It is estimated that the axial tilt of the earth varies between 22.1 and 24.5 degrees over a 42,000 year period. (src: Wiki)
Does the tilt angle affect the rate of precession? If so, what is the relationship?
It is estimated that the axial tilt of the earth varies between 22.1 and 24.5 degrees over a 42,000 year period. (src: Wiki)
Does the tilt angle affect the rate of precession? If so, what is the relationship?
Reading the wiki, the Earth's axial precession is torque-induced precession caused mainly by the tidal effects of the Sun and Moon on Earth's equatorial bulge.
There is no term for axial tilt in the equation for torque-induced precession in the wiki for precession. The wiki on axial precession says the torque of the Sun and Moon on the Earth does depend on their declination and right ascension which depend on the Earth's axial tilt, but averaged out over a year the effects cancel out.
So from what I gather, it does not affect the mean rate of precession.
Thanks for your answer "boom stick". I assumed it would change since the shape of the ellipsoid slicing through the equatorial bulge would change as the earth tilt changed. I think this would affect the moment of inertia. But the math is complicated and I am too far out of school to handle it.
No. But if you followed any of the recent ATM thread about the Binary Sun, the changing rate of precession was a major point for the proponent. I am wondering how much of the changing rate of precession could possibly be due to the obliquity cycle?
I understand the bulge is formed by the rotation. If the tilt angle changes, the resultant shape of ellipsoid formed by the intersection of the plane of the ecliptic also changes affecting the moment of inertia (or so I think). Perhaps it doesn't change greatly but we are talking about a movement that is very slow to begin with. But if the rate of precession changes 0.1 arcseconds per year, it is significant.
The shape of the intersection doesn't matter. This wiki has a pretty nice picture in the cause section and below that are the equations. You can see that there is no dependency on the earths axial tilt in the averaged out version. http://en.wikipedia.org/wiki/Axial_p...onomy%29#Cause
They might not be the whole truth, but pretty close to it anyway.
Let's see, that links says the updated value of precession is 5,029 sec per century, so that's close to what I calculated above.
But doesn't that say the precession is dependent upon epsilon (the angle between the equatorial plane and the ecliptic plane)? The difference between the cosine of 22.1 degrees and 24.5 degrees is a little less than 2%.
Yes. That may be the key I am looking for, as used in calculating average torque.
Good find.
Its ok boom_stick. I appreciate your efforts to help. Thanks.