The Precession of the Equinoxes

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his supject comes to mind because I am reading Acharya S's book "The Christ Conspiracy" (to be reviewed here later) which I bought from Amazon.com just before Christmas. I knew that it was about the Earth wobbling on it's axis every 24.000 years or so ... but that's about it.

Here's the big picture

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The Celestial Sphere is just all the stars and stuff you see at night. Since it doesn't change much from one epoch to another, it's our frame of reference. Imagine all the stars are stuck on the surface of a balloon. That's what it looks like.

The Plane of the Ecliptic is the plane of the Earth's orbit. Imagine that as the intersection of the the ecliptic plane with the celestial balloon (a circle).

The celestial equator is the plane of the Earth's equator advanced out to the celestial balloon. Again the intersection is another circle ... but ... it's not the same as the plane of the ecliptic because the earth's axis of rotation is tilted 23 degrees to the plane of its orbit.

Now, these two circles drawn on the celestial sphere intersect at two points. These are the vernal (March 21st) and autumnal (September 21st) equinoxes. Imagine a line from one to the other. When the Earth crosses the line twice each year, the length of the day and night is equal (equinox) and the earth's axis isn't tilted toward or away from the sun (though it's always tilted relative to the celestial sphere).

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Now imagine what would happen if the Earth precessed like a top. Instead of having its axis' orientation always constant relative to the celestial sphere, it would rotate around and the intersecting points of the circles (blue and red) would shift around on the celestial sphere.

equinox3.gif - 7kb This is just what happens every 25,600 years. Since each "house" of the Zodiac is 30 degrees wide (twelve of 'em), it takes 1/12th of that time to move from one age to another ... about 2100 years. So, the year "1 AD" is the beginning of the age of Pisces (fish) which was the ending of Aries (ram) and now ... "This is the dawning of the Age of Aquarius" (water bearer). Thus, over large amounts of time, people noticed that at midnight of the Vernal equinox (for instance) ... the constellation Aries was no longer overhead and instead it was Pisces ... now ... going into Aquarius.

People noticed these things because it was very important to them. And ... they were able to notice them because they lined up the stars with a faraway mountaintop and observed the setup on the same night year after year and ... noticed a slight change over the period of just one lifetime.

.014o change per year x 40 years = .56o ---- that's half a degree in one lifetime ... the width of the moon ... That's something actually observable with eyes only.

The heavens are stable but gradual changes over the year correspond to the seasons ... so really, really gradual changes must correspond to really, really big changes for the Earth (and its inhabitants). Plus, way back then, before smog and TV and electric lights, all there was to look at at night was the sky ... and ... it was really, really grand. I know because I once saw (down in Rivera TX about 100 miles south of Corpus Christy - 1966) ... ALL THE STARS ... AND ... THE MILKY WAY. That's the only time I've seen the sky as it was seen in pre-industrial times. It was truly impressive. I don't expect ever to see it again.

But ... why does this "precession" happen?

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The Earth's equatorial bulge (red) is pulled by the moon more on the side nearest the moon because of the inverse square law. There is therefore a small net downward vector on the bulge tending to right the earth's spin axis relative to the moon's orbital plane. The axis then precesses like a top, moving at right angles to the force trying to straighten its axis. Regardless of what side of the Earth the moon is on, the direction of precession is the same ... so the effect is cumulative. After 25,600 years, it comes around full circle.

In addition to the foregoing there are additional little bumps in the road coming from (mainly) the fact that the moon's orbit is tilted relative to the Earth's orbital plane ... and ... it precesses also, i.e. the bulges of the Earth attract the moon and tend to right its plane of rotation (action-reaction) causing a full precession every 18.6 years. Therefore there are "nutations" every 9.3 years since the "nodes" (points where the orbit of the moon intersects the plane of the ecliptic) occur in the same place twice as the precession occurs (at 180o and 360o)

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Also, when the moon is at a "node" the force trying to right the Earth's axis is zero since the bulge is in the same line as the Earth's center. So there are "nutations" every half month ... and ... every half year when the moon's orbital plane turns around relative to the Earth (which is going around the sun dragging the moon with it).

But wait, it gets more complicated still. There are additional contributions from the sun and planets and asymmetries in the Earth's crust (it's lumpy) and from God knows where else ... but ... these are minor contributions.

And ... there is also a General Relativistic precession which I didn't see anyone going into on my travels through the web. Since inertia and gravity are equivalent (by theory) ... it must be that there exists a precession whenever there is a gravitational change in the surroundings of a rotating body because such a change is exactly equivalent to pushing the axis over to a new orientation. But this is probably unmeasurable at present.

The Tides

There are tides on opposite sides of the Earth because the Earth-moon system revolves about a common center of mass which lies beneath the surface of the Earth. Since the moon is only 1/81st the mass of the Earth, the distance from the Earth's center to the balance point of the Earth-moon system is ... 240,000 / 82 = ~2900 miles. The Earth has a radius of 4000 miles. See? It's 1100 miles beneath your feet.

Thus, on the side facing the moon, the sea is pulled by the moon toward the moon ... and ... some extra centrifugal force is throwing it up toward the moon as well. While on the opposite side, a greater centrifugal force is throwing the water away from the direction of the moon with a smaller attendant attraction.

Most of these things about gravity were solved by Newton in his Principia. This is why he is held in the greatest esteem. Things that were observed since the dawn of civilization were finally explained all at once by one man with one idea ... universal gravitation.

My head is spinning ...

Declination means ... the latitude in degrees north or south of the celestial equator.

Right Ascension means ... the angle subtended by the arc from a given star to the vernal equinox as measured going east ... and ... it's given in hours-minutes-seconds rather than degrees with 24 hours representing 360o. Why? Because the stars are moving round the Earth and astronomers can simply subtract the right ascension of one star from another to know how long before that star will appear in their telescopes. If they measured in degrees they would have to make another calculation. Get it? I think that's usin yur noggin.

Solar Time ... is the length of the day as measured by the sun, day-night-day-night ...

Sidereal Time ... is the length of the day as measured relative to the stars. It's not quite the same because the Earth has one revolution per year relative to the stars that isn't a revolution relative to the Sun. Think ... if the Earth didn't revolve at all (kept one face to the sun) the length of the solar day would be forever ... but ... the length of the day relative to the stars would be "one" because the Earth turned once on its axis to remain facing the sun over the course of a year. The difference is therefore about 1/365th of a day per day (about four minutes).

My grandmother asked me this question many years ago in a childlike and sincere manner when she was about 75 (before Alzheimer's) ...

Where does the sun go at night?

I shall not attempt to answer this question.



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