Āryabhaṭīya/Chapter 03
वर्षम् द्वादशमासास् त्रिंशत्दिवसस् भवेत्सस्मासस्तु ।
षष्टिस्नाड्यस्दिवसस् षष्टिस्च विनाडिका नाडी ।। ३.१ ।।
A year consists of 12 months. A month consists of 30 days. A day consists of 60 nadis. A nadi consists of 60 vinadikas (or vinadis).
Āryabhaṭīya/Chapter 03
गुरुअक्षराणि षष्टिस्विनाडिका आर्क्षी षटेव वा प्राणास् ।
एवं कालविभागस्क्षेत्रविभागस्तथा भगणात् ।। ३.२ ।।
A sidereal vinadika is equal to (the time taken by a man in normal condition in pronouncing) 60 long syllables (with moderate flow of voice) or (in taking) 6 respirations (pranas). This is the division of time. The division of a circle (lit. the ecliptic) proceeds in a similar manner from the revolution.
Āryabhaṭīya/Chapter 03
भगणास् द्वयोस् द्वयोस्ये विशेषशेषास्युगे द्वियोगास्ते ।
रविशशिनक्षत्रगणास्सम्मिश्रास्च व्यतीपातास् ।। ३.३ ।।
(a-b) The difference between the revolution-numbers of any two planets is the number of conjunctions of those planets in a yuga. (c-d) The (combined) revolutions of the Sun and the Moon added to themselves is the number of Vyatipatas (in a yuga).
Āryabhaṭīya/Chapter 03
स्वौच्चभगणास्स्वभगणैस्विशेषितास्स्वौच्चनीचपरिवर्तास् ।
गुरुभगणास्राशिगुणासश्वयुजऽद्यास्गुरोरब्दास् ।। ३.४ ।।
(a-b) The difference between the revolution-numbers of a planet and its ucca gives the revolutions of the planet's epicycle (in a yuga). (c-d) The revolution-number of Jupiter multiplied by 12 gives the number of Jovian years beginning with Asvayuk (in a yuga).
Āryabhaṭīya/Chapter 03
रविभगणास्रविअब्दास्रविशशियोगास् भवन्ति शशिमासास् ।
रविभूयोगास्दिवसास्भऽवर्तास्च अपि नाक्षत्रास् ।। ३.५ ।।
The revolutions of the Sun are solar years. The conjunctions of the Sun and the Moon are lunar months. The conjunctions of the Sun and Earth are (civil) days. The rotations of the Earth are sidereal days.
Āryabhaṭīya/Chapter 03
अधिमासकास्युगे ते रविमासेभ्यसधिकास्तु ये चान्द्रास् ।
शशिदिवसास्विज्ञेयास्भूदिवसऊनास्तिथिप्रलयास् ।। ३.६ ।।
The lunar months (in a yuga) which are in excess of the solar months (in a yuga) are (known as) the intercalary months in a yuga; and the lunar days (in a yuga) diminished by the civil days (in a yuga) are known as the omitted lunar days (in a yuga).
Āryabhaṭīya/Chapter 03
रविवर्षं मानुष्यं ततपि त्रिंशत्गुणं भवति पित्र्यम् ।
पित्र्यं द्वादशगुणितं दिव्यं वर्षं विनिर्दिष्टम् ।। ३.७ ।।
A solar year is a year of men. Thirty times a year of men is a year of the Manes. Twelve times a year of the Manes is called a divine year (or a year of the gods).
Āryabhaṭīya/Chapter 03
दिव्यं वर्ष सहस्रं ग्रहसामान्यं युगं द्वि५षट्कगुणम् ।
अष्टौत्तरं सहस्रं ब्राह्मस्दिवसस्ग्रहयुगानाम् ।। ३.८ ।।
12000 divine years make a general planetary yuga. 1008 (general) planetary yugas make a day of Brahma.
Āryabhaṭīya/Chapter 03
उत्सर्पिणी युग अर्धं पश्चातपसर्पिणी युग अर्धं च ।
मध्ये युगस्य सुषमा आदौ अन्ते दुष्षमा इन्दुउच्चात् ।। ३.९ ।।
The (first) half of a yuga is Utsarpini and the second half Apasarpini. Susama occurs in the middle and Dussama in the beginning and end. (The time elapsed or to elapse is to be reckoned) from the position of the Moon's apogee.
Āryabhaṭīya/Chapter 03
षष्टिअब्दानां षष्टिस्यदा व्यतीतास्त्रयस्च युगपादास् ।
त्रिअधिका विंशतिसब्दास्तदा इह मम जन्मनसतीतास् ।। ३.१० ।।
When sixty times sixty years and three quarter yugas (of the current yuga) had elapsed, twentythree years had then passed since my birth.
Āryabhaṭīya/Chapter 03
युगवर्षमासदिवसास्समं प्रवृत्तास्तु चैत्रशुक्लऽदेस् ।
कालसयं अनादिअन्तस्ग्रहभैस् अनुमीयते क्षेत्रे ।। ३.११ ।।
The yuga, the year, the month, and the day commenced simultaneously at the beginning of the light half of Caitra. This time, which is without beginning and end, is measured with the help of the planets and the asterisms on the Celestial Sphere.
Āryabhaṭīya/Chapter 03
षष्ट्या सूर्याब्दानां प्रपूरयन्ति ग्रहास्भपरिणाहम् ।
दिव्येन नभस्परिधिं समं भ्रमन्तस्स्वकक्ष्यासु ।। ३.१२ ।।
The planets moving with equal linear velocity in their own orbits complete (a distance equal to) the circumference of the sphere of the asterisms in a period of 60 solar years, and (a distance equal to) the circumference of the sphere of the sky in a yuga.
Āryabhaṭīya/Chapter 03
मण्डलं अल्पं अधस्तात्कालेन अल्पेन पूरयति चन्द्रस् ।
उपरिष्टात्सर्वेषां महत्च महता शनैश्चारी ।। ३.१३ ।।
The Moon completes its lowest and smallest orbit in the shortest time; Saturn completes its highest and largest orbit in the longest time.
Āryabhaṭīya/Chapter 03
अल्पे हि मण्डले अल्पा महति महान्तस्च राशयस्ज्ञेयास् ।
अंशास्कलास्तथा एवं विभागतुल्यास्स्वकक्ष्यासु ।। ३.१४ ।।
(The linear measures of) the signs are to be known to be small in small orbits and large in large orbits; so also are (the linear measures of) the degrees, minutes, etc. The circular division is however, the same in the orbits of the various planets.
Āryabhaṭīya/Chapter 03
भानां अधस्शनैश्चरसुरगुरुभौमार्कशुक्रबुधचन्द्रास् ।
एषां अधस्च भूमिस्मेधीभूता खमध्यस्था ।। ३.१५ ।।
(The asterisms are the outermost). Beneath the asterisms lie (the planets) Saturn, Jupiter, Mars, the Sun, Venus, Mercury, and the Moon (one below the other); and beneath them all lies the Earth like the hitching peg in the midst of space.
Āryabhaṭīya/Chapter 03
सप्त एते होराईशास्शनैश्चरऽद्यास्यथाक्रमं शीघ्रास् ।
शीघ्रक्रमात् चतुर्थास् भवन्ति सूर्यौदयात्दिनपास् ।। ३.१६ ।।
The (above-mentioned) seven planets beginning with Saturn, which are arranged in the order of increasing velocity, are the lords of the successive hours. The planets occurring fourth in the order of increasing velocity are the lords of the successive days, which are reckoned from sunrise (at Laaka).
Āryabhaṭīya/Chapter 03
कक्ष्याप्रतिमण्डलगास् भ्रमन्ति सर्वे ग्रहास्स्वचारेण ।
मन्दौच्चातनुलोमं प्रतिलोमं च एव शीघ्रौच्चात् ।। ३.१७ ।।
(The mean planets move on their orbits and the true planets on their eccentric circles). All the planets, whether moving on their orbits (kaksya-mandala) or on the eccentric circles (prati-mandala), move with their own (mean) motion, anticlock-wise from their apogees and clockwise from their sighroccas.
Āryabhaṭīya/Chapter 03
कक्ष्यामण्डलतुल्यं स्वं स्वं प्रतिमण्डलं भवति एषाम् ।
प्रतिमण्डलस्य मध्यं घनभूमध्याततिक्रान्तम् ।। ३.१८ ।।
The eccentric circle of each of these planets is equal to its own orbit, but the centre of the eccentric circle lies at a distance from the centre of the solid Earth.
Āryabhaṭīya/Chapter 03
प्रतिमण्डलभूविवरं व्यास अर्धं स्वौच्चनीचवृत्तस्य ।
वृत्तपरिधौ ग्रहास्ते मध्यमचारात् भ्रमन्ति एवम् ।। ३.१९ ।।
(a-b) The distance between the centre of the Earth and the centre of the eccentric circle is (equal to) the semi-diameter of the epicycle (of the planet). (c-d) All the planets undoubtedly move with mean motion on the circumference of the epicycles.
Āryabhaṭīya/Chapter 03
यस्शीघ्रगतिस्स्वौच्चात्प्रतिलोमगतिस्स्ववृत्तकक्ष्यायाम् ।
अनुलोमगतिस्वृत्ते मन्दगतिस्यस्ग्रहस् भवति ।। ३.२० ।।
A planet when faster than its ucca moves clockwise on the circumference of its epicycle and when slower than its ucca moves anticlockwise on its epicycle.
Āryabhaṭīya/Chapter 03
अनुलोमगानि मन्दात्शीघ्रात्प्रतिलोमगानि वृत्तानि ।
कक्ष्यामण्डललग्नस्ववृत्तमध्ये ग्रहस्मध्यस् ।। ३.२१ ।।
The epicycles move anticlockwise from the apogees and clock-wise from the sighroccas. The mean planet lies at the centre of its epicycle, which is situated on the (planet's) orbit.
Āryabhaṭīya/Chapter 03
क्षयधनधनक्षयास् स्युर्मन्दौच्चात्व्यत्ययेन शीघ्रौच्चात् ।
शनिगुरुकुजेषु मन्दात् अर्धं ऋणं धनं भवति पूर्वे ।। ३.२२ ।।
(a-b)The corrections from the apogee (for the four anomalistic quadrants) are respectively minus, plus, plus, and minus. Those from the sighrocca are just the reverse. (c-d) In the case of (the superior planets) Saturn, Jupiter and Mars, first apply the mandaphala negatively or positively (as the case may be).
Āryabhaṭīya/Chapter 03
मन्दौच्चात्शीघ्रौच्चात् अर्धं ऋणं धनं ग्रहेषु मन्देषु ।
मन्दौच्चात्स्फुटमध्यास्शीघ्रौच्चात्च स्फुटास्ज्ञेयास् ।। ३.२३ ।।
Apply half the mandaphala and half the sighraphala to the planet and to the planet's apogee negatively or positively (as the case may be). The mean planet (then) corrected for the mandaphala (calculated afresh from the new mandakendra) is called the true-mean planet and that (true-mean planet) corrected for the Sighraphala (calculated afresh) is known as the true planet.
Āryabhaṭīya/Chapter 03
शीघ्रौच्चात् अर्धऊनं कर्तव्यं ऋणं धनं स्वमन्दौच्चे ।
स्फुटमध्यौ तु भृगुबुधौ सिद्धात्मन्दात्स्फुटौ भवतस् ।। ३.२४ ।।
(In the case of Mercury and Venus) apply half the sighraphala negatively or positively to the longitude of the planet's apogee (according as the sighrakendra is less than or greater than 180°). From the corrected longitude of the planet's apogee (calculate the mandaphala afresh and apply it to the mean longitude of the planet; then) are obtained the true-mean longitudes of Mercury and Venus. (The sighraphala, calculated afresh, being applied to them), they become true (longitudes).
Āryabhaṭīya/Chapter 03
भूताराग्रहविवरं व्यास अर्धहृतस्स्वकर्णसंवर्गस् ।
कक्ष्यायां ग्रहवेगस्यस् भवति सस्मन्दनीचौच्चे ।। ३.२५ ।।
The product of the mandakarna and the sighrakarna when divided by the radius gives the distance between the Earth and the planet. The velocity of the (true) planet moving on the (sighra) epicycle is the same as the velocity of the (true-mean) planet moving in its orbit (of radius equal to the mandakarna).