Tim Cullen: Planetary Rotation Part 3 – Mars, Earth and Venus

Posted: January 24, 2013 by tallbloke in Astronomy, Astrophysics, atmosphere, Electro-magnetism, general circulation, solar system dynamics

In the final part of his study on planetary-atmospheric co-rotation, Tim Cullen extends his heuristic formula to the inner planets, with surprising results.

Planetary Rotation – Mars, Earth and Venus
Tim Cullen – MalagaBay – January 2013


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.

Non-thermal oxygen spatial distribution in the meridian plane.

Z is along the North/South poles of Mars and X is set so as XZ to be meridian plane.


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.


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 [neat 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


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

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.

Tim Cullen


January 2013

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


    By the time our planet has rotated around the sun, we will have seen one point on the sun 13 times.
    If our planet did not orbit the sun, how many times would it have rotated?

    Venus is the only planet to rotate backwards.
    That would have a vast amount of friction against it by the sun comparing with the rest of the planets that generally are in sequence in rotation.

  2. tallbloke says:

    Well, I think the coincidence of Tim’s formula with the Earth’s plasmasphere diameter is pretty cool.
    It’s appropriate that the theoretical corotation period for Venus pans out at 1.6 days too. Phi times Earth’s axial period. Earth and Venus’ orbital periods are in the golden section too.

  3. Tim Cullen says:

    Regarding the rotation of Venus the latest observational evidence 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.


  4. oldbrew says:

    Some more Earth/Mars/Venus comparison data here.

    ‘At this website, we present recent model results that illustrate the thermal, compositional and dynamical responses of the upper atmospheres of Venus, Earth, and Mars to solar EUV-UV flux variability making use of the Venus VTGCM, the Earth TIEGCM, and the Mars MTGCM three-dimensional models. Each of these models has been developed and exercised at the National Center for Atmospheric Research (NCAR) using its CRAY computers.’


  5. tallbloke says:

    With so little Angular Momentum, Venus will be more easily affected by other solar sys perturbations and solar variability.

  6. Tim Cullen says:

    Joe’s World {Progressive Evolution} says: January 24, 2013 at 1:04 pm
    If our planet did not orbit the sun, how many times would it have rotated?

    Pass. My head is spinning on that one 🙂

    Venus is the only planet to rotate backwards.
    That would have a vast amount of friction against it by the sun comparing with the rest of the planets that generally are in sequence in rotation.

    That’s a distinct possibility if Venus is slowing down [or speeding up]
    But [I reckon] you need to define your driving mechanism first.

  7. tallbloke says:

    There is talk of 500mph winds on Venus. It would take 50 hours to go round the equator at that speed.

  8. Tim Cullen says:

    tallbloke says: January 24, 2013 at 5:25 pm
    Venus will be more easily affected by other solar sys perturbations and solar variability.

    Makes good sense… also makes the subject of TSI even more “sensitive”

  9. Tim Cullen says:

    tallbloke says: January 24, 2013 at 5:35 pm
    There is talk of 500mph winds on Venus.

    Rotating in the same direction as the planet?

  10. Tim Cullen says:

    Wikipedia references the 4 day superrotation winds at 500 km/h

    Ultraviolet surveys of Venus show a Y-shaped pattern of cloud formation near the equator indicating that the upper layers of the atmosphere circulate around the planet once every four days, suggesting the presence of winds of up to 500 km/h (311 mph). These winds exist at high altitudes, but the atmosphere at the surface is relatively calm, and most images from the surface reveal little evidence of wind erosion.

  11. tallbloke says:

    My mistake. Make that 80 hours then.

  12. Sparks says:

    Some further reading to blow your mind, from The American Astronomical Society. (I think I have to lie down now)

    On the Corotation Torque in a Radiatively Inefficient Disk

  13. Eric Fithian says:

    This formula brings up a Very Interesting question:
    If, circa 70 million years ago, Earth had four times the present pressure (in order for all those Archosauric megafauna to function), what was its rotation rate at that time?
    The population doesn’t seem to have been dealing with hurricane-force winds…

    This fits into the same category (to me) as that essay regarding the obvious high heat of Earth’s interior– and how it simply *cannot* be left over from the aggregation process of 4 billion years ago….

    We need one of Mr. Wells’s machines to go look!

  14. oldbrew says:

    Eric Fithian says: ‘We need one of Mr. Wells’s machines to go look!’

    Or one of Mr. Mathis’ papers…


  15. oldbrew says:

    Tim C says (in Part 3):
    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.

    Miles Mathis questions existing Coriolis theory, proposing magnetic forces instead.

    ‘Vortex experiments should be done at equator and pole, and compared, not only for direction but speed. Then magnetic fields should be applied, to see how these affect the speed at both places. Then ions should be introduced in varying amounts, to see how this affects the speed of the vortex. Various liquids should be introduced as media for the vortices, using liquids of high and low conductivity. I expect the liquids with higher conductivity would create quicker vortices. Any or all of these experiments would immediately doom the Coriolis explanation, since the Coriolis Effect could not possibly be increased or decreased with ions, magnetism, or varying amounts of conductivity.’


  16. Greg says:

    would not expect Venus to comply with such a rule. Its day is nearly as long as its year and it is turning backwards. This suggests strongly that it has had a “troubled childhood” and suffered at least one massive impact that inverted its rotation.

    It seems to go agains so many other patterns of solar planetary patterns , I would be more surprised if it did fit than if it didn’t.

  17. Max™ says:

    Why doesn’t Venus have a moon?

    What could have cause it to lose a moon?

    What effect would a moon deorbiting have on the surface?