Tim Cullen: Planetary Axial Tilt Demystified

Posted: April 8, 2015 by tallbloke in Celestial Mechanics
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The Earth is from Saturn - The Moon is from Jupiter

The concept of Axial Tilt [aka Obliquity] is very straightforward.

In astronomy, axial tilt, also known as obliquity, is the angle between an object’s rotational axis and its orbital axis, or, equivalently, the angle between its equatorial plane and orbital plane.

https://en.wikipedia.org/wiki/Axial_tilt

Earth Moon

However, the concept has gone pear-shaped thanks to some Eccentric Astronomers.

gone pear-shaped
British slang for events taking an unexpected turn for the worse.

http://www.urbandictionary.com/define.php?term=gone%20pear-shaped

Firstly, there are two “standard methods” for specifying Axial Tilt.

Secondly, neither of these “standard methods” conform to the definition of Axial Tilt.

This is because the two “standard methods” [for whatever reasons] confuse the simple concept of Axial Tilt by:
a) Introducing conflicting concepts of a North Pole.
b) Conflating the concept of Axial Tilt with Rotation.
c) Applying arbitrary adjustments to the concept.

The IAU looks for inspiration from a wobbly invention called the Invariable Plane.

The International Astronomical Union (IAU) defines the north pole as that which lies on the north side of the invariable plane of the Solar System; under this system Venus’ tilt is 3°, it rotates retrograde, and the right hand rule does not apply.

https://en.wikipedia.org/wiki/Axial_tilt

The invariable plane of a planetary system, also called Laplace’s invariable plane, is the plane passing through its barycenter (center of mass) perpendicular to its angular momentum vector.

In the Solar System, about 98% of this effect is contributed by the orbital angular momenta of the four jovian planets (Jupiter, Saturn, Uranus, and Neptune).

The invariable plane is within 0.5° of the orbital plane of Jupiter, and may be regarded as the weighted average of all planetary orbital and rotational planes.

All planetary orbital planes wobble around the invariable plane, meaning that they orbit their primary while their inclinations with respect to the invariable plane vary, both of which are caused by the gravitational perturbation of the other planets.

https://en.wikipedia.org/wiki/Invariable_plane

NASA, on the other hand, applies the “right hand rule” when it grapples with Axial Tilt.

Right Hand Rule

NASA defines the north pole with the right hand rule, as above; under this system, Venus is tilted 177° (“upside down”) and rotates direct.

https://en.wikipedia.org/wiki/Axial_tilt

Wikipedia thinks the “results are equivalent and neither system is more correct”.

Perhaps, when they state that “neither system is more correct” what they really mean is that both systems are wrong and misleading.

In their Geocentric Wisdom the Sun is awarded [under both systems] an Axial Tilt relative to the Geocentric Ecliptic as if the Sun orbited the Earth.

NASA excels in Geocentric Wisdom by randomly awarding the Moon an Axial Tilt relative to the Geocentric Ecliptic instead of its orbital axis.

Wikipedia - NASA - IAU

https://en.wikipedia.org/wiki/Axial_tilt

Considering Axial Tilt data is in short supply its very surprising the usual suspects are so casual with their data.

This impression is reinforced when it comes to the Axial Tilt of Ceres because the Eccentric Astronomers just quote nice round numbers like three or four or five.

Axial tilt ≈ 3°
http://en.wikipedia.org/wiki/Ceres_%28dwarf_planet%29

Ceres has a very small axial tilt of 4±5 degrees.
http://solarviews.com/eng/ceres.htm

This means that Ceres’ axial tilt is very small—about 3°.
http://www.cs.mcgill.ca/~rwest/link-suggestion/wpcd_2008-09_augmented/wp/c/Ceres_%2528dwarf_planet%2529.htm

But throughout Ceres’s year (4.6 Earth years), you wouldn’t see much seasonal temperature changes because of the object’s low axial tilt (3 percent).
http://www.space.com/28640-living-on-ceres-asteroid-belt.html

Ceres is a celestial body that is by far the largest and most massive asteroid in the belt between Mars and Jupiter.

It revolves around the sun every 1679.819 days with a very small axial tilt.
http://www.universetoday.com/48671/celestial-body/

Unpicking and correcting the NASA data results in the following table based upon the [original] simple concept of Axial Tilt.

Axial Tilt - Planets

Upon first inspection, the planetary Axial Tilt data appears to be just random data.

Axial Tilt - Plot

There is no obvious relationship between Axial Tilt and Heliocentric Inclinations.

Axial Tilt vs Inclination

But when the data is sorted by Axial Tilt the terrestrial planets conspicuously fall into two sequenced groups – where only [the Velikovskian] Venus is very modestly out of kilter.

Planetary Groups

However, it is not unreasonable to assume that the Axial Tilt of Venus will be fully assimilated into the Jupiter Group sequence when her slowing retrograde rotation finally becomes a fully spun up prograde rotation.

Spinning Venus is slowing down
Over its four-year mission, NASA’s Magellan orbiter was able to watch surface features rotate beneath it, allowing scientists to determine that the length of a day on Venus was 243.0185 Earth days.

However, the landforms seen by Venus Express some 16 years later could only be lined up with those observed by Magellan if the length of the Venus day is on average 6.5 minutes longer.

ESA – Major Discoveries by Venus Express: 2006-2014
http://sci.esa.int/venus-express/54064-3-spinning-venus-is-slowing-down/

All the planets of the Solar System orbit the Sun in an anti-clockwise direction as viewed from above Earth’s north pole.

Most planets also rotate on their axes in an anti-clockwise direction, but Venus rotates clockwise (called “retrograde” rotation) once every 243 Earth days – the slowest rotation period of any planet.

https://en.wikipedia.org/wiki/Venus

Periodic close contacts with a “cometary Venus” (which had been ejected from Jupiter) had caused the Exodus events (c. 1500 BCE) and Joshua’s subsequent “sun standing still” (Joshua 10:12 and 13) incident.

https://en.wikipedia.org/wiki/Immanuel_Velikovsky

The clear implication is that [both] Jupiter and Saturn are ejecting Moons [and Cometary Blobs] into the inner Solar System where they finally settle to become terrestrial planets.

There are 173 known natural satellites orbiting planets in the Solar System, as well as eight known to orbit IAU-listed dwarf planets.

Of the inner planets, Mercury and Venus have no natural satellites; Earth has one large natural satellite, known as the Moon; and Mars has two tiny natural satellites, Phobos and Deimos.

The giant planets have extensive systems of natural satellites, including half a dozen comparable in size to Earth’s Moon: the four Galilean moons, Saturn’s Titan, and Neptune’s Triton.

Saturn has an additional six mid-sized natural satellites massive enough to have achieved hydrostatic equilibrium, and Uranus has five.

https://en.wikipedia.org/wiki/Natural_satellite

Planetary Groups Graph

This is hardly surprising given the large collection of Moons accumulated by Jupiter and Saturn.

Moons
In the 1992 John Gray realised that Men Are from Mars, Women Are from Venus and in 2015 it is evident that The Earth is from Saturn – The Moon is from Jupiter.

Men Are from Mars, Women Are from Venus is a book written by an American author and relationship counselor John Gray.

It has sold more than 50 million copies and according to CNN it was the “highest ranked work of non-fiction” of the 1990s and spent 121 weeks on the bestseller list.

The book states that most of common relationship problems between men and women are a result of fundamental psychological differences between the genders, which the author exemplifies by means of its eponymous metaphor: that men and women are from distinct planets – men from Mars and women from Venus – and that each gender is acclimated to its own planet’s society and customs, but not to those of the other.

https://en.wikipedia.org/wiki/Men_Are_from_Mars,_Women_Are_from_Venus

The satellite systems of the four giant planets

As Above So Below – Georgi Gladyshev
https://malagabay.wordpress.com/2014/05/05/as-above-so-below-georgi-gladyshev/

Comments
  1. oldbrew says:

    The Venus rotation period only needs to slow slightly more, i.e. from its current 243.018 days to 243.5 days, to fall into an exact 3:2 ratio with Earth’s orbit period. Also at 243.426 days it would be exactly 12:13 with its own orbit period.

    NB Venus ‘length of day’ is a different thing altogether: 116.75 days.
    See ‘orbital parameters’: http://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html

  2. Roger Clague says:

    The Earth is from Saturn – The Moon is from Jupiter.

    I noticed these 2 groups of axial tilt values a few years ago
    .
    The clear implication is that [both] Jupiter and Saturn are ejecting Moons [and Cometary Blobs] into the inner Solar System where they finally settle to become terrestrial planets.

    Are there more Moons to come from Jupiter and Saturn?
    What causes a Moon to form from J and S?
    Why is the J group tilt near 0 and the S group 23-28?

    There is theory that the Earth tilt is because it is a spinning tetrahedron.
    tetrahedral angle = 20. Moon adds 3.
    A terahedron is the natural shape for a cooling body.

    http://en.wikipedia.org/wiki/Tetrahedral_hypothesis
    Especially:
    William Lowthian Green (1875). Vestiges of the molten globe, as exhibited in the figure of the earth, volcanic action and physiography. London: E. Stanford. OCLC 3571917.

    This is brilliant book.

  3. Paul Vaughan says:

    @ Roger Clague

    Thanks for the (Tetrahedral ) Tip – —- The True “Asian Edge” …

    “Be very sure that science to-day is committed to nothing but “guesses” on the still unknown figure of the Earth. We are doing to-day, in the last analysis, no more than that first man, whoever and wherever and whenever he was, who said, “Perhaps it is like this,” and set down his crude lines of an island in a sea. We know a great many facts about a great many things, and a great many things about a great many facts; and this multitude of facts and things is just exactly our confusion. The facts are facts, but they are contradictory facts; they have not fused into the one great truth about the one Earth of which we know–a little. We have girdled the globe in ships on the surface of its waters, we have rounded the unknown line of its curve under its waters, and we are making our own curves through its air as we fly above it. But no man has ever seen the Earth. It is invisible. We talk of the secrets of the frozen North; they are no more than a handful of the secrets of the Earth. It lies over the Sun and under the Moon, giving everything, but forever withholding the sum of everything–the right image of its own true, unimaginable form.”

    Amen.

  4. oldbrew says:

    ‘The Moon is from Jupiter’ – maybe that’s why 2 Jupiter orbits equals 25 Draconic years?

    http://en.wikipedia.org/wiki/Year#Draconic_year

  5. tim cullen says:

    @ Roger Clague says: April 8, 2015 at 2:28 pm
    Interesting link – thank you

    @ oldbrew says:April 8, 2015 at 7:54 pm
    I was wondering whether there might be some new resonance to find…
    Looks like that angle of attack might prove fruitful… good luck digging.

  6. rishrac says:

    Right now the earth circles the sun in an almost even plane around the sun at the equator. Suppose at some point the earth starts to orbit around the sun where it is above and below the equator at a 10 deg angle. Would the solar radiation be the same as it is now? I can see how that could happen. A nearby star could pull the sun off it’s current trajectory and the earth, and other planets, would have to spiral towards the sun. A change of direction, up or down. It might be recurring. I think the higher the angle, the less radiation, relatively. For instance, if the earth were circling the sun at sun latitude 30 deg. would the earth be colder?

  7. oldbrew says:

    136 Jupiter orbits = 1431 full moon cycles = 1700 draconic years
    In Fibonacci numbers:
    136 = 34 x 2²
    1431 = 13 x 55 x 2, +1
    1700 = 34 x 5² x 2

    Jupiter orbits: FMC is a 100% match, draconic years is 9.4 days less (in 1613.315~ years).

    http://en.wikipedia.org/wiki/Full_moon_cycle#Explanation

    FC = full moon cycle, SM = synodic month, AM = anomalistic month

  8. husq says:

    > Roger Clague says:, There is theory that the Earth tilt is because it is a spinning tetrahedron.<

    Hmm….(page 7)

    A further statement from Rudolf Steiner gave the impulse: In a lecture about the causes of earthly volcanism, Steiner indicated that on the basis of his spiritual scientific researches, the earth
    in its foundational form was not a sphere but rather had at its basis a “kind of tetrahedron”:
    In Middle America, at the south pole, in the Caucasus (mountains) and in Japan, are the four corners of the tetrahedron, a form that was created out of the cosmos through the joining together of four triangles.

    http://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CCEQFjAA&url=http%3A%2F%2Fwww.frankchester.com%2Fwp-content%2Fuploads%2F2012%2F03%2FNew-Forms-Technology-Booklet-v3-black-web.pdf&ei=QF4mVbSVD4PuaNimgZgD&usg=AFQjCNHHU3X1ZpBa58PafyAlKQ9yZWPh0g&bvm=bv.90237346,d.bGg

    In 2008, scientists at Uppsala University in Sweden published findings that appeared to confirm that the core of the earth is a cube (Translator note: Specifically, the round earth’s core has a cubical iron crystalline structure and not a hexagonal one as assumed in older models)

    http://www.sciencedaily.com/releases/2008/02/080208091314.htm

  9. Roger Clague says:

    husq says:
    April 9, 2015 at 12:17 pm

    Interesting article, especially about the Earth being chesterhedron, a tetrahedron rotated in a cube.
    Miles Mathis convincingly claims atoms are made up of tetrahedral alpha particle

    My theory is that the 23-28 tilts for Earth, Mars, Saturn and Neptune are because of the tetrahedral inner shape, plus effect of moons.
    Cooling produces solid blocks (continents) that migrate to the corners of a tetrahedron.
    Tetrahedron has least surface/volume ratio. Thus best shape to prevent further cooling, according to Le Chatilier Principle.
    The planet tilts to lower the C.G.
    Mercury and Venus are too hot for solid blocks to form and migrate.
    Uranus, on its side is stable for a tetrahedron rotating.
    The only problem is why is Jupiter not at 23-28 tilt?
    Possibly because it has a large mass and magnetic field, too much energy for core to form solid blocks which can migrate.

  10. Power Grab says:

    Can’t remember where I heard it, but some say the New Jerusalem will be a pyramid (perhaps “tetrahedron” would be more accurate).

  11. ferdberple says:

    The Venus rotation period only needs to slow slightly more
    ======
    venus rotates to show the same face to earth at closest approach.

  12. husq says:

    >Power Grab says:
    April 9, 2015 at 11:20 pm

    Can’t remember where I heard it, but some say the New Jerusalem will be a pyramid (perhaps “tetrahedron” would be more accurate).<

    A tetrahedron gives you the four corners (points) of the Earth.

    And after these things I saw four angels standing on the four corners of the earth, holding the four winds of the earth, that the wind should not blow on the earth, nor on the sea, nor on any tree.

  13. husq says:

    Don’t know if this would be any interest to you guys on here?

    Goetheanum mathematisch-astronomische sektion (English)

    http://mas.goetheanum.org/1650.html?L=1

  14. P.A.Semi says:

    It is not that simple at all… The correct value for Venus is 177 (which is physically reasonable), not 3 (which is just an administrative approach of a clerk). The slowing down of Venus spin may be actually a periodic oscillation arround the correct meet-time beat with Earth (12:8 spin, 13:8 orbit)… Let’s wait some more few decades to see, if it is linear slow-down or an oscillation, which I conjecture… Even if it was slowing, it will not get over 0 to positive direction, it will stay tidal-locked with Sun, as is Moon locked with Earth…

    Mercury spin/orbit is also tidal-locked in 2/3 ratio, so it’s little inclination is very probably related to damping…

    The Moon comes from Earth, as has been analysed by radioisotope analysis of rocks, brought by Apollo crew back from moon (unless they picked them up on Earth and just pretend they brought them from Moon, which I do not believe). Beside else, it is noted in Gn2:21 – the rib, taken from red Adamah Earth, is named Luna and not Eve, which appears later in Gn3:20 in a different context… (also considering, that “adam” is no individual person, but simply a “man” or “human”, meaning all and any humanity…)

    The Moon axial tilt was largely damped by tidal effects to differ little from it’s orbital plane, which moreover precesses fastly (18.6 years), so by not-differing from its orbital plane considering that it comes from Jupiter is plainly not correct…

    About least surface/volume ratio, that is surely the sphere, the shape of raindrops (perfectly spherical)…
    Steiner made a great spiritual work to improve a human by some meditations and imaginations, but his physical knowledge was very poor and misleading, and his thoughts are little related to reality, which does not mean they are not useful…

    And as the Solar system is too perfectly tuned to be random, I think and believe, that Earth 23° tilt is done _in_order_to_ have changing weather seasons, by design…

  15. hunter says:

    Axial tilt has long interested me.
    What would the sky from an Earth like planet with the tilt of Uranus would look like?

  16. husq says:

    P.A.Semi says:
    April 10, 2015 at 5:53 pm

    >Steiner made a great spiritual work to improve a human by some meditations and imaginations, but his physical knowledge was very poor and misleading, and his thoughts are little related to reality,<

    The heart is not a pump: a refutation of the pressure propulsion premise of heart function:

    http://www.vascular-flow.com/clinical-abstracts/heart-pump-refutation-pressure-propulsion-premise-heart-function/

  17. Roger Clague says:

    P.A.Semi says:
    April 10, 2015 at 5:53 pm

    About least surface/volume ratio, that is surely the sphere, the shape of raindrops (perfectly spherical)…

    You are right. Tetrahedron is the shape with the greatest surface/volume ratio. I was wrong.

    My Tetrahedral Earth theory still stands. It explains the two most significant features of the Earth:
    1. The position of the continents.
    2. The tilt of the rotation
    The theory can be extended to all the planets.
    It is based on simple heat transfer in a solid and geometry.

    There is a temp gradient between the core and the surface. This gradient is best removed when the core has maximum surface area, so max heat flow out . That is the core is a tetrahedron. The crust collapses onto it. Continents are along the edges and at the corners. Oceans are in depressions in the faces.

  18. David E.Slee says:

    The retrograde spin of Venus and the motion of the Moon have been covered, but I wonder what the situation is when the direction of rotation of all the satellites of Jupiter and Saturn (let alone those of Uranus and Neptune) is considered. Any comments?

  19. oldbrew says:

    Is Venus retrograde or just upside down?

  20. David E.Slee says:

    Oldbrew,
    I agree that it is better to think of Venus as only being upside down. What I was (rather hurriedly) trying to ask in my earlier comment is — how consistent is the rotations and Axial tilts etc of the larger satellites of Jupiter and Saturn with those of the host planets themselves? Do they move so as to support this theory about the satellites originating from their hosts? Or are they all different such that past events gave rise to random capture of these satellites by the present hosts?

  21. oldbrew says:

    The rotations of the satellites are almost all synchronised (‘tidally locked’) 1:1 with their own orbit periods, the same as our Moon. The axial tilts often do closely match that of the host planet, or fall into groups e.g. Jupiter’s moons.

    http://nssdc.gsfc.nasa.gov/planetary/factsheet/joviansatfact.html

    The major moons have almost exactly the same rotational axial tilt as Uranus’s (their axes are parallel to that of Uranus) – Wikipedia
    http://en.wikipedia.org/wiki/Moons_of_Uranus

  22. Roger Clague says:

    David E.Slee says:
    April 15, 2015 at 6:37 am

    how consistent is the rotations and Axial tilts etc of the larger satellites of Jupiter and Saturn with those of the host planets themselves?
    Do they move so as to support this theory about the satellites originating from their hosts?

    Good questions. What do the tilts of the planets (moons) of the planets tell us
    These are what I get from Wikipedia
    Planet large moons
    Earth 23 0
    Mars 25 0
    Jupiter 3 0, with at group of 5 at 28-30
    Saturn 27 0
    Uranus 90 +8 0
    Neptune 28 triton 157 ( 180 -23)
    This confirms there are only 2 values for the tilt, near 0 or 23-30.

    The moon is not from Jupiter, as Cullen says. The moon is from Earth.

    I suggest that there are only 2 tilts is caused by geometry and cooling history.

    A slowly cooled or cooling body will tend towards a tetrahedron.. A tetrahedron has the maximum surface to volume ratio allowing fastest heat loss from core. The body will be stable at 23-30
    A rapidly cooled body will be homogeneous and spherical, so no tilt.