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Robert Tulip
2012-Jul-29, 10:35 AM
Ice core records show a 100,000 year cycle of glaciation, which Milankovitch Theory suggests is probably driven by orbital eccentricity due to the torque on earth's orbit from Jupiter and Venus.

Ice Ages and Astronomical Causes by Muller and MacDonald states "major causes of such torque are the planet Jupiter, because it is massive, and Venus, because it comes so close." (p32) Eccentricity includes cycles of period 95 kyr, 125 kyr and 400 kyr, apparently producing the 100,000 year glacial cycle.

In reading this book, I did not find answers to the following questions:

1. How does this planetary torque produce such slow cycles?

2. Is it due to periodic alignments of perihelions?

3. Is the 100,000 year climate cycle entrained by precession? (M&M 6.4.4, 8.1)

Thank you.

By the way, Professor Muller has an op-ed in the New York Times today The Conversion of a Climate Change Skeptic (http://www.nytimes.com/2012/07/30/opinion/the-conversion-of-a-climate-change-skeptic.html?pagewanted=all).

Ivan Viehoff
2012-Jul-30, 04:27 PM
Q1/2. This is something that was sufficiently tricky it wasn't until the 19th century that people devised a theory to explain it, although they were aware of it (the changes in orbits, not the climate effect) much earlier. The simple story is that each time two planets come fairly close an impulse is applied. http://en.wikipedia.org/wiki/Perturbation_(astronomy) The periods are long because the kicks are small. Clearly when orbits become aligned the kicks can be a bit bigger than usual, but it is the regular kick each time they come close that is the major factor.

Q3. Axial precession gives a 26,kyr year cycle, which is plainly likely to interact strongly with a 100kyr cycle. Orbital inclination also has an approx 100 kyr cycle. http://en.wikipedia.org/wiki/Milankovitch_cycles

More broadly, the reason 100kyr is apparently the dominant climate cycle remains the key open question in this area. http://en.wikipedia.org/wiki/100,000-year_problem

Robert Tulip
2012-Jul-30, 09:45 PM
Q1/2. This is something that was sufficiently tricky it wasn't until the 19th century that people devised a theory to explain it, although they were aware of it (the changes in orbits, not the climate effect) much earlier. The simple story is that each time two planets come fairly close an impulse is applied. http://en.wikipedia.org/wiki/Perturbation_(astronomy) The periods are long because the kicks are small. Clearly when orbits become aligned the kicks can be a bit bigger than usual, but it is the regular kick each time they come close that is the major factor.
Thanks Ivan. I'm still wondering how annual kicks lead to a 400,000 year cycle. I imagine it is that there is orbital inter-relationship between periods of the perihelion, so for example the gravity would be strongest when Jupiter's perihelion aligns to earth's aphelion. But I cannot find anything to confirm this. NASA does not even include the period of the perihelion on its Jupiter Fact Sheet (http://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html).

Q3. Axial precession gives a 26,kyr year cycle, which is plainly likely to interact strongly with a 100kyr cycle. Orbital inclination also has an approx 100 kyr cycle. http://en.wikipedia.org/wiki/Milankovitch_cycles

More broadly, the reason 100kyr is apparently the dominant climate cycle remains the key open question in this area. http://en.wikipedia.org/wiki/100,000-year_problem
The axial precession period is modulated by the movement of the perihelion to give climate cycles of 24, 22 and 19 kiloyears, in a way I have not seen a simple explanation for, except that Muller and McDonald call eccentricity 'the envelope of precession', and state "because the perihelion does not move smoothly but lurches, the perihelion in this moving systems is a superposition of several periods, the most important being 24, 22 and 19 kyrs." Again, these main cycles of terrestrial climate seem to be driven by the period of Jupiter's perihelion cycle around the ecliptic, because that seems to be the main driver of the eccentricity cycle, but I could find no information on what this Jupiter period is.

Hornblower
2012-Jul-31, 02:34 AM
Here is a NASA/JPL source which includes rates of change for all orbital elements of all of the planets.

http://ssd.jpl.nasa.gov/txt/aprx_pos_planets.pdf

Note that for Saturn and Neptune, the perihelion precession is retrograde.

It should be noted that the rates of change given for orbital eccentricity are for the short term. I have seen plots of Earth's eccentricity variation over long periods and it looks very irregular. That must be the aforementioned superposition of several periods. It has varied from near zero to about 0.05, compared to the present value of about 0.017. I would have to do some searching to find good online references. Right now I am going on memory of Sky and Telescope articles from decades ago.

Once again, the perihelion precession is slow because the perturbations are weak. For comparison, the Moon's perigee goes around in under 9 years in response to the severe perturbations by the Sun.

Ivan Viehoff
2012-Jul-31, 10:54 AM
Thanks Ivan. I'm still wondering how annual kicks lead to a 400,000 year cycle.
Because, simplified, the size of the kick it gets each (not exactly a) year is of the appropriate magnitude to move it just enough that it produces a 400,000 year cycle. It isn't due to a geometric relation in the orbital characteristics of the two objects, except in the trivial sense of how often they approach and how closely: if the masses were different but the geometrical characteristics of the orbits the same, it would produce a cycle with a different periodicity, because the kick would be different.

Robert Tulip
2012-Jul-31, 02:31 PM
It isn't due to a geometric relation in the orbital characteristics of the two objects, except in the trivial sense of how often they approach and how closely
Orbital eccentricity is the roundness or ellipticity of the path of a planet around the sun. Earth's orbit has three cycles of eccentricity, with periods, 95, 125 and 400 kyr, oscillating between near circular and more oval. What I don't get from your reply is what would cause the turning points of the cycle, ie if Jupiter pulls our orbit steadily towards a more oval shape, what changes the cycle to make Jupiter then pull earth towards a more round orbit? Isn't this where "how closely" the two planets approach each other is likely to be decisive? When Jupiter perihelion aligns to earth's aphelion, surely that would make earth's orbit more oval since the gravitational pull would be at its strongest? And conversely, would the alignment between both perihelions cause Earth's orbit to be more circular? Or is earth's orbit most circular when Jupiter's (or Venus's) perihelion is at the semi-minor axis?

Hornblower, thank you for that link. It is for experts who are familiar with computation using the data it provides, and does not actually state the period of Jupiter's perihelion against the fixed stars. Jupiter passes its perihelion once per orbit, and last did so in 2011, when the planet was in the sidereal constellation of Pisces. I am wondering how long it will be before the perihelion travels right around the ecliptic to once again be in Pisces.

It seems to me this is basic information for a simple understanding of Milankovitch cycles, as the primary actual influence of other planets on terrestrial climate, but I cannot find it anywhere.

ctcoker
2012-Jul-31, 03:42 PM
Hornblower, thank you for that link. It is for experts who are familiar with computation using the data it provides, and does not actually state the period of Jupiter's perihelion against the fixed stars. Jupiter passes its perihelion once per orbit, and last did so in 2011, when the planet was in the sidereal constellation of Pisces. I am wondering how long it will be before the perihelion travels right around the ecliptic to once again be in Pisces.

It may not give it explicitly, but it does give you a number that lets you easily calculate it. The fifth column of Table 2a gives the longitude of perihelion and its rate of change in deg/century. For Jupiter, this is about 0.182 deg/cty according to the table, which corresponds to a precession period of ~2,000 centuries, or ~200,000 years. That number probably approximates the true answer, but does not include the facts that a) Pisces is not a single point, and b) the rate of change is not constant, especially over the timescales involved. If you want a more precise answer, you'll need to integrate the solar system's orbits over that period of time.

Of course, after such a long time, the constellation of Pisces won't really exist anymore, but hey...

Hornblower
2012-Aug-01, 02:11 AM
The orbital eccentricities of the planets vary in a long, slow oscillation in which the planets are exchanging angular momentum and perhaps some energy. If Earth's orbital period stays the same but the eccentricity increases, its angular momentum is slightly reduced. Since the total angular momentum of the solar system is conserved, at least one planet has its angular momentum increased, which means a reduction in its eccentricity. The mechanism of this variation is of course gravitational interaction. If I remember correctly, an article in Sky and Telescope some decades ago described such an exchange between Earth and Mars, where at any given time one planet's eccentricity was increasing when the other was decreasing. My educated guess is that when one of the orbits becomes circular or nearly so, and the perturbations continue, the exchange reverses itself. Perhaps perihelion alignments also play a role in the reversal. With Venus also making close approaches and Jupiter throwing its weight around, I can imagine how the pattern would become very complex.

Once again, I am guessing a lot, and finding those old references is a beastly job. Don't take everything I say as authoratative.

Robert Tulip
2012-Aug-01, 03:08 AM
Thanks ctcoker, that is a big help. I have keyed in this data and got the following results for perihelion periods and alignments. For a minute there I thought EM Bary was the architect of Covent Garden! :)


Degrees per Year Perihelion Period
Jupiter 0.00181992 197,810.94
Earth 0.003179526 113,224.42
Venus 0.000567965 633,842.10

Using the formula which Hornblower kindly gave me a few years ago (http://cosmoquest.org/forum/showthread.php/71027-Jupiter-influencing-sunspots?p=1206711#post1206711), C = 1/(1/A - 1/B), gives the following periods in years for perihelion conjunctions


Jupiter Earth 264,782.51
Earth Venus 137,848.58
Jupiter Venus 287,550.32
Unfortunately for my supposition that the eccentricity cycles might be a function of alignment of perihelions, these numbers are nothing like the 400, 125 and 95 ky periods I hoped to see. So I am still stumped as to why Jupiter and Venus would produce terrestrial orbital eccentricity cycles of this length. I will simply take Hornblower's latest post as an indicator that the calculations are far too complicated for me to worry about, although a simple explanation of this basic process would have added to the Muller and McDonald book.

To illustrate what I thought would be the answer, but it seems is not, I made the attached diagram showing the elliptical alignments. Any further enlightenment appreciated.

ctcoker
2012-Aug-01, 02:25 PM
Well, like I said, the rate of change of the longitude of perihelion (of any of the orbital parameters, really), is not constant. If you look in Table I, for Jupiter the rate of change of the longitude of perihelion is all of a sudden 0.213 deg/cty! That's a 15% change from the value in Table 2a, and that's just based on choosing different lengths of time to average over (Table I uses 250 years, Table 2a uses ~6,000 years). I would imagine this variability could end up changing the true answer by as much as a factor of two or more if you integrated it out. If you want to really see if the forcing periods match up with the Milankovitch Cycles to any precision better than about 50% or so, you'll need to find a Keplerian integrator (or write your own) and integrate the orbits.

Robert Tulip
2012-Aug-02, 11:58 PM
Here is a NASA/JPL source which includes rates of change for all orbital elements of all of the planets.

http://ssd.jpl.nasa.gov/txt/aprx_pos_planets.pdf

Note that for Saturn and Neptune, the perihelion precession is retrograde.

It should be noted that the rates of change given for orbital eccentricity are for the short term. I have seen plots of Earth's eccentricity variation over long periods and it looks very irregular. That must be the aforementioned superposition of several periods. It has varied from near zero to about 0.05, compared to the present value of about 0.017. I would have to do some searching to find good online references. Right now I am going on memory of Sky and Telescope articles from decades ago.

Once again, the perihelion precession is slow because the perturbations are weak. For comparison, the Moon's perigee goes around in under 9 years in response to the severe perturbations by the Sun.

I don't understand this concept of superposition (http://en.wikipedia.org/wiki/Superposition). The perihelion moves around the ecliptic over about 113 kyr at its current speed, passing the solstices and equinoxes in 'superposition' cycles of 19, 22 and 24 kyr, due to the 'envelop of precession' caused by the slow oscillations of eccentricity at 95, 125 and 400 kyr driven mainly by Jupiter and Venus. These superpositioned cycles overlap. How could that occur for the movement of the perihelion, given that the precession/perihelion cycle as main climate driver is an actual time period? Is the 'lurch' of the perihelion speed causing these different wavelengths to occur simultaneously or successively?

Hornblower
2012-Aug-03, 12:52 AM
I don't understand this concept of superposition (http://en.wikipedia.org/wiki/Superposition). The perihelion moves around the ecliptic over about 113 kyr at its current speed, passing the solstices and equinoxes in 'superposition' cycles of 19, 22 and 24 kyr, due to the 'envelop of precession' caused by the slow oscillations of eccentricity at 95, 125 and 400 kyr driven mainly by Jupiter and Venus. These superpositioned cycles overlap. How could that occur for the movement of the perihelion, given that the precession/perihelion cycle as main climate driver is an actual time period? Is the 'lurch' of the perihelion speed causing these different wavelengths to occur simultaneously or successively?For the details, this is a question for the orbital mechanics experts who are armed with supercomputers for the numerical integration number crunching. The math is way too complicated to describe in a forum like this one.

Robert Tulip
2012-Aug-03, 02:03 AM
Okay, no worries, I was just hoping someone might be able to provide a "superposition for dummies" explanation as it relates to earth's orbital precession and eccentricity.