + rotational ).

That does not seem consistent with the idea that SS was formed by accretion of a gaseous disc. How could one of the planets end up with such a proportion of the total ang. momentum? It would seem necessary to implicate at least one interaction with a very significant mass not in the current body count.

I don't understand why you think this follows. I see no problem/contradiction indicated by Jupiter having so much of the solar system's angular momentum. It's big! Really big!

Could you explain what the issue is that you see?

 

[rootone]

The mass of Jupiter is well over twice the mass of everything else orbiting the Sun combined.
It doesn't seem surprising therefore that it would account for over half of the solar system's angular momentum.

 

[fizzy]

The mass of Jupiter is well over twice the mass of everything else orbiting the Sun combined.
It doesn't seem surprising therefore that it would account for over half of the solar system's angular momentum.

Well the also-rans don't really matter. But the sun is three orders of magnitude more massive than Jupiter. So if 99.9% of the material in the supposed gaseous disk collapsed to form the sun and the other 0.1% ended up as Jupiter, even if that 0.1% was the outer 0.1%, it does not seem right that is should contain 60% of the a.m.

Without drawing up detailed model or integrating from 0 to 99.9% of the disk and 99.9% to 100% , it seems totally disproportionate.

 

[Chronos]

Assuming the suns orbit around the SSBC is about one solar radius [695700 km] and the orbital radius of Jupiter is 778000000 km [>1000 times that of the solar orbital radius]. That difference has to be squared to obtain orbital angular momentum, so, Jupiter has ~ a million times the angular moment of the sun all else considered equal. Of course the sun is about 1000 times more massive than Jupiter so we may reasonably conclude its orbital angular momentum wrt SSBC is merely around a thousand rather than a million times smaller than Jupiter's - in other words insignificant.

 

[Vanadium 50]

but the sun is three orders of magnitude more massive than Jupiter.

And Jupiter's orbital radius is three orders of magnitude greater than the sun's radius.

 

[russ_watters]

Well the also-rans don't really matter. But the sun is three orders of magnitude more massive than Jupiter. So if 99.9% of the material in the supposed gaseous disk collapsed to form the sun and the other 0.1% ended up as Jupiter, even if that 0.1% was the outer 0.1%, it does not seem right that is should contain 60% of the a.m.

Without drawing up detailed model or integrating from 0 to 99.9% of the disk and 99.9% to 100% , it seems totally disproportionate.

Yeah, I probably should have specified that not only is Jupiter Really Big, it is also Really Far Away from the axis of rotation of the solar system. The sun is, of course, not very far from the axis of rotation of the solar system. Angular momentum is a function of speed, mass and distance.

 

[fizzy]

That difference has to be squared to obtain orbital angular momentum

L=rmw ??

The last three replies all manage to miss the whole point. Why is the ang. momentum of the sun so small if it contains 99.9% of the mass of the SS formed from the supposed accretion disk?

 

[Vanadium 50]

The last three replies all manage to miss the whole point

Oh, there's point missing going on all right.

Let's start here, L = rmω is not correct. What is the correct expression?

 

[fizzy]

Oh, there's point missing going on all right.

Let's start here, L = rmω is not correct. What is the correct expression?

I think you are missing the point about missing the point. You ignore the quote above what I wrote to which I was replying. Chronos suggested ang.momemtum was proportional to distance squared presumably because it has ML²T^-1 dimensions. So I posted L = rmω to job his memory. The questionmarks were "n'est pas" .

So having once again sidestepped the main question , maybe you'd like to try again.

Why is the ang. momentum of the sun so small if it contains 99.9% of the mass of the SS formed from the supposed accretion disk?

 

[256bits]

Why is the ang. momentum of the sun so small if it contains 99.9% of the mass of the SS formed from the supposed accretion disk?

Maybe that's not the correct question.
Maybe the question is " Where did all the angular momentum from the gaseous cloud that the solar system formed from, go?"
It can't be in the sun, else the proto sun would never have formed due to excess rotational velocity.
So somewhere along the way, the angular momentum of the cloud had to be shed.
And that is an area of research, and as far as I know, not that I know much, still unresolved to completion.

Consider this - if Jupiter had grasped enough material so that the sun and Jupiter were a binary star system, and with equal masses, the orbital angular momentum of both ( albeit if equal in this fictitious case ) would be less than that of the cloud.

Your question would then not be why is the orbital angular momentum greater than the rotational angular momentum - which is what you are asking for the present state of the solar system, regarding Jupiter and the Sun.

 

[fizzy]

thanks, some interesting points.

Maybe that's not the correct question.
Maybe the question is " Where did all the angular momentum from the gaseous cloud that the solar system formed from, go?"

That does not contradict my qu: why is it so small, it simply pushes towards inserting an answer. Maybe it is so small because it disappeared. I have not found anyone promoting that kind of answer who says how it looses nearly all the a.m. but retains 99.9% of the resulting mass.

Consider this - if Jupiter had grasped enough material so that the sun and Jupiter were a binary star system, and with equal masses, the orbital angular momentum of both ( albeit if equal in this fictitious case ) would be less than that of the cloud.

... and the rest being rotational ? I don't see what that tells us.

Your question would then not be why is the orbital angular momentum greater than the rotational angular momentum - which is what you are asking for the present state of the solar system, regarding Jupiter and the Sun.

Well that is an interesting way of rephrasing the question but it neither answers nor negates the question. That way of looking at it may be enlightening though.

Maybe that's not the correct question.
And that is an area of research, and as far as I know, not that I know much, still unresolved to completion.

Yes, this seems to be a sizeable problem. Thanks for your comments.

 

[Vanadium 50]

So having once again sidestepped the main question , maybe you'd like to try again.

And maybe instead of getting all huffy, you might answer the question

L = rmω is not correct. What is the correct expression?

because so long as you are miscalculating angular momentum, you're not going to get to the bottom of this.

 

[fizzy]

And maybe instead of getting all huffy, you might answer the question
because so long as you are miscalculating angular momentum, you're not going to get to the bottom of this.

Sorry, careless typo. L=rmv ; BTW, I did not calculate anything. I linked to another source that had done that.

I did not get the sense of your previous post , I did not realize that your were a school teacher. A simple correction would have been more helpful.
The point being that it is the moment of inertia, not angular momentum which is r². I was pointing out the Chronos was in error by three orders.

I'm not being "huffy" but do prefer someone able to answer a question rather than being cryptic instead of simply posting a correction where appropriate and not answering the question.

 

[256bits]

I have not found anyone promoting that kind of answer who says how it looses nearly all the a.m. but retains 99.9% of the resulting mass.

Don't know what to say.

http://adsabs.harvard.edu/abs/2013prpl.conf1K039C

The loss of angular momentum is inevitable in star formation processes, and the transportation of angular momentum by a molecular flow is widely thought to be one of the important processes

 

[Vanadium 50]

I'm not being "huffy"

I did not realize that your were a school teacher. A simple correction would have been more helpful.

Looks huffy to me. And you'll make more progress if you take that great big chip off your shoulder and reread some of the previous posts.

If L = rmv, and m goes down by a factor of ~1000 and r goes up by a factor of ~1000 and v remains mostly unchanged (actually goes up by a factor of a few) what happens to L? And doesn't that answer your question?

 

[russ_watters]

L=rmw ??

The last three replies all manage to miss the whole point. Why is the ang. momentum of the sun so small if it contains 99.9% of the mass of the SS formed from the supposed accretion disk?

You should be able to see that the equation (even the wrong one) includes both an "m" and an "r". So I can't imagine why you can't see the relevance of the previous replies. Or to answer the question directly: it is because mass isn't the only component of angular momentum! How could this be any more obvious?

Heck, at this stage, it should be possible for you to actually calculate the angular momentum of both the sun and Jupiter and compare them.

 

[fizzy]

Heck, at this stage, it should be possible for you to actually calculate the angular momentum of both the sun and Jupiter and compare them.

thanks Russ, you seem to have missed the first sentence of the first post.

 

[fizzy]

Don't know what to say.

http://adsabs.harvard.edu/abs/2013prpl.conf1K039C

The loss of angular momentum is inevitable in star formation processes, and the transportation of angular momentum by a molecular flow is widely thought to be one of the important processes

Yes, that is exactly the kind of thing I have seen too. Hand waving generalities that do not explain how it can loose the ( alleged ) majority of the ang. momentum whilst retaining 99.9% of the mass. It's not 1:1 , obviously, but shedding the majority of a.m. whilst retaining the vast proportion of the mass needs some explaining.

It seems that this is a major problem with simple accretion models that has not in any way been solved.

 

[russ_watters]

thanks Russ, you seem to have missed the first sentence of the first post.

I certainly didn't; if you don't believe numbers given to you, the best way to deal with that is to calculate them yourself and see what you get.

If you do not fix your attitude, this thread will be locked.

 

[russ_watters]

Never mind my last post:

...shedding the majority of a.m. whilst retaining the vast proportion of the mass needs some explaining.

It seems that this is a major problem with simple accretion models that has not in any way been solved.

This is a personal theory of yours - which explains why you are refusing to try to understand what people are telling you - and PF does not permit development of personal theories here. This thread is locked.