Expert: Philip Stahl - 7/11/2008

Question
QUESTION: "Question
I live in Milwaukee,WI. It's January and the temps have been around 40-50 degrees fareneheit. I can see the effects of global warming all around me happening rapidly it seems. Can the tilt of the Earths axis be directly related to global warming? If so, what is causing the Earth to go off tilt? "

Hello,

I saw your question quoted above as I was searching for the causes of climate change. I wonder if you are aware of a significant astronomical turning point in recent times that brought that question to your mind. If so, is it cyclic, when did it happen last, and what is the period of this cycle?

Thank you


ANSWER: Hello,

Earth's axial tilt has nothing to do with the current global warming acceleration, which is entirely attributable to the concentration of CO2 in the atmosphere- currently 430 parts per million by some estimates (cf. The Financial Times, July 9).

However, there is something called the “Milankovitch hypothesis" which claims that the obliquity of the ecliptic (inclination of Earth to its orbital axis) varies from 21 to 24 degrees over a 41,000 period.  It is claimed that this change, along with changes in the Earth's eccentricity can account for the Ice ages.

However, none of the claims of this hypothesis have been validated from an astrodynamic (ceslestial mechanics) point of view. Indeed, you will not find it referenced in any Celestial Mechanics texts, not even in footnotes. At least none that I have seen.

Astronomers-astrometrists recognize no such period or differential of axial tilt. The following is from the book, Astronomy- Principles and Practice  by A.E. Roy and D. Clarke, 1978, Adam Hilger Books, p. 118:

“Because of the nutational wobble in the Earth’s axis of rotation, the obliquity of the ecliptic (KP in Fig. 10.32) varies about its mean value. The magnitude on either side is about 9.”2.”

For the benefit of non-astronomers, the magnitude cited (9.”2) isn’t even one hundredth of a degree! Indeed it is nearly a factor 4 LESS than a hundredth of a degree! (which translates to 36”-   there are 3600” = 1 degree))

Going now to Eichhorn and Mueller’s standard text in astrometry and geodesy-   p. 69, “astronomic nutation’:

”The main term of astronomic nutation is produced by the non-coincidence of the Moons’ orbit with the ecliptic in conjunction with the retrograde moton of the lunar nodes. This results in a periodic change in the obliquity of the ecliptic termed nutation in obliquity, denoted by delta(Eta).

delta Eta =

(9.”2100 + 0.”00091t) cos Z  -  (0.”0904  - 0.”0004t) cos 2Z – (0.”0024 cos (2w_ m + Z)  +  0.”0002 cos (2w _s – Z) + 0.”0002cos 2 ( w _m + Z) + (0.”5522 – 0.”00029) cos 2L _s


where t denotes the time interval measured from 1900 January 0.5 d ET in Julian centuries (1 JC = 36525 mean solar days),  Z is the longitude of the mean ascending node of the lunar orbit on the ecliptic measured from the mean equinox of date, w_m is the ‘argument’ of the point where the Moon is nearest the Earth (i.e. from the lunar perigee), w _s is the mean longitude of the solar perigee measured from the mean equinox of date, and L_ s is the geometric mean longitude of the Sun measured from the mean equinox of date.

Most interesting in the above – which I merely give for the sake of completeness-  is that even jacking up the value of t by 41,000 yrs. (e.g. 410 JC) doesn’t appreciably alter the magnitude from seconds of arc – very small seconds of arc (e.g. about 8.”85 with Z = 160 deg and counting only the first order term).

So we come to the key question: How could the Milankovitch Cycles cause a global change in climate? Also, Milankovitch cycles can only account for a temperature difference of 1° to 2°. How is it possible then that sediment records show temperature differences of 7° to 10°? The 100,000 yr. (eccentricity change) cycle is dominant in the record, yet it has the weakest astronomical effect; moreover, in  the record, it doesn’t always occur at 100,000 years - ranges from 80,000 to 125,000. How can these variances be explained without recourse to mere geological correlations? Until they are – most astronomers won’t embrace the theory.

For a theoretical change in obliquity from 21 to 24 degrees one can work out the change in angular momentum that’s required:

Since: L = w I_p (ñ + cos ^2 (v)]

where w is the radial velocity, I_p the polar moment of inertia, ñ a direction in space and v the angle from vertical.

Then

d L = w I_p ( cos^ 2 (v2) – cos^ 2 (v1)]

since we do not expect the magnitude of either w or I_p to change significantly (the rotation axis z' itself is not shifting wrt the Earth, e.g. actual coordinate shift in lat. and long.)

then if v2 = 24 deg = 0.419 rad

v1 = 21 deg = 0.367 rad

Using I_p = 0.3307M r^2 = 0.3307 (6.0 x 10^ 24 kg) (6.378 x 10^6 m)2

I_p = 8.07 x 10^ 37 kg- m^2 (polar moment in appropriate units)


dL = {7.272 x 10^ -5 rad/s) 8.07 x 10^ 37 kg- m^2 ) x ( cos ^2 (v2) - cos^2 (v1)]


= (5.87 x 10^33 kg-m2 s-1) (0.871 - 0.834) = 2.17 x 10 32 kg-m2/s

This is an enormous change in angular momentum of the planet – even given a 41,000 year period to accomplish it. WHERE is the external force coming from to make this change in angular momentum? We don’t know – since the Milankovitchites can’t say. All they have is an empirical correlation schema – as opposed to a bona fide theory with self-consistent explanatory power for the changes postulated. (And let's bear in mind these changes occur on the +/- side of each cycle, it's not merely a one time change!)

Let’s consider only what may be the present cycle and assume the obliquity  is headed for 24 deg from its current 23.5 value.

How much has the enormous demand for the source of angular momentum change been reduced? So now we have v1 = 23.5 deg = 0.410 rad.

Then

dL = {7.272 x 10^ -5 rad/s) x (8.07 x 10^ 37 kg- m^2 ) x ( cos ^2 (0.419) - cos^2 (0.410)]


= (5.87 x 10^33 kg-m^2 s^-1) (0.871 - 0.841) = 1.761 x 10^32 kg-m^2/s

which is still an enormous amount! (one hundred seventy -six million trillion trillion kilograms meters-squared per second!) Note: the L value can be worked out for greater or less w (say, 5 x 10^-6 < w < 5 x 10^ -4) , and the magnitude of L is still enormous.

Thus, we need to know – before “time expires” – where all the external torque is coming from to alter the Earth’s angular momentum by such a vast amount! Even allowing for the length of time- the magnitude of angular momentum must be accounted for. It has to come from somewhere – it simply cannot materialize in vacuo. One of the first or primary principles in all of legitimate science is to formalize causal principles, explanatory interpretations. Without this, one has something more in the way of 'tea leaf reading' than science.

The bottom line here, even if these calculations escape you, is that thje Earth's axial tilt has no role in global warming. As a further reinforcement of this, a recent paper in Eos Transactions observed that NO more Ice ages will occur at all, with the CO2 concentration over 400 ppm.





---------- FOLLOW-UP ----------

QUESTION: Thank you much for the detailed answer. I am afraid my question may have been misunderstood. I wasn't specifically referring to the earth's axial tilt. Perhaps, I should have clarified that more in my earlier question. I should have also made clearer that I don't underestimate the significance of the level of carbon dioxide in the atmosphere. My interest was more about the relative positions of the earth, the sun, and other known stars. I am a layperson for astronomy, but I would guess that their relative positions have a cyclic nature. If so, was there a significant turning point that occurred in the second half of the last century?

Thank you again.

Answer
Hello,

Yes, I guess I misunderstood your question. This is fairly easy since the claim of Milankovitch "periodicities" incorporates cyclic changes for the Earth's eccentricity as well as axial tilt.

Again, there is only one known (and widely circulated) proposal to account for climate change based on changing relative positions and that is the "Milankovitch hypothesis". But, as I noted, it has plenty of problems - and no seriuous climatologists I know take it seriously as the key explanation for global warming any more than astronomers take it as a useful theory for celestial mechanics.

Re: the alleged cycles (especially the 100,000 yr. eccentricity one) in the hypothesis, the orbital fluctuations can not be the whole story. We know that over large parts of Earth's history there were no ice sheets, and the orbital character of the Earth fluctuated in the same way. In fact, there is ample evidence of climate fluctuations on Earth at times that the ice sheets were much smaller than today's ice sheets, or even absent, at Milankovich periodicities. (NONE of which occurred or altered orbital parameters as recently as the previous century)

Then why did these fluctuations not cause ice ages during these earlier periods of Earth history?

The best answer so far is that high CO2 concentrations in the atmosphere prevented it, just as the high current concentrations (> 400 ppm) will likely prevent any more ice ages. (According to currently published work)