Several months ago I attempted to find some sort of data or graph on the angular momentum (AM) of the Jovian planets. After an exhaustive search it seemed as though nothing would be forthcoming. While there have been attempts to graph the Jovians using the solar system barycenter (SSB) as the orbit axis point, my research has suggested all the solar system planets orbit the Sun. Using the SSB as an axis point might be useful for some analysis, but it still remains an inaccurate method of calculating a planets AM if the orbit axis point is the Sun. The orbit axis point of the Jovians is still a contentious issue, but I believe the results of this project will add further evidence that indeed the Sun is king.

Using JPL Horizons I can retrieve the necessary XYZ coordinates and velocities and plug them into Gerry’s angular momentum formula. Many thanks go to Gerry, this project would not have been possible without him.

It must be noted that the JPL data for each planet uses the Sun centre for calculating distance. Technically this is still not correct and the Sun/Planet barycenter would be more accurate but at this stage I am not aware of this data being in existence.

**Jupiter Angular Momentum Graph**.

Very evident is the influence of Saturn along with the timing of the Jupiter perihelion (closest orbit point) and aphelion (furthest). The blue line is a moving average with the background grey areas being the actual data taken every 5 days. Because the centre of Sun was used as the axis point the actual data is a little choppy (theory). Although the modulation of the planet AM is obvious, very little of this change would be felt at the Sun. For further data on the Jupiter axis point and orbit perturbations see my previous article here: http://landscheidt.auditblogs.com/2009/04/03/which-point-do-the-jovian-planets-orbit/

**LINK.**

*Although over a shorter period the Planet AM graphs using the SSB as axis point showing a clear difference…http://arnholm.org/astro/index.htm*

**Neptune Angular Momentum Graph.**

The Neptune angular momentum graph is quite different, being on the outskirts of the solar system the data is less choppy and the clear influence of Jupiter every 13 years approx is quite staggering. The majority of Neptune’s orbit perturbations are in line with Jupiter, only the modulation of the peaks and troughs is influenced by the remaining Jovians.

*Notice the very clear difference between the 2 axis points. Source* *http://arnholm.org/astro/index.htm*

The SSB derived Neptune graph is clearly a product of the sun moving away from the SSB and dragging Neptune with it, this gives a false reading in the Neptune distance measurement which can also be seen on the Jupiter SSB graph at 1970. I believe the latest Jovian AM graphs prove the existence of the Jovian orbit axis point and also show the correct planet AM data (as near as possible to date). Another outcome of this research will be to nail down exactly what proportion each planet contributes to the overall AM at the Sun. The project is still incomplete but the Jupiter proportion looks to be about 60%. Saturn and Uranus graphs to follow.

UPDATE: P.A.Semi has a paper at http://arxiv.org/ftp/arxiv/papers/0903/0903.5009.pdf

where he produces graphs of all planets calculating planet AM using both axis points. His data is in complete agreement with mine (using Gerry’s formula) and he also shows long term views of the SSB axis graphs.

This long term view of Neptune is particularly interesting, its shows the 172 year down spike each time Uranus is in conjunction, which moves Neptune closest to the SSB and also shows a background trend. The elephant in the room though is that all SSB graphs show a modulation of planet/SSB distance, where as the Sun centered graphs show the planetary perturbations. The failure of the SSB centered graphs to show the all important planetary perturbations suggests to me that all our solar system planets have the Sun as their axis point.

Gerry and I are currently working on a project looking for the missing AM that could finally give a solid link to the Spin-Orbit Coupling debate. Our initial results are very encouraging but we need to double check the data…stay tuned.

I have told you this before Geoff. The orbit axis point of all the planets is the barycenter of the planet and the center of mass the planet is orbiting.

The inner planets are so small compared to the Sun that their orbit point is very close to the center of the Sun. Also because the inner planets are so small, the orbit point of Jupiter is very close to the barycenter of Jupiter and the Sun (not the SSB). The orbit point will be closer and closer to the SSB as you move away from the Sun so the orbit point of Pluto is very close to the SSB. As you can see from your Neptune graphs, the AM is much more stable referenced to the SSB than referenced to the Sun.

REPLY:My research suggests all the solar system planets orbit the Sun. I think you are getting confused with Neptunes orbit, the Sun centered graph shows the stable orbit pattern along with the expected planet perturbations.The Sun centered graph does not show the perturbations. It shows that every 13 year Jupiter is ‘pushing’ the Sun away from Neptune. In a two-body system Sun-planet the planetary AM is constant around the barycenter, not around the Sun. See your graphs, AM is almost constant in the SSB centered.

REPLY:The highs and lows on the sun centered graph is a result of planet perturbations, the fluctuating acceleration changing the AM. The planets influence the solar distance from the SSB but the planets are dragged along with those movements following the Sun instantaneously. AM is never constant regardless of where you measure the axis point, and what we are looking for is not a constant, Neptune via the sun centre is freely able to show the proper fluctuations. If you look closely at the Neptune SSB centered graph you can still see the 13 year trends, but they are masked because the SSB is not the axis point. Do a distance check on JPL and you will see the same.AM is never constant because of the perturbations but in case of Neptune the SSB is a far more accurate axis point than the Sun is. It is of course not exact because the SSB also includes Neptune itself (and Pluto ++)

Put a planet in an orbit ten times that of Pluto and it’s orbit would be the same whether you kept the existing solar system as is or you put all the mass in the existing SSB. The axis point of this new planet would be the barycenter of the existing SSB and the planet, again, not the Sun.

REPLY:I would be very happy if you could prove me wrong, as it would leave to door open to a form of spin orbit coupling. The only way you can do that is via JPL, it should be easy, just use the dates on the peaks of the Neptune Sun centered graph and measure to the SSB, if you are right the distances should all be about the same, make sure you do the measurements over a full orbit cycle. You could also easily show the Sun being “pushed” away from Neptune at that point also.No, the AM should be the same, not the distance, Neptune also has some eccentricity.

REPLY:Going on your logic the distance has to vary (Neptune to Sun), the 171 year period of eccentricity is large and should not come into it in this case. If you need help getting the figures out of JPL just email me.Of course the eccentricity come into this case. The differece between aphelion and perihelion is 100 mill. kilometers, so devide by 10 to get a rough estimate of the average change in 13 years.

Speaking of JPL: I would like to know how to get from the JPL vectors to the AM excel sheet of Carsten. Very detailed and simple explanation of course if I am to make it đź™‚

REPLY:I am in the middle of doing it for Neptune with SSB as axis, will make the spreadsheet available soon.UPDATE:I have been working more on Neptune…its an interesting planet. I plotted the Neptune/Sun distance from 1901-2040 and the plot is quite clear. Only the perihelion and aphelion come into play which should consolidate the axis point, there is no real Jupiter effect.Also here is the Neptune/SSB graph ala Carsten, but using JPL. Notice how choppy the record is, had to smooth it substantially to get a curve, but both graphs look to be very similar. Must admit I am at a loss why 1990 is the low point, velocity and distance look to be strong…I must be missing something, only thing that seems plausible is the Uranus effect on velocity.

http://www.landscheidt.info/images/nep_ssb1901-2040.xls

And if you plot the nep_ssb_distance that will be even smoother than the nep_sun_distance graph.

REPLY:But its not the smoothness we are looking for, what are your comments on the the Neptune/Sun distance graph?Geoff, I have a request: Can you convert your dates (on the x-axes of your graphs) to a more readable format? – say, years in steps of 10? If you are willing to follow-through, I might be able to (in the days/weeks ahead) share some Excel notes on how to do the format-conversions.

REPLY:The date data from JPL is very large, any help with reformatting to a more readable style would be appreciated.lgl,

I misread your comment “And if you plot the nep_ssb_distance that will be even smoother than the nep_sun_distance graph” taking it to mean AM instead of distance.

Finding it difficult to obtain the Neptune_SSB distances but think I have found them in the orbital elements data where they specify semi-major axis. Once plotted the data looks identical to the Neptune/SSB AM graph.

Here is a link to that graph: http://www.landscheidt.info/images/nep_ssb_distance.jpg

Some of this is becoming clearer, if this information is correct then 1990 is actually the closest point between the SSB and Neptune and explains the correlation in distance/AM. At 1990 J is opposite N/U/S putting the Sun on the SSB.

If this data is correct there can be no doubt on the axis point. The Sun is not being pushed away by Jupiter in the Sun/Nep distance graph and the normal elliptical patterns are seen as you would expect from the correct axis point. The SSB/Nep distance graph like the SSB/Nep AM is very messy (the grey shaded area’s being the actual data) and clearly shows a non axis point relationship. I believe using the SSB to calc Neptunes AM is grossly inaccurate, although I can see it being useful in certain situations.

Past attempts to find a balance between the solar AM and planet AM I believe are severely floored. If Gerry or someone else can come up with a formula that calculates the net planet AM in relation to their respective positions I will have a go at trying to do this correctly using 2 methods. I will calculate net planet AM from both the SSB and Sun centre axis points and compare to solar AM, the results could be very interesting.

No, this isn’t the Nep-SSB distance. There is a ‘RG Range; distance from coordinate center (km)’ in JPL vectors and it makes a perfectly smooth curve: http://virakkraft.com/Nep_SSB_dist.xls

REPLY:If the data you have displayed is correct I will have to admit you are on to something. I think we need to check the validity of the data before proceeding. I was tentative of the semi-major axis data because I have seen semi_major axis definitions that vary. Sometimes it is treated as the middle point in an elliptical orbit, but that may not be the focal point. I have plotted the RG values for Sun & SSB and the result is outstanding if correct, the SSB plot is so smooth and yes I can see the Jupiter effect on distance. But I still have questions, if the 2 plots are so close, why do the AM graphs vary so much, and why does the Nep/SSB distance graph I made almost mirror the Nep/SSB AM graph? Perhaps Gerry can offer some advise, but if the planets outside Jupiter do indeed orbit the SSB it will mean there are major consequences that I have been looking for.Nep/SSB/Sun distance RG graph here: http://www.landscheidt.info/images/nep_ssb_sun_distance_rg.jpg

“why do the AM graphs vary so much?”

Because in a perfect world (two-body system) the AM of each of the bodies would be constant around the barycenter, it’s Kepler and Newton.

No planets orbit exactly the SSB (comets probably very close) but the approximation gets better and better the more of the total mass is inside the orbit.

You should delete this whole post and start over again. (It’s mostly a dialog between you and me anyway so nobody should care)

REPLY:That still doesn’t adequately explain the different in the 2 AM graphs, they are vastly different and I am confident of the source data. But the jury is out on the distance data, more work to be done.Why not? AM is supposed to be nearly constant around the SSB but not around any other point. (and the Sun is just any other point in this context). If you believe the JPL data are correct the jury is not out.

REPLY:Its how you use the JPL data I think, it can be a minefield when looking at distance only, I want to get some verification on the Neptune distance. Back to the AM graphs, if the distance is almost the same that only leaves a change in velocity, I might also look into that. There is something here I can smell it.I guess the only thing I can think of to suggest is to obtain a JPL barycentric planetary ephemeris file such as DE 405 or 406 for all the planets, major asteroids, and the Sun. Then compute the angular momentum for each planet&moons barycenter with respect to the SSB using the cross product of position and velocity. Same for each asteroid and planet without moons. Sum all these AMs at each time point. Now do the barycentric angular momentum calculations for the Sun at those same time points, using the same ephemeris file for consistency. Any difference between the total planetary, moons, and asteroids and the Sun’s AM at the same time points could reasonably be attributed to solar AM transfer from orbit AM to rotational AM. Isn’t this what Carsten attempted to do originally? Because the amount of AM going into solar rotation is probably very small, you will have to actually compare the numbers with high precision, not just eyeball the total AM curves.

REPLY:Agree, that would be my plan but believe the netting of the planet AM would be the hard part, also your last statement sums it up well.I would be interested to see what you could come up with for Neptune/SSB distance figures from 1900-2040. Is the RG value on the vectors table correct to your knowledge?, I have seen some other “R” values on the observer table that calculate distance from the Sun centre even if the SSB is selected.

I am not familiar with the current nomenclature, but it should be explained somewhere. It sounds like ‘RG’ may be the range vector to the osculating ellipse, in which case I’m not sure it has any value to you.

I need to clarify my remark about differencing total planetary and solar AM. What I should have said is that if you add those two quantities you should get some near-constant nonzero value that is close to the total angular momentum of the solar system. What you are looking for are deviations from a constant value over time. Hopefully you would be able to make the case that small deviations from a constant value represent solar orbit to solar rotation AM transfer.

Geoff,

If your JPL Horizons data includes the asteroids Juno, Vesta, Ceres, and Pallas, and if it has the heliocentric coordinates of the planet-moon barycenters of planets with one or more moons, you should be able to calculate exactly the same near-constant solar system AM just by adding up the AMs of the individual planets, asteroids, and planet-moon barycenters, based on their heliocentric coordinates. In this (heliocentric) inertial frame, the Sun’s orbital angular momentum is exactly zero. The contribution of the Sun’s barycentric motion will have been absorbed by the planetary AMs, saving you the trouble of adding it in separately, as I first suggested.

As in my previously suggested scenario, any variations in the totals of the planetary AMS can be construed to be from AM transferred into solar rotation changes.

REPLY:Looking at JPL all that data should be available, but I am not sure adding the planet AM together is going to prove anything, it will always be a greater value regardless of the axis point used? Perhaps I have not explained myself fully when speaking of netted planet AM, what I would like to calculate is the residual planet AM ie how the position of each planet effects the total. If Jup and Sat are together you would add the 2 values together, if opposed the subtract one from the other. To do this you would need to measure every planets longitude in relation to Jup then calculate how that planets AM would be either added or subtracted from the Jup AM. Sounds like a program more than a formula? but once we have this value there should be a direct mathematical relationship between the solar AM and planet AM residual.Yes, it will be the sum total of the orbital angular momentum in the entire solar system. It should be exactly what you need – constant because of the Law of Conservation of Angular Momentum except for small variations from solar spin-orbit coupling. The only things you add together are the individual AMs at each time point. The constant value of total solar system AM is the baseline and variations from that baseline can be examined to the full precision available. I suggest you do it in Excel at some epoch time in the future and pull the calculation columns down as far as you like into the past. Then calculate the mean value of all your total AM points, subtract that from each AM and voila – you have your solar rotational variation curve.

I understand you now, sounds like a job for next week. Thanks GerryREPLY: