Indian Astronomy (a source book)
by B. V. Subbarayappa | 1985 | 203,062 words
This book explores the extensive tradition of astronomy in India, presenting nearly 3000 verses from various original Sanskrit texts, translated into English with notes and tables. The book seeks to elucidate the scientific methodologies, instruments, and mathematical procedures developed by Indian astronomers, emphasizing their commitment to preci...
Chapter 20 - Conjunction of Stars and Planets (graha-naksatra-yuti)
20. grahanaksatrayutih - CONJUNCTION OF STARS grahanaksatrayutih viksapamsasca 20. 1. 1. yogabhagasamah sarvah samyukto laksyate grahah | adhikonakalakalavijnanam canupatatah || 5 || farrier: AND PLANETS udagdiso'rkabhutani yamye panca diso bhavah | udag rasastaya vyoma daksine munayo'mbaram || 6|| udagarkastatha visve daksine munayo'svinau | saumye rasakrtih saika yamye sardhastriyagnayah || 7 || abdhayo vasavah sardhah sapta sailastatah param | udak trimsat krtih sannam yamye liptastrisatkakah || udagarkasca visve ca dvirabhyasta nabhastatha | viksepamsah kramad drstah panditairvajibhaditah || 6 || (Bhaskara I, Laghubhaskariya , 8. 5-9 ) Conjunction of stars and planets , All planets, whose longitudes are equal to the longitude of the junction-star of a naksatra can be seen in conjunction with that star. (Of a planet and a star) whose longitudes are unequal, the time of conjunction has to be determined by proportion. Latitudes of the junction-stars (5) North, ten, twelve, five; south, five, ten, eleven; north, six, zero; south seven, zero; north, twelve, thirteen; south, seven, two; north, thrity-seven ; south, one and a half, three, four, eight and a half, seven, seven; north, thirty, thirty-six ; south, eighteen minutes of arc; north, twenty-four, twenty-six, and zero-these have been stated by the learned to be the degrees (unless otherwise stated) of the latitudes of the junction stars of the naksatras beginning with Asvini in their serial order. (6-9). (Kripa Shankar Shukla) grahatarasamagamanyayah 20. 2. 1. dhruvakadunah pascadadhikah pragvakrite'nyatha yogah | anyadgrahamelakavad dhruvakranterbhaviksepah || 7 || ' (Brahmagupta, Khandakhadyaka, 1. 9. 7.) 1 Dhruvaka of a yogatara is the distance on krantimandala between the beginning of Mesa and the point where the dhruvaprota passing through the yogatara meets the krantimandala. Viksepa of a yogatara is the distance of the yogatara from its dhruvaka measured on dhruvaprota. Principle of star-planet conjunction If the longitude of a planet corrected by the ayanadrkkarmakala is less than the dhruvaka of the yogatara, the conjuction is yet to take place; if greater, the conjunction has taken place. This rule is applicable when the planet has direct motion. If the planet is retrograde, the rule is reversed. The rest of the calculation (as regards the time of conjunction, etc.) is the same as in the case of the conjunction of the two planets. (7) grahataracchadanam 20. 3. 1. chadayati yogataram manarthonadhikad bhaviksepat | sphutaviksepo yasyadhikonako bhavati sa samadiksthah | | viksepom'sadvitayadadhiko vrsasya saptadasabhage | yasya grahasya yamyo bhinatti sakatam sa rohinyah || 15 || viksepe'ntye saumye trtiyataram bhinatti pitryasya | indubhinatti pusyam pausnam varunamaviksiptah || 16|| (Brahmagupta, Khandakhadyaka, 1.9.14-16) Occultation of stars by planets When a planet is on the same side of the ecliptic as the yogatara of any naksatra, the planet will occult the yogatara, if its sphutaviksepa is either greater than the difference of its semi-diameter and the viksepa of the yogatara or less than the sum of the two. 1 (14) When the longitude of a planet, corrected by the ayanadykkarmakala, is 1 sign 17° and its viksepa is greater than 2° S, it occults the Cart of Rohini (15) When the Moon has the maximum north viksepa it occults the third star of Magha. When it has no viksepa it occults Pusya, Revati and Satabhisaj. (16). (Bina Chatterjee) rohinisakatabhedah 20. 4. 1. vrse saptadase bhage yasya yamyom'sakadvayat | viksepo'bhyadhiko hanyad rohinyassakatam tu sah || 13 || grahavad dyunise bhanam kuryad drkkarma purvavat | grahamelana vijneyam grahabhuktya dinadikam || 14 | Occultation of Rohini by planets (Suryasiddhanta , 8. 13-14) In Taurus, the seventeenth degree, a planet of which the latitude is a little more than two degrees, south, will 1 For a demonstration see, Khandakhadyaka:Bina Chatterjee, I. p. 135-36.
split the wain of Rohini (i.e., the V-shaped constellation of Hyades. (13) Calculate, as in the case of the planets, the day and night of the asterisms, and perform the operation for apparant longitude (drkkarman), as before: the rest is by the rules for the conjunction (melaka) of planets, using the daily motion of the planet as divisor: the same is the case as regards the time. (14). (Burgess) 1 gavi 'nagaku 'lave khago'sya ced 20. 4. 2. yamadigisuh 'khara ' guladhikah | kabhasakatamasau bhinattyasrk sanirudupo yadi cejjanaksayah || 7 || svarbhanavaditibhato'starksasamsthe sitamsuh kabhasakatam sada bhinatti | bhaumayomh sakatabhida yugantare syat sedanim na hi bhavatidrsi svapate || 8 || (Ganesa, GL, 11. 7-8) If any planet with 17 degrees in Vrsabha has its southern latitude exceeding 50 angulas, it cuts the sakata of the star Rohini (i.e. the V-shaped constellation of Hyades). If Mars, Saturn and Moon do so, then it brings greater calamity to the people. (7) If Rahu stays in any of the eight stars counting from Punarvasu the Moon always cuts Rohini. This bheda with respect to Mars and Saturn will happen in the next aeon (yuga). Their patas are such that it will not happen in this yuga.2 (8) candranaksatrayogah 20. 5. 1. yavatya yaddasaksiptya yavamstarasamagamah | tavatya taddisaksiptya tavaninduh samo bhavet || 10 || astirdasaguna lipta viksepasya yadottare | nirunaddhi tada vyaktam krttikatarakam sasi || 11 || uttaram paramam ksipti gatva sisiradidhitih | avrnoti svabimbena maghamadhyasthatarakam || 12 || arohati sasi sastya prajesasakatam sphutam | astivargena yamyayam yogatara vilikhyate || 13 || yamyagam pancahinena satena tvastratarakam | maitram satena sardhena dvisatya sakratarakam || 14|| saptasitya sasi hanti taram saumyavisakhayoh | yamyago daksinasastho vyaktam satabhisagjinaih || 15 || you stooj a great fremfae famne: 1 yastiyuktakalaksiptya bhedah syad grahadhisnayoh || 16 || (Bhaskara I, Laghubhaskariya , 8. 10-16) 1 For notes, see Su.Si : Burgess, pp. 248-49. * For the rationale see GL: RCP. II. p. 103-4. Occultation of stars by the Moon 272 The Moon is in (absolute) conjunction with a junction-star when its longitude and celestial latitude, both in magnitude and direction, are the same as the longitude and celestial latitude of the star both in magnitude and direction. (10) Latitudes of the Moon occulting certain stars When the Moon atains 160 minutes (of arc) of north latitude, it clearly covers the junction-star of the nakstara Krttika (i.e., the Pleiades). (11) Having attained her maximum northern latitude, the Moon covers with its disc the central star of the naksatra Magha. (12) With its latitude 60' (south), the Moon clearly occults the cart of Rohini (i.e., the V-shaped constellation of Hyades); and with latitude 256' south it covers the junction-star (of Rohini) (i.e., Aldebaran). (13) With its latitude 95 (minutes of arc) south, (the Moon covers the junction-star of) the naksatra Citra (i.e., Spica); with 150 (minutes of arc) south, (the junction-star of) the naksatra Anuradha; and with 200 (minutes of arc) (south), (the junctuion-star of) the naksatra Jyestha (i.e., Antares). (14) With latitude 87 (minutes of arc south), the Moon clearly occults (the brighter of) the two northern stars of the naksatra Visakha; with 24 (minutes of arc) south, (the junction-star of) the naksatra Satabhisak (i.e., Aquarii). (15) The Moon, situated at its ascending Node, occults (the junction-star of) Pusya and Revati (i.e., Piscium). The above occultations (bheda) of the stars by the planet (Moon) are based on the minutes of latitude determined from actual observation by means of the instrument (called) Yasti. (16). (Kripa Shankar Shukla) 20. 5.2. prajapatyadale sthitastu himaguryamyaih saramsaistribhi- vitryamsah sakatam bhinatti vidalaistaih pancabhi rohinim | saumyaih pancabhiramsakaisca vidalaistaram madhamadhyamam viksepena vivarjitastu gurubham pausnam tatha varunam || (Lalla, Sisyadhivrddhida , 11. 11) The Moon, when in the middle of the asterism of Rohini, pierces the Cart (of Rohini), if its southern latitude is 2° 40', and occults the principal star, Rohini, when its southern latitude is 4° 30'. Again, the Moon occults the middle star of the asterism Magha, when it has a north latitude of 4° 30'. When it has no latitude, it occults Revati, Pusya and Satabhisa. (11). (Bina Chatterjee)
273 naksatra prayogasamayah 19. CONJUNCTION OF PLANETS 20.6 1. vidheyamayanam grahe svadrstikarma purvavat | sphutasca khetasayako grahayogasiddhaye || 6 || yutikalajnanam grahavantare kala nabhogabhuktibhajitah | gatagataptavasarairyutirgrahe'dhikonake || 10 || viloma nabhascare gatasyataviparyayah | graharksadaksinottarantaram nabhogayogavat || 11 || (Bhaskara II, Siddhantasiromani . 1.11. 9-11.) Time of star-planet conjunction The ayana-drkkarma is to be done (with respect to the 20. 6. 1 planet) and the sphutasara is to be computed to know the time of (polar latitudinal) conjunction. (9) The difference in the longitudes of the planet and the star, divided by the daily motion of the planet, gives the number of days approximately after or before the moment of conjunction. 1 ( 10 ) If the planet be retrograde, the conjunction past future will be in the reverse, i.e. future or past. (11). (Arka Somayaji) or 1 For the rationale, see Siddhantasiromani : Arka Somayaji, pp. 512-13.