The Moon’s eccentric orbit

As far as I can tell no long term study of lunar eccentricity has been done, so  I decided to begin investigating this myself, even though I am a complete novice in astronomical calculations. The key resource for all planetary motions in the solar system is the JPL ephemeris, and the easiest way to access it is through their Horizon web interface. Initially I ran a simulation of the lunar orbit relative to the earth-moon barycentre over a 10 year period beginning in december 2000.

I was amazed  to discover that the moon’s orbit around the earth is anything but simple and the quoted parameters are just approximations. The eccentricity of the orbit is changing almost on a daily basis due to complex variations in gravitational  effects depending on the relative positions of the sun and the earth, and also Jupiter and Venus. Figure 1 plots the eccentricity from Dec 12 2000 until October 12 2010 on a daily basis. The eccentricity varies in total between the extreme values of  0.026 and 0.077. This is a huge range which can alone  change the strength of lunar tides up to a maximum of 20%.

Figure 1: Variations in eccentricity of the moon's orbit around the Earth-Moon barycentre.

Figure 1: Variations in eccentricity of the moon’s orbit around the Earth-Moon barycentre. The blue curve is a fit to two oscilations with time periods 31.8 days and 205.9 days. Click to expand.

There are at least 2 regular resonances which at first sight seems odd because neither coincide with the orbital period of the moon (27.32days) nor that of the earth (365.25 days). There are also beats in the amplitude. Following this german article, I made a least squares fit shown as the blue curve which reproduces almost perfectly the signal .

eccentricity(d) = 0.55 + 0.014cos(0.198*d + 2.148) + 0.0085cos(0.0305*d +10.565)

This variation in eccentricity changes the perihelion distance from the earth significantly causing  large variations in the strength of spring tides on a yearly basis. The eccentricity becomes a maximum when the semi-major axis of the orbit lines up with the sun. This happens every 205.9 days – more than half a year due to the precession of the orbit every 18.6 years.  The 31.8 day variation is I think  the regular orbital change in distance from the sun.

Horizons only goes back as far as 8000 BC, so in order to investigate paleoclimate effects of eccentricity of lunar orbit around the time of the last interglacial we now need to find another tool.

 

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24 Responses to The Moon’s eccentric orbit

  1. Euan Mearns says:

    Clive, the Moon is far to easy ;-) What I’d be interested to see is the eccentricity of Venus, Jupiter and Saturn combined compared with Earth – do they rhyme? Or even hum. And by way of education, what causes Earth’s obliquity to change. And since Earth is a gyroscope, does changing obliquity have the same effect as rotating a gyroscope about its axis? What is that force called?

    • Euan Mearns says:

      And thought flow… Earth is a magnetic gyroscope, wobbling about its axis inside the magnetic field of The Sun. I’m not sure anyone understands what causes Earth’s dipole to flip “randomly”. Does the polarity have any impact on Earth’s dipole ability to deflect cosmic rays? I’m writing a post on 10Be, and while I have a PhD in isotope geochemistry, I’m way out of my depth on certain things.

    • Clive Best says:

      The JPL ephemeris models all planets, moons, satellites and asteroids. NASA use it to plan their space probes. So yes it can give you changes in eccentricity of Jupiter, Venus etc. The numerical integration of all gravitational interactions results I the Milankovitch cycles. I have only just started to look into this – I hope I can get out the other end. Much of the pioneering work was done by French matehmaticians.

      I have a steep learning curve here but intend to keep my feet on terra firma.

  2. Clive Best says:

    The flip of the earth’s magnetic field is another mystery which no-one has explained. I think the last inversion was a couple of million years ago and another is also due.

    The origin must be astronomical as well. It would cause complete havoc if the field switched over tomorrow morning !

  3. Pete Russell says:

    I’m sure that at school sometime in the middle of the last century, I was told that the Earth’s orbital period was about 365.25 days. When did that change, or am I missing something?

  4. John F. Hultquist says:

    I was amazed to discover that the moon’s orbit around the earth is anything but simple …”

    The Moon’s path about the Sun has nearly the same look as does the Earth’s.
    Said another way: The often seen diagram of the Moon literally going around Earth is a false representation.
    Picture a blue car traveling in the center lane of a 3-lane highway with a white car behind. The white car can accelerate and pull into the right hand lane. Going faster than the car in the center lane, the white car will eventually pull ahead. Then it can cross to the left in front of the blue car and when, having achieved a position in the left lane it can slow down. Now the blue car can pass the white car. As the blue car pulls ahead the white car can return to the center lane. Repeat. Neither a circle nor an ellipse is anywhere to be found . . .

    . . . except as a mathematical construct.

    http://www.wired.com/wiredscience/2012/12/does-the-moon-orbit-the-sun-or-the-earth/

    • Clive Best says:

      This is very true. The moon really orbits the sun but is “locked into” the earth’s orbit round the sun. The gravitational attraction of the sun on the moon is about twice that of the earth on the moon. It is only relative to the earth that the moon appears to be in orbit around the earth. However as far as tidal effects of the moon on the earth is concerned the distance of the moon from the earth determines what the tidal force is and this goes as 1/R3. That is why the lunar tide dominates on earth rather than the solar tide, even though the gravitational force of the moon on earth is much less than the sun.

      One could argue that the solar system is also in orbit around the centre of the galaxy, although I wouldn’t know how to plat that one.

  5. A C Osborn says:

    Clive you might like to take a look at E M Smith’s Forum, he posted on the Moon’s orbit almost at the same time as you, he has collected a lot of data links.
    See
    http://chiefio.wordpress.com/2014/01/24/the-moons-orbit-is-wrong-it-can-change-a-lot-and-tides-will-too/
    and
    http://chiefio.wordpress.com/2014/01/25/a-remarkable-lunar-paper-and-numbers-on-major-standstill/

    • John F. Hultquist says:

      When Chiefio moved from the left coast to the other left coast followed by only episodic postings I failed to keep up. Recently, I noticed his comments starting to reappear on WUWT. I guess I should get back in the habit of checking in there.
      The top post you link to there (2014/01/24) has many links to his previous discussions of the moon. One needs some popcorn before starting.

    • clivebest says:

      Thanks for the pointer.

      Indeed E M Smith has some important insights new to me.

      great.

  6. A C Osborn says:

    He is the the thinking man’s Willis Eschenbach.

  7. John F. Hultquist says:

    Clive,
    I don’t think E. M. will object to this but in dealing with him it helps to know that he is sort-of living out of a suitcase for awhile. Not really — but he is from the CA Bay Area but has some unique computer skills and drove to Florida with a car load of things for a short duration job. He moved from one motel to another for a time while finding a way to settle in. As I mentioned above, I haven’t kept up because for a time his posts were rare. The second thing to know is that he is on the very functional end of the Asperger syndrome. If the work he went to Florida to do isn’t what is occupying his time, he could be on to a project or “find.” If that is the case, whatever he comes up with will be interesting.
    For myself, I’m here in comfort and warmth (hydro/electric power) watching most of the US and Canada freeze solid. We have just at freezing temps, total cloud cover, rime ice on everything, no wind, and very little reason to go outside except to exercise dogs and feed horses. I’ve been doing a lot of reading. Cheers.

  8. A C Osborn says:

    Clive, I have never had any problem with him.
    It might be an idea to have a look at his Archives, he has posted some excellent analysis in the past.

  9. A C Osborn says:

    Clive, I have asked him to have a look for your comments in Moderation.

  10. Euan Mearns says:

    “Fascinating and thought provoking!
    I have been trying to use the JPL ephemeris to calculate the moon’s orbital parameters 17,000 years ago. I beginning to conclude that the Milankovitch cycles really only apply to the earth-moon barycentre. The effective moon-earth orbit is far more complex as you have described. Therefore it seems likely that larger excursions in the gravitational coupling between the two must result as the overall eccentricity increases.

    How could we prove this hypothesis ?”

    Clive, you posted this at Chiefio. I have been asking Rog what the origin of Milankovitch is and he never answers – so I guess he doesn’t know. Does anyone know? Or did Milankovitch simply observe the cycles and conclude they were orbital without mathematical evidence?

    I’ve posted my 10Be post, a bit nervous about a complex post like this not being reviewed before hand, and so would appreciate some friendly informed commentary before I start to spread it to the bigger blogs.

    Solar influence of glaciation in Greenland

    I think there is strong evidence that D-O cycles and Bond cycles are linked to solar variability. I will be doing a second post on Bond cycles in the Holocene. I have kind of assumed then that the big changes at glacial terminations are also linked to the Sun, but am not wedded to that idea.

    • clivebest says:

      As far as I know Milankovitch spent many years calculating how the orbits of the other planets vary the gravitational pull on the earth. This cannot be done analytically – even with 3 bodies. He had to do laborious integrations over long periods to get the 100,000 year ellipticity cycle.

      Obliquity and precession are gyroscopic effects and I think this involves also the flattened spherical shape of the earth and the moon ! I don’t know whether Milankovitch was the first to propose them or whether he just put them all together. His actuak “theory” was that summer insolation above the arctic circle determined whether ice sheets wax or wane depending on the amount of solar insolation. If it was low then then the ice sheets slowly grew in size each winter.

      However the data doesn’t really support this. There is a correlation with the differential of ice volume so there is more melting when the obliquity is high and precession is right but it doesn’t explain interglacials at all.

  11. John F. Hultquist says:

    Just for reference because I don’t know without reading more and don’t have the time tonight: Milankovitch issues are discussed by Luboš Motl with link to a paper by Roe:

    http://motls.blogspot.com/2010/07/in-defense-of-milankovitch-by-gerard.html

    http://earthweb.ess.washington.edu/roe/GerardWeb/Publications_files/Roe_Milankovitch_GRL06.pdf

    Also note the comment by Nigel Calder and link there.

    • Clive Best says:

      Yes. This paper gets is correct. The increase in insolation at northern latitudes increases the rate of ice melting – NOT the total volume of ice. Roe’s result explains the details within the ice ages but it doesn’t explain why the ice sheets collapse every 100,000 years into an interglacial. I looked into the Roe paper here http://clivebest.com/blog/?p=4585 There is a clear correlation but it isn’t quite perfect.

      So Roe proved that Milankovitch cycles are at work. In fact before 900,000 years ago glacial cycles were perfect 41,000 y obliquity cycles. However no-one has been able to explain the 100,000y cycle since then.

  12. Roger Andrews says:

    Clive: On the general question of what causes ice ages here’s another theory you can probably discard ;-)

    http://malagabay.wordpress.com/2013/12/28/the-drake-passage-impact-event/

    • Clive Best says:

      For sure the isolation of Antarctica over the South Pole caused the drift to an the series of ice ages starting 3-5 million years ago. Whatever caused the Drake Passage it resulted in S America splitting from Antarctice and seems to have caused the AMOC. Circular winds drive eckman currents kick starting the global MOC.

  13. E.M.Smith says:

    Clive,
    Not ego, just limited time. New commenters go to moderation until white listed, then are instant up for future comments. You are now unmoderated and instant up. As ponted out above, I am in new housing at a new job away from everything and everyone where I lived for 40+ years trying to cope. Picking up wifi at starbucks Iin a slow and hard way to run a blog… I appologized for the delay at my place when your comments went up.

    Per Milankovitch, he did his calculations with pen and paper while in a Nazi prison for several years. Fascinating story in a book an the history of the discovery of the ice ages titled something like: The Ice Ages

    FWIW; I think you are on the right track with the lunar tides and moving faster than I can, so I’ll be playing catch up with you for a while :-)

  14. Doug Cotton says:

    The IPCC et al are wrong because their basic assumptions are wrong. They need a paradigm shift in your thinking, because planetary temperatures are not controlled by this imaginary radiative forcing concept which I debunked two years ago in my peer-reviewed paper “Radiated Energy and the Second Law of Thermodynamics.” Temperatures are set by the gravito-thermal gradient (modified by inter-molecular radiation) both above and below any planetary surface.

    When a photon from a cooler source strikes a warmer target, that target “recognises” that this photon has the same characteristics of photons which it can emit. It has exactly the right frequency (thus energy) that is required to cause an electron in the target to move up between two quantum energy states. But the process is immediately reversed, and a new identical photon is emitted as part of the target’s “quota” as per its Planck function. So the target does not need to convert some of its own thermal (kinetic) energy to electron energy (then to a photon) and so it cools more slowly as a result of the back radiation, as we all know.

    But non-radiative processes can increase their rate of cooling to compensate for slower radiative cooling.

    Furthermore, most slowing of surface cooling (and cooling of the 2 metre high surface layer of the troposphere where we measure climate) is caused by slowing of conduction into nitrogen and oxygen molecules.

    Have you ever wondered why the temperatures don’t keep falling at a rapid rate all through the night when upward convection almost ceases? It’s due to the fact that the “environmental lapse rate” is a state of thermodynamic equilibrium in which the non-radiative processes have a propensity to form a -g/Cp thermal gradient, but this is reduced (usually by no more than about a third) by the temperature levelling effect of inter-molecular radiation. For example, on Uranus the -g/Cp gradient of about 0.76K/Km is reduced to about 0.72K/Km by radiation between just a small percentage of methane molecules, whereas on Venus it is reduced more like 25% by carbon dioxide, which thus leads to a significantly lower surface temperature on Venus. On Earth it is reduced mostly by water vapour which reduces the insulating effect of the atmosphere by inter-molecular radiation, just as it reduces the insulating effect between the panes of double glazed windows as it helps energy leap-frog across the gap at the speed of light, overtaking the far slower diffusion heat transfer.

    And it is because of all this that we actually have evidence that the gravito-thermal gradient exists, and thus the greenhouse conjecture is demolished and there is zero (warming) sensitivity to carbon dioxide. It actually cools by a mere 0.1 degree at most.

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