Tim Cullen: Planetary Rotation Part 2 – The Gas Giants

Posted: January 23, 2013 by tallbloke in Astronomy, Astrophysics, atmosphere, Cycles, general circulation, solar system dynamics

The first part of this post found a statistical relation between the planetary period of rotation [in days] and the diameter [in kilometres] for the Gas Giants of the Solar System.

image1

However, describing this statistical relationship in more detail is problematical because of our limited understanding of the Gas Giants.

There are various observations, theories, models and calculations in the published literature regarding the Gas Giants. Unfortunately [for me], I find it impossible to separate fact from fiction [speculation] in the literature. This is especially true when the author liberally quotes from other sources that may [or may not] be equally speculative.

Wikipedia [for example] generally provides plenty of introductory bluster that can easily be mistaken for “fact” while their more detailed “small print” is littered with speculation, uncertainty and doubt.

Jupiter

Jupiter is thought to consist of a dense core with a mixture of elements, a surrounding layer of liquid metallic hydrogen with some helium, and an outer layer predominantly of molecular hydrogen.

Beyond this basic outline, there is still considerable uncertainty.

The core is often described as rocky, but its detailed composition is unknown, as are the properties of materials at the temperatures and pressures of those depths

http://en.wikipedia.org/wiki/Jupiter#Internal_structure

Saturn

Standard planetary models suggest that the interior of Saturn is similar to that of Jupiter, having a small rocky core surrounded by hydrogen and helium with trace amounts of various volatiles.

http://en.wikipedia.org/wiki/Saturn#Internal_structure

Uranus

While the model considered above is reasonably standard, it is not unique; other models also satisfy observations. For instance, if substantial amounts of hydrogen and rocky material are mixed in the ice mantle, the total mass of ices in the interior will be lower, and, correspondingly, the total mass of rocks and hydrogen will be higher. Presently available data does not allow science to determine which model is correct.

http://en.wikipedia.org/wiki/Uranus#Internal_structure

Neptune

Neptune‘s internal structure resembles that of Uranus. Its atmosphere forms about 5% to 10% of its mass and extends perhaps 10% to 20% of the way towards the core, where it reaches pressures of about 10 GPa. Increasing concentrations of methane, ammonia and water are found in the lower regions of the atmosphere.

http://en.wikipedia.org/wiki/Neptune#Internal_structure

Wikipedia is fairly precise regarding the measurement of planetary radius for the Gas Giants. Unfortunately, we don’t know precisely what they have measured. It’s definitely not a “rocky core” because there is no certainty regarding their existence. Wikipedia is also fairly precise regarding the measurement of surface temperature and surface gravity. Unfortunately, we don’t know precisely which surfaces have been measured. Again, all I know is that it’s definitely not the “core”.

From the perspective of “atmospheric corotation” it is impossible to know whether the outer observed surfaces [of the Gas Giants] are corotating with the central “core” of the planets.

Therefore, at this stage, I will assume that the figures used in this analysis are general proxies that represent [for the Gas Giants]:

1) The diameter of the “corotating atmosphere”.

2) The rotational period of the “corotating atmosphere”

The initial analysis of “diameter versus rotation” returned 0.9921 for “R Squared”.

Using these very limited data items it is possible to compare the “rotational period” with other attributes that are derived by calculation, such as: radius, circumference, rotation surface velocity, circular surface area and spherical surface area.

Subsequent analysis of these calculated [derived] values returned 0.9988 for “R Squared” when the “circular surface area” is plotted against the “rotation surface velocity”.

image2

Interestingly, this suggests that the unknown “attribute” of the Solar System that may be driving planetary rotation [of the Gas Giants] is associated with their “circular surface area” [visual profile].

image3

Using the derived formula it is possible to calculate a generalised view of the relationship between the “Corotational Radius” and the ”Corotational Period” of the planets in the Solar System.

image4

image5

The next step in the analysis is to determine whether these generalised formulae have any predictive ability when applied to the Terrestrial Planets that have corotating atmospheres.

TO BE CONTINUED….

Footnote

This analysis has “followed the data” – not the glimpse of Phi that appeared in the initial analysis.

However, for anyone looking for an elegant Phi approximation then here is one possibility:

image6

Tim Cullen

MalagaBay – January 2013

Comments
  1. Greg says:

    “Wikipedia [for example] generally provides plenty of introductory bluster that can easily be mistaken for “fact” ”

    Wikipedia generally provides plenty of introductory bluster that can easily be mistaken for “fact” on a lot of topics. Have a look at the bullshit they have about tides (then go and look at what tides really do).

  2. tallbloke says:

    Now this is getting really intersting. R^2=0.9988 when considering cross sectional area of the planetary disc against axial rotation. I like it.

    I suspect Miles Mathis will like it too.

  3. Greg says:

    What about the other “gas giant” in the middle of the solar system? ;)

  4. Greg says:

    TB: Now this is getting really interesting. R^2=0.9988 when considering cross sectional area

    Could be anything proportional to radius squared, Total surface for ex. Don’t get too excited about R2 on just four data points.

  5. Greg says:

    I just did the rad vs period fit from the last post and got a power relation of -1.6594 ~ 5/3
    as a volume vs period that would be p^5

    Tim’s area vs velocity plot shows 1.237 ~ 5/4

    I wondering whether there is a period^5 in here somewhere.

  6. tallbloke says:

    Greg, please elucidate.
    What might period^5 signify?

  7. Greg says:

    No idea, just an observation.

  8. Joe's World {Progressive Evolution} says:

    Tim,

    It is much more complex than that as your single calculation does NOT regenerate an orb. It is based on the planet as a pancake with that single calculation assuming it is at the equator.

    The other problem is that you did not include the SUN also rotates and generates a vast amount of debris coming off of it considering it’s massive size. It is only slightly faster than the planets or we would NOT be able see and to track the sunspots.

    Other than that, you are doing EXCELLENT!

  9. Greg says:

    Actually, I don’t think this level of fit indicates it’s even close to any real relationship. The new offering looks better because two of the planets are very close to each other but any number of functions could be fit that would be a lot closer to the 3 or 4 points.

    Unless there is some fundamental reason for this kind of model I’m not sure it shows anything interesting.

    If there is a curvature and the presumption of a relation to be seen in those four points, I’d be more inclined to see some base line constant.

    Adding a constant and fitting against rotational frequency it looks close to forth power.

    A gas giant of 40000km would not co-rotate. Or to view it the other way around: a rotating body of less the 40000km would not be a gas planet. Maybe that’s why we only see “gas giants”.

  10. Tim Folkerts says:

    Every reference I can find list the period of Neptune as ~ 16.1 hr = ~ 0.67 days, not 0.768 days. That messes up pretty much all of your hypotheses.

    [Reply] The planet observers handbook gives 17hrs 50mins +/- 5 mins for the atmosphere, determined from cloud observations. The magnetic field rotates at the rate you state.

  11. Tim Folkerts says:

    1) The speeds of the other planets matched for both (the number at the top of the post) and (my other sources). That would suggest that these sources consider 16.1 hr = 0.67 hr as an “apples to apples” comparison of rotation speeds.

    2) Which number should be used — the rotation of the “planet” or the “top of the clouds”? Or somewhere in between? Why?

    3)This whole “theory” so far is based on curve-fitting. There has been no fundamental reason given why a larger planet should spin faster.

    4) The fit given above — 360 x^-0.618 — cannot possibly extrapolate much above the size of Jupiter. As a planet got much bigger, it would spin much faster, soon reaching the point where it would spin itself apart. And before hypothesizing that this is why Jupiter is the biggest planet, remember that many other stars have planets much bigger than Jupiter.

    [Reply] Always assuming we have correctly estimated the distances of these star/planet systems. Given Halton Arp’s work, it’s clear we cannot rely on redshift as the final word.

  12. Greg says:

    Tim Folkerts says: That messes up pretty much all of your hypotheses.

    What hypothesis was that? All I can see is an attempt to find a possible mathematical relationship between four points.

    That is not an hypothesis. It is examination of the data. If a relationship is found someone may then develop a hypothesis as to what that relationship means and use it to make a testable hypothesis, which will be falsifiable.

  13. Greg says:

    Tim Folkerts says: 3)This whole “theory” so far is based on curve-fitting.

    Which is why it not a “theory” or even a hypothesis. Only you are calling calling one in order to say it isn’t.

  14. tallbloke says:

    Well said Greg.
    Oi! Folkerts, wind yer neck in!

    And if we’re including magnetosphere’s, what is Earth’s polar ‘diameter’?

  15. tallbloke says:

    “Neptune’s rotation period was established when Voyager 2 detected radio bursts associated with the planet’s magnetic field and having a period of 16.11 hours. This value was inferred to be the rotation period at the level of the planet’s interior where the magnetic field is rooted”

    http://www.britannica.com/EBchecked/topic/409330/Neptune

    So, 16.11 is below the visible outer cloud layer, which was Tim Cullen’s perfectly reasonable definition for diameter. And since the interior is rotating more slowly, there’s no reason to expect gas giants bigger than Jupiter to fly apart like grenades.

  16. Tim Folkerts says:

    Tallbloke,

    The surface gravity of Jupiter is ~ 25 m/s^2, with a centripetal acceleration of ~ 4 m/s^2.

    If you double the radius of Jupiter, the acceleration due to gravity would be expected to about double.

    But the centripetal acceleration at the surface a(c) = r (omega)^2 will rapidly increase, because r is increasing and (by Tim C’s hypothesis) the angular speed will ALSO be increasing rapidly. The net result is that the centripetal acceleration should be expected to increase faster than the gravitational acceleration. At some point the centripetal acceleration would exceed the gravitational acceleration, at which point the outer layers would be unstable and would not be able to stay with the planet. (and the planet would get greatly flattened before this happened.

    This is why the relationship cannot extend to much larger planets.

  17. Joe's World {Progressive Evolution} says:

    Tim,

    Place a hunk of mud on the underside of a Frisbee and it will wobble due to mass imbalance.

    Planetary tilting does not effect water flow at 48 degree latitude change but it does effect the prevailing winds.
    How is a snowflake created?
    Water vapor at freezing has to rotate in order to generate a flat plane of ice crystals to spread out.
    I have actually been through fresh open water in a boat at 26 below C in very calm air. The evaporation balls stung real good on the face when travelling through them, That was evaporation without wind shear.

  18. tallbloke says:

    Tim Folkerts: “This is why the relationship cannot extend to much larger planets.”

    OK Tim F, you’ve convinced me….

    …. That you mainstream radiative theorists really don’t have a clue about planetary atmospheres, basic physics or the actuality of gravity, mass and pressure.
    On a rough estimate, the pressure at the middle of Neptune is going to be on the order of 2 million bar. That’s about 29 million pounds per square inch. On a planet bigger than Jupiter it will be considerably higher.

    That’s one heck of a containment vessel. Why would a ‘rocky core’ (actually a metallic core in a molten silicate sludge) ‘fly apart’ when it is subjected to that sort of pressure from all around it, even if it were to be rotating a multitude of times a minute?

  19. Tim Cullen says:

    Greg says: January 23, 2013 at 9:26 pm
    That is not an hypothesis. It is examination of the data.

    Precisely: Thank you!

  20. Tim Cullen says:

    Greg says: January 23, 2013 at 3:07 pm
    A gas giant of 40000km would not co-rotate.
    Or to view it the other way around: a rotating body of less the 40000km would not be a gas planet. Maybe that’s why we only see “gas giants”.

    Very interesting… thank you.

  21. tallbloke says:

    If as the voyager data shows, lower layers of Neptune’s atmosphere are rotating faster than the visible cloud layer near the top of the atmosphere, there is shear. That will create turbulence, and friction. Friction generates heat. Neptune radiates more energy than arrives from the Sun. Where is the extra energy coming from:

    1) The core (Radioactive decay?)
    2) Somewhere else ??

  22. Greg says:

    I was thinking that forth power relationships are unusual though not unknown. Two examples that sprang to mind are total radiation from black body is T^4 and flow rate of laminar flow in cylindrical pipe is r^4.

    The latter is interesting. The r^2 dependence of the section is obvious, the other r^2 comes from the parabolic profile of the velocity due to viscous drag, zero at edge, max in middle.

    Now there’s a lot of turbulence in these gas giants but maybe some lamination between different levels. Maybe there is a similar pair of power laws operating here.

    If that idea is feasible, it would seem to suggest top down or atmospheric driving being slowed by the core.

  23. tallbloke says:

    Thanks Greg, interesting thoughts. Given that Jupiter’s great spot has been there for hundreds of years, it does seem that there is layering as well as turbulent interactions between layers. Ray Tomes has a fascinating video of Jupiters north pole, showing the harmonics of the cloud interactions.

  24. Tim Folkerts says:

    tallbloke,

    You somehow managed to completely miss the point.

    I was not talking about the whole ball of gas spinning itself to nothing — that would be silly. I was talking about the centrifugal acceleration growing more rapidly then the gravitational acceleration as more mass was added. If the relationship

    R = 13,595 T^(-1.6276)

    holds true, then a gas ball not too much larger than Jupiter would not be able to hold on to the OUTER atmosphere. Hence, there would be an upper limit to the size. Even Jupiter shows a noticeable bulge around the equator as centrifugal force counteracts gravity to a consider extent. A little bigger and faster, and that bulge would become so pronounced that any new material that was added would “spin off”.

    And to head of a potential objection, I offer a dose of a marvelous web comic … http://xkcd.com/123/

    And now back to more important things.

    [Reply] Tim, measurements show that the outer layers of Neptune are spinning SLOWER than deeper layers. As I pointed out above when discussing friction and heat. Do keep up.

  25. Greg says:

    Thanks TB, that is quite remarkable.

    Though r^4 surprised me at first, if there is a driving force that is proportional to either total surface or (more likely) cross-sectional area exposed to sun/solar wind that give r^2 . Then a parabolic verticle velocity gradient would give r^4.

    On the previous thread Wayne has said he’s done some calculations but I don’t really understand what he’s proposing as mechanism. Hopefully he can expand on what he’s done.

  26. tallbloke says:

    Greg,
    Yes, and yet mainstream planetary science hasn’t remarked on it. Why not?

    Considering Earth, looking down on the north pole, we see beach ridges on the post glacially uplifting shores of Siberia and Canada spaced at 45 year intervals (inner planet’s return), with bigger ridges every 90 years (Gleissberg?) and even bigger ridges every 180 and 360 years (gas giant’s plus inner planet’s returns).

    http://tallbloke.wordpress.com/2011/06/30/further-terrestrial-evidence-of-planetary-cycles-affecting-climate/

    Cycles related to these periodicities also turn up in the Nile delta:

    http://tallbloke.wordpress.com/2012/08/18/gale-combs-more-evidence-of-long-term-climate-cycles/

    Conclusion: Harmonics are far more important in the organisation of the solar system than the mainstream is prepared to admit to itself, let alone us.