The Workings Of The Eclipses, Explained By Varahamihira, The Polymath 

Varahamihira is, perhaps, the most prolific of Indian astronomers, based simply on the number of his works that have survived. He was not just an astronomer, but a polymath, with a refined sense of humour, to whom we sadly pay very little attention.

While Aryabhata’s treatise Aryabhateeyam is famous for its brevity, Varahamihira’s Brhat Samhita by its very name — the Grand Compilation — is encylopaedic in ambition.

In the chapter on Agastya Chaara (Transit of the star Agastya, viz Canopus), for example, Varahamihira waxes poetic and eloquent about the deeds and nobility of the sage Agastya.

In another chapter, Gochaaraa adhyaaya (Transit of Planets), he uses a different meter, chandas, for each stanza, while incorporating the name of the chandas into the poem. Quite like some Carnatic musicians inserting the name of the ragas into their lyrics.

Varahamihira’s Pancha Siddhantika is a comparative study of five great astronomical texts. It is quite unique, there is no other such text in astronomy or mathematics, though there are books on comparative philosophy like Madhava’s Sarva Darshana Sangraha.

Siddhantas, authored either by Rishis in the 18 Siddhanta era or Manuja in the early Classical era, do not include a single scientific proof in their texts. Hence, some historians have claimed in the past, that mathematical proofs are purely a Greek invention.

In the 20th century, GH Hardy frequently expressed a similar frustration with Ramanujan’s apathy regarding proofs.

It is only with Bhaskaracharya in the 12th century that an effort to provide proofs begins in the Siddhantas themselves. Later, in the 16th century, the Kerala mathematician, Jyeshtadeva, dealt with proofs extensively in his Malayalam book, Yuktibhaasha.

But much earlier, the commentators of Siddhantas, have discussed and explained proofs of mathematical statements in their bhashyaas.

Proof by Argument

Strangely, the only scientific explanation of an astronomical phenomenon, which can be understood even by an illiterate person with common sense, needs no mathematical expertise, simply but logically overturns the old religious superstition, and is verifiable by any observer, is provided by Varahamihira in his Brihat Samhita.

I refer to the first few slokas in the chapter on Raahuchaara, which explains how eclipses are caused, not by mythological snakes Rahu and Ketu, but by the shadows of the earth on the moon and the moon blocking the sun.

Remarkably, unlike Brahmagupta who severely condemns and insults earlier astronomers like Aryabhata and Vishnuchandra, though in enjoyably poetic hyperbole, Varahamihira is respectful of religious tradition and makes no personal attacks whatsoever.

Varahamihira uses four arguments — Geometry, Direction, Timing, and Size Difference — to explain the eclipses as shadows and debunk the snake explanation.

In Pancha Siddhantika, Chapter 15 Jyotishopanishad, verse 10, Varahamihira mentions that he has explained this proof in his work Brhat Samhita.

Additionally, in verse 5, he states that those living at or near Meru (north pole) never see an eclipse, because the sun and moon aren’t high enough above the horizon.

वृक्षस्य स्वच्छाया यथैकपार्श्वे भवति धीर्घचया ।

निशि निशि तद्वद्भूमेरावरणवशाद्दिनेशस्य ॥

Transliteration: vRukshasya (of tree) svacchaayaa (self shadow) yatha (how) eka paarshvE (on one side) bhavathi (becomes) dheerghachayaa (increases)

nishi (night) nishi (night) tadvad (so too) bhumEH (of Earth) aavaraNavashaath (covers) dinEshasya (the Sun’s)

Meaning: As tree’s shadow grows longer on one side, so the Earth’s shadow elongates on one side, because of the Sun. This is a simple, obvious, but profound, metaphor and explanation, to show that the Earth casts a shadow in space, like a tree casts a shadow on the ground!

भूच्छायां स्वग्रहणे भास्करमर्कग्रहे प्रविशतिन्दुः ।

प्रग्रहणमतः पश्च्चान्नेन्दोर्भानोश्च पूर्वार्द्धात् ॥

Transliteration bhu (Earth) chaayaam(shadow) sva grahaNE (in self eclipse, i.e. lunar eclipse) bhaaskaram (Sun’s disc) arka grahE (in solar eclipse) pravishath (enters) indu (the Moon)

pragrahaNam (Eclipse) athaH (hence) paschaath (from west) na (not) indu (Moon) bhaanu (Solar) cha (and) poorvaardhaath (from east)

Meaning: In a lunar eclipse, the Moon enters the shadow of the Earth. In a solar eclipse, it enters the Sun’s disc. Hence, lunar eclipse does not begin in the western side, and solar eclipse does not begin in eastern side.

Invariant Direction: This is proof by direction. Varahamihira explains why eclipses always proceed in one direction, east-to- west for lunar; west-to-east for solar. This is because both eclipses are caused by the Moon’s orbit, which is from west-to- east around the Earth.

Hence the direction of the lunar eclipse (which is Earth’s shadow on the moon) is East-to-West. See picture for visual explanation.

In a solar eclipse, the Moon continues to move from West to East relative to the Earth, so covers the Sun from the Sun’s western edge onwards.

आवरणं महदिन्दोः कुणठविषाणस्ततोऽर्द्धसञ्छन्नः ।

स्वल्पं रवेर्यतोऽतस्तीक्ष्णविषाणो रविर्भवति ॥

Transliteration: aavaraNam (Covering) mahad (Large) indOH (of the Moon, i.e. by the Earth) kuNTha (blunt) vishaaNaaH (horns) tathaH (so) arddha sanchannaH (half covered)

su alpam (small) ravEr (of the Sun) yathaH (because) athaH (then) theekshNa (sharp) vishaaNaaH(horns) raviR(of sun) bhavathi(becomes)

Meaning: The object covering the Moon is large, hence, the shadow’s horns are blunt, whereas the object covering the Sun is small, so the horns are sharp.

Size Difference: The horns here refer to the uncovered portions of the Moon or Sun during partial eclipses. KuntaVishaaNaa and TheekshNaVishaaNa are beautiful scientific terms in Sanskrit.

Varahamihira casually mentions that the two blocking objects are of two different sizes, the Moon is smaller and the Earth’s shadow larger, which would not be the case if they were blocked by the same Rahu.

Incidentally, he reserves the term Ketu, for comets, and never uses the term in the context of a solar or lunar eclipse.

Geometry and Timing: There were several beliefs about Rahu: that he only has a head or tail, that he is a full bodied snake, that he is dark and invisible except during eclipses.

Jain astronomers proposed that there are two Rahus (along with two suns and two moons). I’ve excluded these verses for brevity, and only list below Varahamihira’s verses refuting each of these concepts of Rahu.

यदि मूर्त्तो भविचारी शिरोऽथवा भवति मण्डली राहुः ।

भगणार्द्धेनान्तरितौ गृह्णाति कथं नियतचारः ॥

Transliteration Yadi (if) moorttO (body) bhavicaari (sky goer) shira(head) athavaa(then) bhavati(becomes) maNDalee (circular) raahuH

bhagaNaarddhEna (by half sky) antherithou(intervalled) grhNaati (grasps) katham (how) niyathachaaraH (fixed mover)

Meaning: If Rahu has a body, and is identified only by a head, how does he sieze the Sun or the Moon when they are half the sky apart, when his motion is fixed (i.e. he moves in a regular orbit)?

अनियतचारः खलु चेदुपलब्धिः संख्यया कथं तस्य ।

पुच्छाननाभिधानोऽन्तरेण कस्मान्न गृह्णाति ॥

Transliteration aniyatacaaraH (non-fixed mover) khalu ched (if only) upalabdhi (is obtained) sankhyayaa (by calculation) katham (how) tasya (its)

puchcha (tail) aanana (face) abhidhaana(names) antarENa kasmaat (how) na (not) grhNaathi (grasps)

Meaning: If his motion is not fixed, how can the eclipses be calculated in advance (as astronomers have done for centuries)? And if Rahu only has face and tail, why does he not seize the Sun and Moon, except when they are half-the sky apart?

अथ तु भुजगेन्द्ररूपः पुच्छेन मुखेन वा स गृह्णाति ।

मुखपुच्छान्तरसंस्थं स्थगयति कस्मान्न भगणार्द्धम् ॥

Transliteration atha tu (Now, if) bhujagEndra (snake king) roopa (form) pucchEna (by tail) mukhEna (by mouth) vaa (or) sa (he) grhNaati (grasps)

mukha puccha antara samstham (region between face and tail) sthagayati (covers) kasmaat (how) na (not) bhagaNaarddham (half sky, i.e. half zodiac)

Meaning: Now, if he is in the form of a full snake, but only graps by mouth or tail, why doesn’t he hide all the stars between the Sun and Moon, i.e half the Zodiac?

राहुर्द्व्यं यदि स्याद् ग्रस्तेस्तमितेऽथवोदिते चन्द्रे ।

तत्समगतिनान्येन ग्रस्तः सूर्योऽपि दृश्यते ॥

Transliteration: raahurdvayam (Two Rahus) yadi (if) syaad (exist) grastE (grasps) astamitE (during setting) athavaa (or) uditE (during rising) candrE (of Moon)

tat(That) samagati(co-moving) na (not) anyEna (by other) grastaH sooryO(Sun) api(also) drshyatE (is seen)

Meaning: If there are two Rahus, then, when one Rahu grasps the Moon during rising or setting, why is the other Rahu not seen grasping the Sun simultaneously?

With these arguments, weaving geometry timing and logic, Varahamihira demolishes the Rahu-as-snake theory, and establishes that shadows of the Earth and Moon cause the eclipses.

Teaching eclipses in schools

In Indian schools today, eclipses are taught with rote instruction, as though only Europeans explained them, and in very early classes. Since almost all teachers of science are ignorant of Sanskrit, such a simple but elegant proof is not included in any syllabus. Indian astronomers, except Aryabhata, are considered orthodox and superstitious. But here is the very orthodox Varahamihira, with a very scientific explanation!

Note: The next solar eclipse is an annular, or ‘ring of fire’ eclipse that will take place on 26 December 2019. It will be visible from Saudi Arabia, India, Sumatra and Borneo, with a partial eclipse visible in Australia and much of Asia.