Many thanks indeed for your query as it has given me a chance to talk something about the VJ!
Let us try to get it straight from the "mouth" of the Vedanga Jyotisha itself as to what "notions" it has/had about the meaning of Jyotisha!
The Date of the Vedanga Jyotisham:
First of all, let us see how "old" it is
The first---viz. the "earliest"!---and the last work available in India as Vedanga Jyotisha is the "Vedanga Jyotisha" itself. It comprises two astronomical tracts titled the Aarcha or Rik Jyotisham and the Yajusha Jyotisham.
The 5th and 6th Mantras of the Rik Jyotisham (which are the 6th and the 7th mantra of Yajusha Jyotisham) say:
स्वराक्रमेते सोमार्कौ यदा साकं सवासवौ । स्यात् तदादियुगं माघस् तपः शुक्लो अयनम्ह्युदक्।।
प्रपद्येते श्रविष्ठादौ सुर्याचन्द्रमसावुदक् । सार्पार्धे दक्षिणार्कस्तु माघ श्रावणयोः सदा।।
"When the sun and the moon while moving in the sky, come to Vasava (Dhanishtha, Alpha Delphini/Beta Delphini ) star together, then the Yuga, the Magha (month), the Tapas (season), the light half of the month, and the winter solstice, all commence together.
The sun and the moon turn towards North in the beginning of Dhanishtha and towards South in the middle of Ashlesha. The sun always does this in the respective months of Magha and Shravana". (S B Dikshit's translation).
These shlokas talk of certain astronomical phenomena which do not repeat themselves at least over a period of twenty-five thousand years! E.g, though the sun and the moon come together after about every 29.53 days (synodic lunar months) and it is Udagayana (Winter Solstice) after about every 365.25 days but these phenomena will not be in the vicinity of the star Dhanishtha (Alpha-Delphini or Beta-Delphini).
Some strict conditions have been stipulated here---the sun has to be in the "start of Dhanishtha" nakshatra and it has to be a new moon also besides being the shortest day of the year! Similarly, when the sun "turns South" it has to be in the middle of Ashlesha nakshatra (Epsilon Hydrae) and it has also to be a full moon!
The attachment VJ-1399BC-stars gives the exact position of both the stars of Dhanishtha as almost exact 270 degrees, thus "conjunct" Udagayana! Similarly, the star Alpha Cancri (Ashlesha) was about 86.5 degrees whereas Dakshinayana means the sun at 90 degrees. Above all, since the VJ says that Krittika was the first nakshatra, we find the longitude of eta Tauri (Alcoyne-2) almost 13 degrees! Thus the Vernal Equinox was in the starting point of Krittika division vis-a-vis precession!
From the attachment VJ-NM, it was a New Moon on January 2, 1399 BCE.-i.e. 14th century BCE!
Pingree theories decimated:
It decimates the presumption of David Pingree in his "The Mesopotamian Origin of Early Indian Astronomy" (JHA-IV (1973), 1-12; and Witzel etc.
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We simply do not know where Lagadha would have placed the beginning of the equal nakshatra Dhanishtha with respect to the fixed stars nor do we know the accuracy with which he could have determined the sidereal longitude of the Sun at Winter Solstice, since a displacement of the beginning of the equal nakshatra by some 10°, or an error of 10 days in computing the date of the winter solstice, or some combination of these two effects is all that is required to bring the date from the twelfth century to fifth century BC, we should not lend much weight to this chronological arguments.
Their claim is that it is not clear as to from where they started the nakshatra divisions so the "conjunction" with Dhanishtha and the middle of Ashlesha could be later by several hundred years!
No! It was not like that!
Acharya Lagadha has said specifically that the Winter Solstice was in the starting segment of Dhanishtha division. The nakshatra divisions started from Krittika, as the VE was in conjunction with the same. Dhanishtha nakshatra division therefore ranged from (Dhanishtha minus Krittika =) 20 X 13.333333 degrees = 266.7 degrees to 280 degrees And as is clear from the attached star chart the longitudes of Alpha Delphini and Beta Delphini were almost 270 degrees, which is within the first division of Dhanishtha division i.e. "Shravishthaadau"!
Similarly, Ashlesha nakshatra ranged from (Ashlesha minus Krittika =) 6X 13.33333 degrees= 80 degrees to 93.3333 degrees. And the longitude of the star viz. Alpha Cancri was 86.5 degrees ---exactly the midpoint of Ashlesha Nakshatra division saarpaardhe dakshinaarkastu!
Witzel's stance full of looplholes:
Similarly, Michael Witzel has said in his "Autocthonous Aryans? The evidence from old Indian and Iranian texts"
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Only if one is convinced that Lagadha intended the solstice to be exactly at alpha Delphini of Dhanishtha, one can date his observation back to the late second millennium. Since that cannot be shown beyond doubt, since the composition of the text is in Late Epic language, and since its contents have clear resemblances to Babylonian works, the text must belong to a late period, to the last centuries BCE.
Unquote
It appears Witzel has tried to evaluate the VJ without having read it thoroughly!
VJ is being narrated by "Shuchih" who claims that he was only "narrating the science of Time that had been propounded by Mahatma Lagadha"!
Shuchi has not said anywhere as to how he came across the same, nor has he said anything about as to how long ago it was before him! All he has done is given the basic and fundamental arguments and astronomical facts as had been adumbrated by Lagadha!
Thus it is not clear as to how "non-Vedic" the language of "Mahatma Lagadha" originally was but there is every possibility that Shuchih had "heard" the basic theory from his ancestors or he had just chanced on the same from some other source and then narrated it in his own style and language which could be even later than 15th century BCE!
Where could the VJ have been compiled?
The VJ has indirectly proved that the Winter Solstice is the shortest day of the year and has given the increase in the day length from that date as "one prastha of water"-- which is 4/61 nadis. After calculating its Ascensional Difference etc, S B Dikshit has proved in his "History of Indian Astronomy" page 90 that the latitude for which it was calculated was between 34° 45'.8 and 34° 54' North. It is the approximate latitude of Wullar Lake in Kashmir, which was known as Maha-Padmasar in earlier days!
Thus it is really amazing as to how about 3500 years back in the cold climes of Kashmir, on the banks of Wullar (Maha-padmasar) lake, on the shortest day of the year, when about a meter long icicles keep on hanging from the trees there, Mahatma Lagadha was able to detect all such astronomical phenomena, that too without any "vardaan" (वरदान) from any god or goddess, unlike the fictional Maya Mahasura!
What is the position of Acharya Lagadha about his notions of Jyotisha?
Without mincing any words, Acharya Lagadha has made his "position" as well as "notion" clear about Jyotisham in the following words!
The purpose of the "Vedanga Jyotisham" first--in the 2nd mantra of Yajusha Jyotisham (the 3rd mantra of Rik Jyotisham) according to him is
ज्योतिषामयनं कृत्स्नं प्रवक्ष्याम्यनुपूर्वशः | विप्राणां सम्मतम् लोके यज्ञकालार्थसिद्धये||
"I shall write systematically about the effect of time on the movement of luminaries meritorious by itself and accepted by learned Brahmanas for the purpose of defining the proper time for different sacrifices"--Dr K V Sarma translation.
In the 36th mantra of Rik Jyotisham (which is the 3rd mantra of Yajusha Jyotisham), the purpose of compiling the VJ has been clarified once for all
वेदा हि यज्ञार्थमभिप्रवृत्ताः कालानुपूर्व्या विहिताश्च यज्ञाः । तस्मादिदं कालविधानशास्त्रं यो ज्योतिषं वेद स वेद यज्ञान् ।।
"The Vedas have indeed been revealed for the sake of the performance of the sacrifices. But these sacrifices are dependent on the various segments of time. Therefore, only he who knows the lore of time viz. Jyotisha, understands the performance of the sacrifices fully" (K V Sarma translation)
Then in the 35th mantra of the Rik Jyotisham we read
यथा शिखा मयूराणां नागानां मणयो यथा| तद्वत्वेदाङ्ग शास्त्राणां ज्योतिषं मूर्धनि स्थितम् ||
"Like the combs of the peacocks and the crest jewels of serpents, so does the lore of jyotisha stand at the head of the lores forming the auxiliaries of the Vedas" K V Sarma translation
It is interesting to note here that the word "jyotisha" has been replaced by "Ganita" in the 4th verse of Yajusha Jyotisha! That means jyotisha = ganitam (and not phalitam!) as per the VJ.
ये बृहस्पतिना भुक्ताः मीनात् प्रभृति राशयः| त्रिवृत्ताः पञ्चभिर् भूत: यः शेषाः स परिग्रहः||
It is not found in Rik-Jyotisham and has been given without any number by Somakara in his commentary . It talks of Mina Rashi for naming the starting month in the five year yuga!
This mantra has been termed as interpolation by one and all. This is what Dr. Sarma has said on page 50 of "The Vedanga Jyotisham" published by INSA, New Delhi (Attached herewith)
This verse is an interpolation. Firstly it is unnumbered and found only in Yajusha recension. Secondly the word Rashi itself, meaning the division of zodiac of 30° each, named Mesha, Vrishabha etc. is of foreign origin and came to India only during the first centuries A.D. along with Greek astrology. Upto and including the early astronomical samhitas of the last centuries BC, the only zodiacal divisions known in India were the nakshatra divisions.
As per the attachment VJh (Hindi translation by) Dr. Sureshchandra Mishra, Jyotishacharya has come down heavily on the person who has made such an interpolation!
Shivraj Acharya Kaundinyayana of Nepal has written an exhaustive commentary in Hindi and Samskrit on the VJ. As per the attachment Kaundinyayana2, he has also made it very clear that Mesha, Vrisha etc. Rashis are not of Indian origin!
Same is the case with all the other commentators and translators of the VJ, who have declared in one voice that there were no Mesha etc. Rashis in India till the early centuries of CE!
वेदास्तावद्यज्ञकर्म प्रवृत्ता यज्ञा: प्रोक्तास्तेतु कालाश्रयेन || शास्त्रादस्मात् काल बोधो यतः स्यात् वेदान्गत्वं ज्योतिषस्योक्तमस्मात्|| " Vedas have advised to perform yajnyas; and the yajnyas have to be performed in proper timings. Because from this shastra (of jyotisha) we can calculate such proper timings (for yajnyas), that is why jyotisham is called a Vedanga".
As per the attachment, Bhaskara-jyotisha3, Bhaskaracharya-II is all praise for "jyotihs" and has called it the eyes of the Vedas (not for predictive astrology but) for its being able to calculate proper timings for yajnyas!
To sum up this long mail, my "position on what notions Jyotisa as a Vedanga operated" is the same as that of Mahatma Lagadha of 15th century BCE to Bhaskaracharya-II of 12th century CE----Jyotisha is a Vedanga only because it enable us to calculate proper timings for yajnyas!
And celebrating festivals are a form of yajnyas, and we must celebrate them on proper dates and timings and not as per the whims and fancies of niraayana niraadhaar "Vedic astrologers" who are not following Veda either in letter or in spirit!
The tail piece is that the actual Dipavali as per all the shastras was on September 28, 2019 but, ironically, we celebrated Mahalayaa--Sarvapitra-Amavasya_- on that date!
thanks to "Vedic astrology" and "Vedic astrologers"