The second part of this post calculated a generalised view of the relationship between the “Corotational Radius” and the ”Corotational Period” of the planets in the Solar System.
This third [and final] instalment examines whether these generalised formulae have any predictive ability when applied to the Terrestrial Planets with atmospheres.
Precise measurement of the rotational periods of Mars, Earth and Venus allows the generalised formula to be used to predict an atmospheric “corotation radius” for each planet with an atmosphere.
The predicted “corotation radius” for Mars is 13,040 kilometres.
Unfortunately, I haven’t [yet] found any published papers that provide detailed information regarding the corotation of the Martian atmosphere [so please comment if you know of any].
However, I have found one paper that indicates the atmosphere of Mars does corotate:
The dawn-dusk flow asymmetry is of particular interest, because it relates to the ionosphere/upper atmosphere co-rotation and super-rotation at Mars and Venus.
Solar wind-ionosphere forcing: Impact on the atmosphere of Mars and Venus
R. Lundin, S. Barabash, H. Perez-de-Tejada
Additionally, I have located a diagram of a “non-thermal oxygen spatial distribution in the meridian plane” for Mars [generated by a Monte-Carlo simulation] that indicates the oxygen atmosphere extends [at least] to 13,000 kilometres.
Mars exospheric thermal and non-thermal components: Seasonal and local variations
M. Yagia, F. Leblanca, J.Y. Chaufrayb, F. Gonzalez-Galindoc, S. Hessd, R. Modolod
Therefore, there is supporting [but not conclusive] evidence that suggests the predicted atmospheric “corotation radius” is within the realms of possibility.
The predicted “corotation radius” for Earth is 13,656 kilometres.
The corotation of the Earth’s atmosphere is generally accepted to extend into the plasmasphere where it eventually breaks down at the plasmapause:
In the case of earth’s magnetosphere, external stresses imposed by the solar wind impede corotation beyond the plasmapause at about 5 earth radii distance [e.g., Brice, 1967].
Inertial Limit on Corotation – T. W. Hill
Space Physics and Astronomy Department, Rice University, Houston, Texas
Journal of Geophysical Research – 1979
Modern satellite images [in the ultra violet spectrum] provide an accurate picture of the Earth’s plasmasphere where the circular boundary of the plasmapause can be clearly identified on the night-side of the Earth.
IMAGE Extreme Ultraviolet Imager
Using “pixel counting” it is possible to calculate a radial distance to the plasmapause of 13,626 kilometres. Although this technique is “subject to some interpretation” it does provide supporting evidence validating the 13,656 kilometres prediction.
One of the more interesting aspects of the derived formula is that it calculates a specific “Corotational Radius” for each “Corotational Period”.
This becomes intriguing when there is evidence showing the Earth’s “Length of Day” [corotation period] has been slowly increasing for million of years because this implies the atmospheric corotation radius has been slowly declining.
400 million years ago, years lasted 410 days, meaning that days were 21 hours long. This is because the Earth’s speed of rotation was once much faster than it is today. When the Earth formed, a day was around 6 hours long; it has been slowing gradually, but slowed more rapidly when liquid water began to form (~3.5Ga).
The Length of the Day: A Cosmological Perspective
Arbab I. Arbab
Unfortunately, the concept of a shrinking atmosphere can be interpreted in several ways, such as a loss of atmospheric gases [to space] or increasing air pressure.
No doubt there are many other possible interpretations.
Another intriguing aspect of this statistical relationship between the Earth and the Gas Giants [through the generalised formula] is that it may be interpreted as supportive of J. M. Herndon’s theory “that Earth originated as a Jupiter-like gas giant”.
New Indivisible Geoscience Paradigm
Marvin Herndon’s Early Earth Formation as a Jupiter-like Gas Giant
The predicted “corotation radius” for Venus is 1.7804 kilometres.
Clearly, this is a massive failure because the radius of Venus is 6,051.8 kilometres.
However, Venus is worthy of further examination because it might provide some insight that explains why this prediction failed – but [needless to say] Venus is a very controversial topic.
One of the curious facets of Venus is its long rotation period of 243.018 days.
In the context of the formula predictions Venus should be a large rock – not a planet.
But Venus is a large terrestrial planet that happens to rotate very slowly.
Another curious facet is that the atmosphere of Venus does not corotate.
The wind speed increases with altitude until [near the clouds tops] the atmosphere has become super-rotational with a rotational period of about four days.
The solid body of Venus rotates very slowly, with a period of 243 days, in the opposite direction to the general rotation of the solar system.
The general circulation of the Venus atmosphere is dominated by rotation of the atmosphere in the same direction as that of the solid planet but increasing in speed with height from the surface up to the cloud tops. It reaches maximum speed near the cloud tops, where the rotation period is about 4 days.
Atmospheric dynamics are thus very different on Venus and on Earth.
Coriolis forces are relatively weak because of slow planetary rotation. Instead, the atmosphere itself develops a rotation by internal mechanisms that are not yet fully understood.
The remarkable spin of the Venusian atmosphere is one of the major puzzles in atmospheric science. In the absence of forcing mechanisms, friction and wave drag would be expected to bring the atmosphere into co-rotation with the solid planet.
Venus – P J Gierasch and Y L Yung – 2003
The spin of the Venus atmosphere is remarkable and puzzling because intuition tells us that in the absence of forcing, friction will bring the atmosphere into corotation with the solid planet. But the nature of “friction” is also unclear, as is its magnitude. It may be that the Venus atmospheric rotation is controlled by balances between different large-scale flow components, and that friction, in the sense of molecular viscosity or small-scale turbulent dissipation, is unimportant.
Venus II: Geology, Geophysics, Atmosphere, and Solar Wind Environment
Stephen Wesley Bougher,Roger J. Phillips
Surprisingly, for the mainstream, the superrotating upper atmosphere is transferring momentum downwards towards the surface.
Maintaining superrotation in Venus’ atmosphere is a concern, because the faster, high-level regions and the slower, lower-level regions exert drag forces on each other. This tends to slow the air at the higher levels and speed it up at the lower levels, producing a transfer of angular momentum downward.
Solar System Astrophysics – Volume 2 – Eugene F. Milone, William J. F. Wilson
The most important of those forces is due to the dense atmosphere – more than 90 times the pressure of Earth’s and high-speed weather systems, which are believed to change the planet’s rotation rate through friction with the surface.
Evidently, this “top down” transfer of momentum is being explained away by the creative modelling of “vertically propagating waves” and “Hadley driver cells”.
Although this “top down” transfer of momentum is not [apparently] referenced in the context of the climate it may well contribute [via compression and/or friction] to the “anomalies with Venus’ surface temperature”.
Some of the unique elements that are discussed are the anomalies with Venus’ surface temperature (the huge greenhouse effect causes the surface to rise to 460°C, without which would plummet as low as -40°C), its unusual lack of solar radiation (despite being closer to the Sun, Venus receives less solar radiation than Earth due to its dense cloud cover reflecting 76% back) and the juxtaposition of its atmosphere and planetary rotation (wind speeds can climb up to 200 m/s, much faster than Venus’ sidereal day of 243 Earth-days).
Towards Understanding the Climate of Venus
Bengtsson, L.; Bonnet, R.-M.; Grinspoon, D.; Koumoutsaris, S.; Lebonnois, S.; Titov, D.
Interestingly, this “top down” transfer of momentum may cause the planetary rotation period to [very slowly] decrease i.e. the planet begins to spin more rapidly.
In a geological timeframe this would slowly reduce the drag on the upper atmosphere and [probably] result in a corotating atmosphere with [based upon the predictive formula] a corotation period of about 1.6 days.
However, this assumption is contradicted by observational evidence that indicates Venus’ rotation rate is actually slowing down:
New measurements from ESA’s Venus Express spacecraft shows that Venus’ rotation rate is about 6.5 minutes slower than previous measurements taken 16 years ago by the Magellan spacecraft. Using infrared instruments to peer through the planet’s dense atmosphere, Venus Express found surface features weren’t where the scientists expected them to be.
“When the two maps did not align, I first thought there was a mistake in my calculations as Magellan measured the value very accurately, but we have checked every possible error we could think of,” said Nils Müller, a planetary scientist at the DLR German Aerospace Centre, lead author of a research paper investigating the rotation.
Using the VIRTIS infrared instrument, scientists discovered that some surface features were displaced by up to 20 km from where they should be given the accepted rotation rate as measured by the Magellan orbiter in the early 1990s.
Over its four-year mission, Magellan determined the length of the day on Venus as being equal to 243.0185 Earth days. But the data from Venus Express indicate the length of the Venus day is on average 6.5 minutes longer.
On the other hand, other recent atmospheric models have shown that the planet could have weather cycles stretching over decades, which could lead to equally long-term changes in the rotation period. Other effects could also be at work, including exchanges of angular momentum between Venus and the Earth when the two planets are relatively close to each other.