Earth's Obliquity
This page contains discussions from the yahoogroup
http://groups.yahoo.com/groups/Astronomy_Activities_2009/
on this topic.
Q. The World Astronomy Association declared/set the
formula/model for Earth's obliquity (tilt) as follows:
e = 84,381.448 - 46.84024T - (59 × 10-5)T² + (1,813 × 10-6)T³
T is measured in centuries.
I would like to know if any in the group are aware of this formula and their
comments regarding its accuracy. The source is from Wikipedia at the following
URL:
http://en.wikipedia.org/wiki/Axial_tilt
Interesting is the second formula quoted that I believe to be more precise:
e = A + B sin (C(T + D)), with A = 23.496932° ± 0.001200°, B
= - 0.860° ± 0.005°, C = 0.01532 ± 0.0009 radians/Julian century, D = 4.40 ±
0.10 Julian centuries, and T, the time in centuries from the epoch of 2000 as
above.
Any comments?
----------- Clive Ross, Thu Mar 20, 2008 3:41 am
Hello Clive,
Both the formulae that you mention must be analytical approximations to the
complete numerical solutions, valid in some restricted limits, isn't it?
These papers seems to be discussing similar analytical formulae -
http://adsabs.harvard.edu/abs/1994A%26A...282..663S
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WGF-4PKXBVF-2&_user=1\
0&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVers\
ion=0&_userid=10&md5=9e6ba91d32e106dde12f62ad13c7caa5
------------- Rathnasree, Nehru Planetarium, New Delhi. Thu Mar 20, 2008
5:29 am
Rathnasree:
Thanks for those two references. The first site requires a masters in
math...lost after the fourth page of formulation. The second relates most to
Mercury...not that of Earth.
The first of the two formulae I quoted from Wikipedia produces a linear
decrease/increase in Earth's tilt indicating Earth's poles about 508,200 years
ago being 90 degrees offset from present. That being true then the poles would
be located at the equator. That averages Earth rotating from pole to pole at a
rate of 1.00 degree
every 5,600 years...it didn't happen..!
The second formula includes a sinusoidal function producing an oscillation of
Earth's axis from 22.64 deg min to 24.36 deg max over 20,500 years...or a
complete 360 degrees return-cycle of 41,000 years. Of course, this is designed
to fit within the theory of the 41,000-year indicators in polar ice-field
measures.
Having read the reference you offered it is found that these numbers are also
associated or tied into the identical theories…it's only another model
attempting to increase the accuracy of probability from a hair's width to half a
hair's width.
Now here is a fundamental or obvious question to ask. If the cyclical
meting/building of ice fields are the "main"
theoretical function/evidence for tabulation and…we being aware that heat is the
factor for min or max ice build-up, then couldn't it also be possible that the
Sun could have a 41,000 year cycle within its mechanics…similar to its 11+ year
sunspot cycle?
41,000 years in Sun-years is a blink of an eye in our time, yet theorists have
formulated complex angular measures using only 30 years of "precise"
measurements.
------------- Clive Ross Thu Mar 20, 2008 7:55 pm
Hello Clive,
I find this topic to be very interesting, and have started reading about it,
only following your posts. I gave these references because the first one seems
to compare the accuracies of different analytical approximations and the second
seemed interesting from the point of view of comparing obliquities of different
planets with that of Earth.
Your post is asking one to look at whether evidence exists to connect the
glacial cycles to obliquity changes alone or whether there might be some long
term solar variability that could be the major cause?
Perhaps, this issue might currently be unresolved and there must be current
research looking into this very issue.
I am trying to invite Earth climate Scientists and Solar physicists to the
group, who would better be able to discuss the various issues involved in this.
B.T.W., the first link that you posted does mention that the first equation for
the obliquity is only approximately valid for periods around 2000 AD and using
the formula and extending it to periods very far from this epoch would yield
incorrect values, as you have pointed out.
I find discussions like this so very fruitful for learning such different
aspects of Astronomy. I do hope, some of the Earth Scientists and Solar
physicists invited would join soon and help us with these discussions. Anyone
has any thoughts on people to invite for this and other topics under discussion?
------- Rathnasree, Fri Mar 21, 2008 4:04 am
Rathnasree:
"...or whether there might be some long term solar variability that could be the
major cause? ..."
Correct.
"...the first one seems to compare the accuracies of different analytical
approximations..."
The problem with the first is that it's the accepted model by the IAU in 2000,
yet it is probably the worst of all models to use.
An interesting graph that I noticed is here:
http://en.wikipedia.org/wiki/Image:Vostok-ice-core-petit.png
It is a graph from a core sample from the Quatenary glaciation (ice age) and
part evidence used in the Milankovitch cycles. If you look close it can be seen
that increase in dust levels occur when the temperature is lowest. Heat, C02 and
dust elements share the identical cycle of approximately 105ky. It is theorized
that high dust levels are caused by cold dry periods, but you need heat to
create dust. It also indicates that C02 follows the same phase as temperature;
it decreases when temperature drops. That means plants die at colder
temperatures or don't grow at all, creating more dust.
Granted, there are other factors effecting Earth's tilt such as: Moon nutation,
elliptical orbit and outer planets, but none would influence to the degree as
indicated in the graph; it shows a 10C degrees variation...that's one heck of a
large temperature swing!
You mat be wondering why my interest in finding the correct answer to this
issue. I study ancient sites and all measures that I have discovered from 5,000
years ago indicate 23.4-23.5 degrees tilt of Earth (similar to today's measure),
yet the two formulas I referenced indicate a calculated angle of 24.0 degrees.
Technically there is little difference...but...if the ancients knew the exact
angle of Earth's tilt then we have a 5,000 year old reference...not a mere
50-100 years.
---- Clive Ross, Fri Mar 21, 2008 8:14 pm
The discussion is ongoing. Please do join the group
http://groups.yahoo.com/groups/Astronomy_Activities_2009/ and help us with discussions on this and other topics :-)
