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forget
30th Mar 2002, 15:51
This is probably not Tech Log but it's the most likely place to get a sensible answer. Can anyone explain to me the Earth's 26,000 year precession. As I understand it the Earth 'wobbles' with the poles describing a circle. 26,000 years for a full cycle. What I want to know is where are we now, in the cycle, and what is the magnitude of the wobble.

EchoTango
31st Mar 2002, 23:48
From Bowditch - "American Practical Navigator" Vol 1 1977 p 362.

Quote
The axis of the earth is undergoing a processional motion similar to that of a top spinning with its axis tilted. In about 25,800 years the axis completes a cycle and returns to the position from which it tarted. Since the celestial equator is 90 degrees from the celestial poles, it too is moving. The result is a slow westward movement of the equinoxes and solstices, which has already carried them about 30degrees, or one constellation, along the ecliptic from the positions they occupied when named more than 2,000 years ago.
Since sidereal hour angle is measured from the vernal equinox, and declination from the celestial equator, the coordinates of celestial bodies would be changing even if the bodies themselves were stationary. This westward motion of the equinoxes along the ecliptic is called precession of the equinoxes (fig. 1419a). The total amount, called general precession, is about 50".27 per year (in 1975). It may be considered divided into two components, precession in right ascension (about 46".10 per year) measured along the celestial equator, and precession in declination (about 20"'04 per year) measured perpendicular to the celestial equator. The annual change in the coordinates of any given star, due to precession alone, depends upon its position on the celestial sphere, since these coordinates are measured relative to the polar axis while the processional motion is relative to the ecliptic axis.
Due to precession of the equinoxes, the celestial poles are describing circles in the sky. The north celestial pole is moving closer to Polaris, which it will pass at a distance of approximately 28' about the year 2102. Following this, the polar distance will increase, and eventually other stars, in their turn, will become the Pole Star. [ a diagram indicates Vega will be the pole star in AD 14,000] Similarly, the south celestial pole will some day be marked by stars of the false Southern Cross.
The precession of the earth's axis is the result of gravitational forces exerted principally by the sun and moon on the earth's equatorial bulge. The spinning earth responds to these forces in the manner of a gyroscope. Regression of the nodes introduces certain irregularities known as nutation in the processional motion.
Unquote

Regards
ET

oxford blue
1st Apr 2002, 18:56
Have you ever put a gyro - for instance, a child's toy gyro - down at an angle - say 20 or 30 degrees off the vertical? If you have, you'll know that it's axis describes a rotation about the vertical. The gyro is spinning about its axis at a high rotation rate, but it's whole axis is also rotating slowly with respect to the vertical. Eventually, as the gyro slows down, it falls over, but before that happens, the whole axis rotates with respect to the vertical. The Earth does this as well. The reason is that the equatorial diameter of the Earth is slightly greater than the polar diameter. This gives you an Earth which is slightly fatter in the middle. Therefore the Sun's gravity attracts the Equator more than the Poles, pulling the whole Earth slightly inwards. Given a sideways force, the Earth reacts just like any other gyro - it precesses. And guess what - it's axis rotates just like the child's toy gyro - with respect to the plane of the Earth's orbit round the Sun.

Because the difference between the Earth's polar and equatorial diameter's is quite small and because the Earth rotates quite slowly, the whole precession period is quite long -about once every 25,800 years.

Navigators call this "the precession of the First Point of Aries".

As for your other question - whereabouts in the precession cycle are we just now? You can't answer that unless you define where it "starts" and "stops". Your question doesn't really have meaning.

And yes, there are lots of "real" navigators out there.

forget
2nd Apr 2002, 09:26
Right - I've got a handle on why the Earth wobbles - what I want to know is by how much. The Earth's current axis tilt is about 23 degrees, and this determines the position of the Tropics relative to the Equator. Draw a line from the Sun through the Earth (in plan view) and you'll have two maximum points of wobble, 13,000 years apart. As the Sun goes through its wobble cycle the Tropics will gradually shift. At the Earth's furthest from the Sun point of wobble the Tropics will be further North and South than at the Earth's nearest to the Sun point of wobble when the Tropics will be closer to the Equator. Question is - by how much do the Tropics move 'up and down'?

Oxford blue - "As for your other question - whereabouts in the precession cycle are we now? You can't answer that unless you define where it "starts" and "stops". Your question doesn't really have meaning". OK, I'm sure astronomers have a reference point but let's say the start of the wobble cycle, 0 degrees, is when the North Pole is nearest the Sun. So where in the cycle are we now?

oxford blue
2nd Apr 2002, 13:16
You are confusing 2 separate types of oscillation. What I described in my last post was not a change in tilt angle. Imagine a line from the South Pole through to the North Pole, then projecting out into space. It makes an angle of 66 and a half degrees to the plane of the Earth's orbit round the Sun (or 23 and a half degrees to the vertial from the plane of the Earth's orbit round the Sun).

Like the child's toy gyro, that imaginary line rotates about the vertical to the plane of the Earth's orbit round the Sun. At present, it's pointing fairly closely towards Polaris (within about 1 degree). It will be at its closest to the direction of Polaris in 2017. however, at other points in the 26000 year cycle, it points to other stars - in fact sailors in classical Greek times used Vega as the Pole Star.

This type of precession, however, is separate from changes in the angle that the Earth's spin axis makes with the plane of its orbit round the Sun. This is a period of 41,000 years and the angle varies from 21.8 degrees to 24.4 degrees. At present the angle is about 23.4 degrees.

forget
2nd Apr 2002, 13:58
Spot on Blue - now we're getting somewhere. I'm being ridiculed in the pub by my claim that the Tropics move up and down; and your mention of a 41,000 year wobble cycle suggests I'm right. But this cycle is completely new to me. Is it some sort of Masonic secret? Tell us more. What causes it? At what latitude are the tropics at the extremes of this wobble? What difference is there in daylight time, at 50 North say, at the Summer Solstice?

oxford blue
3rd Apr 2002, 11:09
No, it's no secret. Do an internet search for "obliquity of the ecliptic" and you'll find plenty of references. However, think about it - the total change is only 2 and the half cycle is about 20,000 years. This means that the obliquity changes about 1 every 10,000 years - a tenth of a degree every thousand years, or a hundredth of a degree every century.

For the purposes of navigation, this is not too much of a big deal, and therefore most aviators don't get very excited about it. But it is quite well recorded in astronomical literature. The obliquity is now about 23.44, as mentioned. In the Pyramid Age, it was about 24.02. It has been decreasing from a peak of about 24 some 8,000 years ago toward a low of about 22 some 13,000 years hence. The obliquity goes through cycles of varying amplitudes with a period of about 41,000 years. The rate varies-currently it is about 0.47 arcseconds per year.

It is caused by the interaction of gravity from other planets' orbits. The limits of the tropics are whatever the obliquity happens to be at the time - currently 23.44. This means that the tropics also vary between about 24 N/S to about 22 N/S over 20,000 years.

To calculate the difference in the length of daylight precisely would require some spherical trigonometry which I can't be bothered to work out precisely just to answer a casual internet query. But you can get an approximate but pretty accurate answer by saying that 2 difference in the position of the tropics would be like the difference between 50N and 52N - ie, not very much. Work it out from the Air Almanac if you want to - I haven't got one with me right now.

Hope this helps

basil fawlty
9th Apr 2002, 23:22
Ask Denis Slattery!!!

Dan Winterland
9th Apr 2002, 23:33
An interesting thought - an anagram of navigator is vaginarot. :eek:

Peter Eames
10th Apr 2002, 13:20
Another aspect to consider is that the earth orbit is elliptical, with the sun at one of the two foci. My understanding is that our current position in the precession cycle means that we are closest to the sun in this orbit when tilted away from the sun in winter, and furthest from the sun when tilted toward it in summer. This gives us a more moderate climate than will have occurred 13000 years ago or 13000 years in future when we the earth will be closest to the sun while tilted toward it in summer etc..

Can anyone confirm or deny?

oxford blue
10th Apr 2002, 19:21
It is true that perihelion is not as close as it used to be and aphelion is not as far away as it used to be, but this has nothing to do with the precession cycle of 26,000 years.

This is yet another one of these cycles in astronomy that they don't bother to teach you about in pilot school - the ellipticity of the Earth's orbit round the Sun also varies over thousands of years. There is at present almost no difference in the heating effect of the Sun in January 4th (perihelion) or July 3rd (aphelion) because the difference in orbital radius is only about 4% and the change in declination is far more significant. But thousands of years ago, the change in radius was more significant, giving greater extremes of climate.