Apologies for a longish post.

Dear Walter,

The celestial equator is simply the projection of the terrestrial equator onto the celestial sphere. Equator means equalizer of day and night (http://www.etymonline.com/index.php?term=equator), which is a reference to the two equinoxes. When the sun crosses the celestial equator, which happens twice a year, day and night are of equal length. When it crosses the equator from south to north, it is the spring equinox (March 21st), and when it crosses it again from north to south, it is the autumnal equinox (sept. 22nd).

Now, if you want to divide the year in two on the basis of the celestial equator, each half of the year is the period between equinoxes, so one half includes spring and summer (Mar. 21 to Sept. 22), while the second half is made up of fall and winter (Sept. 22 to Mar. 21). But that doesn't correspond to the uttarāyaṇa and the dakṣiṇāyana. The uttarāyaṇā goes from the winter solstice to the summer solstices, and the dakṣiṇāyana from the summer solstice to the winter solstice. In other words, for the ayanas the division of the year in two is made along the line of the solstices, not along the line of the equinoxes.

In any case, to say that the Ekaviṃśa day is the (celestial) equator makes no astronomical sense. The Ekaviṃśa is one day of the year, whereas the (celestial) equator is a great circle of 360 degrees. If you wanted to define the ekaviṃśa with reference to the celestial equator, you'd have to say it is the day on which the sun, in its apparent movement throughout the year, reaches its highest distance to the north of the celestial equator. In astronomical terms, that is the day when the sun reaches its maximum northern declination.

But understanding the uttarāyaṇa and the dakṣināyana doesn't require all these complicated visualizations of celestial circles. Ancient observers of the sky didn't look at it in those terms. For them, it was an observable phenomenon that is easy to track. You watch the sunrise every day for a year facing West, and notice how the sunrise point moves along the horizon as days proceed. There are two maximum points, one when the sunrise point is farthest to the left (North) along the horizon, and the other when it is farthest to the right (South). Those two points are the solstices. That is where the terms uttarāyaṇa and dakṣināyaṇa come from. During the uttarāyaṇa, the sun rises more to the left/North (uttara) every day until the Summer solstice. Then it reverses its movement and starts rising every day further to the right/South (dakṣiṇa) until it reaches the Winter solstice.

That is why the Ekaviṃśa is the day of the summer solstice.

And when the AB says: "By means of the performance of this day, the gods had raised the Sun up to the heavens," that's probably a reference to the fact that at the summer solstice thew sun reaches its highest altitude above the horizon at midday. After that, the maximum altitude of the sun at noon gradually decreases.

Cheers,

Luis
___


On 3/19/2016 12:20 AM, Walter Slaje wrote:
Dear Luis,

the translational usage of "equator" ("dividing the year (into two equal parts)") in contexts related to uttarāyaṇa and dakṣiṇāyana is generally short for "celestial equator".
See https://en.wikipedia.org/wiki/Solstice.

Regards,
Walter

-----------------------------
Prof. Dr. Walter Slaje
Hermann-Löns-Str. 1
D-99425 Weimar
Deutschland

Ego ex animi mei sententia spondeo ac polliceor
studia humanitatis impigro labore culturum et provecturum
non sordidi lucri causa nec ad vanam captandam gloriam,
sed quo magis veritas propagetur et lux eius, qua salus
humani generis continetur, clarius effulgeat.
Vindobonae, die XXI. mensis Novembris MCMLXXXIII.



2016-03-18 23:44 GMT+01:00 Luis Gonzalez-Reimann <reimann@berkeley.edu>:
Dear James,

Although this isn't the subject of your question, I think it is important to consider that the Ekaviṃśa day in the AB is quite certainly the summer solstice, and not the "equator."

Luis
_____

On 3/18/2016 2:28 AM, James Hartzell wrote:
Dear Colleagues

I’ve come across two references in the Brāhmaṇas to the Sun as ‘the twenty-first’ –

ŚB 6.7.1.1: …” It (the plate) is round, for he (the Sun) is round. It has twenty-one knobs, for he is the twenty-first. He wears it with the knobs outside, for the knobs are his (the Sun's) rays, and his rays are outside." (Eggeling 1894:265),”
and
AB 4.18: "They perform the ceremonies of the Ekaviṃśa day, which is the equator, dividing the year (into two equal parts). By means of the performance of this day, the gods had raised the Sun up to the heavens. This Ekaviṃśa day on which the Divākīrtya mantra (was produced) is preceded by ten days, and followed by ten days, and is in the midst (of both periods). On both sides it is thus put in a Virāṭ: (the number ten). Being thus put in a Virāṭ (in the number ten) on both sides, this (Ekaviṃśa, i.e. the Sun) becomes not disturbed in his course through these worlds." (Haug 1977:288-289).

Does anyone have other references to the Sun as the 21st, and any other explanations for this other than these two Brahmana explanations?

Cheers

James Hartzell, PhD(2x)
Center for Mind/Brain Sciences (CIMeC)
The University of Trento, Italy


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