Planetary Rotation of Jupiter, Saturn, and the Earth

Jupiter and Saturn rotate far more rapidly than they logically should! Their extensive and thick atmospheres experience substantial turbulence due to those planets' very rapid rotation. This turbulence must necessarily convert some kinetic energy of rotation into frictional heat. Given the extremely long time that Jupiter and Saturn have existed (probably around five billion years), those frictional heat losses should have extensively slowed the rotation of those planets. However, that is apparently NOT the case!

Taking Jupiter as an example, it is about 11 times the diameter of Earth. It rotates on its axis in about 10 hours, about two-and-a-half times faster than Earth. This means that the equatorial surface of Jupiter moves at about 25 times the speed of Earth's equatorial surface. That means that the portion of Jupiter that we see, at the equator, is traveling at around 25,000 miles per hour!

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The atmosphere above the surface is not physically attached to it, so there must be a continuous "sliding back" of the atmosphere over the surface. This is necessarily true, and it represents one element of the conversion of the kinetic energy of planet rotation into frictional heating of the atmosphere. Evidence of this slippage is the turbulent patterns in the atmosphere of Jupiter.

If the surfaces were similar and the gases of the atmosphere had similar densities and dynamic viscosities to that of the Earth, this effect should be approximately proportional to the square of the velocities involved. This means that this frictional kinetic energy loss for Jupiter would be 625 times as great PER UNIT AREA as for Earth. Since Jupiter's total surface area is around 120 times the area of Earth, this means the TOTAL planetary frictional drag of its atmosphere and surface must be 75,000 times as great at Earth's situation.

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The effects are certainly even larger than this. Due to the low temperatures present in the atmosphere of Jupiter and Saturn, component chemicals such as methane and ammonia are certainly liquid or slush in some parts of the atmosphere, which would have far higher dynamic viscosity and therefore greater frictional loss.

These arguments apply equally within Jupiter's atmosphere, between layers of that atmosphere. With the tremendous velocities involved, even minor differential velocities are huge. The frictional drag effect is again magnified by at least 75,000 over the same effects in the Earth's atmosphere. Considering the extreme depth of Jupiter's atmosphere (compared with the extreme shallowness of Earth's atmosphere), THIS effect is even multiplied MORE for Jupiter, but to an unknown factor.

Collectively, these frictional losses result in heating of the materials of the Jupiter atmosphere, which causes much of the turbulence seen there. Differential heating of the atmosphere causes convection cells. Combining these cells' movements with the planet's rotation causes the visible bands and turbulence areas such as the Great Red Spot.

Given the known mass of Jupiter and its rotational period, and given an estimate of the radial density distribution of the entire planet, it is possible to reasonably estimate the rotational inertia of the planet. With this value, it is easy to calculate the amount of rotational kinetic energy contained in its axial rotation.

It is considerably more involved to estimate the actual atmospheric frictional drag heating that was described above. The logic that it is about 75,000 times the situation for the Earth was based on considering similar gases and similar surface contours, both of which are certainly at least partly incorrect. The case being made here is that the total planetary atmospheric frictional drag heating IS significant. Any preliminary calculations with reasonable assumptions will confirm this. Regardless of what assumptions are made, simple calculations show these energy amounts to be quite substantial.

Since Jupiter has been rotating for around five billion years, and since all theories regarding Jupiter agree that its atmosphere has existed for that entire period, that's five billion years of having its kinetic energy of rotation being slowly converted to kinetic atmospheric heating. Those preliminary calculations mentioned above DEFINITELY imply that the planet should have severely slowed in rotation rate by now. (Since those effects are approximately proportional to the SQUARE of the rotational velocity, and also the square of the planet's radius, the similar slowing effect on the Earth's rotation has been relatively insignificant, but has still been detected and measured.)

But Jupiter presently rotates quite rapidly! Why?

There are only a few possibilities.

The first of these possibilities seems most likely to me. IF this were the case, it would have an interesting implication. It would suggest that the early existence of large gaseous objects like the Sun and Jupiter would invariably involve EXTREMELY rapid rotation rates! If this would turn out to be true, that would imply that some or most or all stars had very high rotation rates early in their existence.

If some version of a nebular origin for the Solar System and its major components is true, this reasoning fits in very well. If a diffuse cloud of particles was initially distributed throughout the space now occupied by the Solar System, those constituent particles would not likely fall perfectly radially inward. They would certainly bring with them tiny components of angular momentum. As this process continued, a favored plane would eventually arise (which we now call the Ecliptic). Since that angular momentum must be maintained by the Laws of physics as we know them, the cloud would necessarily continue to rotate faster and faster as it gravitationally became smaller.

This faster and faster rotation would have allowed eddies to appear, which might condense to form the various planets. By the time that each of the planets and the Sun condensed to about their present size, the rotation rates would have increased, due to that conservation of angular momentum. Each of the larger planets and the Sun would have condensed from a larger initial cloud of particles, which were also initially farther from the ultimate location of the planet. This would allow the great likelihood that larger planets would generally have much more angular momentum as a result and therefore have faster rotation rates.

If this premise is true, it implies that Jupiter and Saturn once rotated far faster than they even do today. This would mean that they would be much more oblate (flattened due to rotation) than they are today. Such very high rotation rates and extreme oblateness, could have represented a possible explanation for the source of the materials for the large satellites that are now in equatorial orbits around them.

Another reason that this premise is particularly interesting is that it could explain a different phenomenon seen in space. If the surface of a new star was uniformly radiative, no unusual effect would be seen by astronomers except for a widening of spectral lines due to the differential limb velocities involved. However, if that extremely rapidly rotating early star had significant persistent star spots (sunspots) then each time the star rotated, relatively regular variations of the intensity of perceived radiation would exist. If the star spots were very persistent, and the early star rotated extremely rapidly, this could give an appearance very similar to the appearance of some of the objects we call variable stars, including irregular variables.

If this line of thought were true, there would be two certain effects that would be recognizable. As the star slowed in rotation, that slowing should be great enough to be measurable, particularly in very young stars, in regular lengthening of the period of the observed variability. As the persistent star spots eventually faded and were replaced by others in different locations on the surface of these rapidly rotating stars, occasional rather sudden apparent shifts should be observed in the exact timing of the received variations.

This presentation is only suggesting the theoretical existence of a frictional slowing of the rotational motion of large planets that rotate rapidly and that have extensive atmospheres. It is left to others to investigate the empirical aspects of this theoretical phenomenon.

The fact that long-term frictional losses of kinetic energy would almost certainly occur represents an entropy situation. It is presented that Jupiter or the Sun had earlier rotated more rapidly, and that frictional effects in their gases/atmosphere have converted some of that kinetic energy of rotation into heat. A consequence of that would be that less rotational angular momentum as well. This would result in a loss of angular momentum over those billions of years. This is not a violation of the conservation of angular momentum because of the frictional energy losses.

Jupiter's Great Red Spot

Associated with this discussion, a possible explanation for the persistence of Jupiter's Great Red Spot might exist. Remembering that the rotational velocity of equatorial gases is around 25,000 miles per hour, there must be frictional losses deep within Jupiter, at where a "surface" might be. On Earth, there are some irregular surface areas, like mountainous areas, where the Earth's atmosphere is "caught" more than happens over smooth oceans. Such irregularities tend to cause differential surface air velocity patterns. In the far faster moving atmosphere of Jupiter, these effects would be greatly increased.

This seems to suggest that there might be such an irregular area on that deep "surface" of Jupiter, roughly under either the northern or southern extent of the Great Red Spot. If the deep atmosphere was therefore caught by such surface irregularities, a persistent velocity differential would result between the northern and southern regions under the Great Red Spot, which would then naturally create a persistent cyclonic rotation.

Most specifically, the location of the Great Red Spot would remain relatively constant in both latitude and longitude with that inner surface. Variations of the differential velocities would be possible, and even likely, which would possibly also explain why the Spot has sometimes seemed to disappear from view, only to later reappear in its original position.

If this is true, then the precise rotation rate of the Great Red Spot would represent an accurate rotation rate of the actual planet surface that we have never seen. This might be a useful new bit of information about Jupiter, and even Saturn, because it might suggest a likely depth of their atmospheres to that "solid" surface.

This presentation was first placed on the Internet in March 1998.

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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago