Of the mean motions of the planets ||1||
1To him whose shape is inconceivable and unmanifested, who is unaffected by the qualities, whose nature is quality, whose form is the support of the entire creation to Brahma be homage!
2When but little of the Golden Age (Krita Yuga) was left, a great demon (Asura), named Maya, being desirous to know that mysterious, supreme, pure and exalted science.
3That chief auxiliary of the scripture (Vedanga), in its entirety the cause, namely of the motion of the heavenly bodies (Jyotis), performed, in propitiation of the Sun, very severe religious austerities.
4Gratified by these austerities, and rendered propitious, the Sun himself delivered unto that Maya, who besought a boon, the system of the planets. The blessed Sun spoke:
5Thine intent is known to me; I am gratified by thine austerities; I will give thee the science upon which time is founded, the grand system of the planets.
6No one is able to endure my brilliancy; for communication I have no leisure; this person, who is a part of me, shall relate to thee the whole.
7Thus, having spoken, the god disappeared, having given directions unto the part of himself. This latter person thus addressed Maya, as he stood bowed forward, his hands suppliantly joined before him;
8Listen with concentrated attention to the ancient and exalted science, which has been spoken, in each successive Age, to the- Great Sages (Maharishi), by the Sun himself.
9This is that very same original textbook which the Sun of old promulgated: only, by reason of the revolution of the Ages, there is here a difference of times.
10Time is the destroyer of the worlds; another Time has for its nature to bring to pass. This latter, according as it is gross or minute, is called by two names, real (Murta) and unreal (Amurta).
11That which begins with respirations (prana) is called real; that which begins with atoms (Truti) is called unreal. Six respirations make a Vinadi, sixty of these a Nadi;
12And sixty Nadis make a sidereal day and night, of thirty of these sidereal days is composed a month; a civil (Savana) month consists of as many sunrises;
13A lunar month, of as many lunar days (Tithi); a solar (Saura) month is determined by the entrance of the sun into a sign of the zodiac: twelve months make a year. This is called a day of the gods.
14The day and night of the gods and of the demons are mutually opposed to one another. Six times sixty of them are a year of the gods, and likewise of the demons.
15Twelve thousands of these divine years are denominated a Quadruple Age (Caturyuga); of ten thousand times four hundred and thirty-two solar years.
16Is composed that Quadruple Age, with its dawn and twilight. The difference of the Golden and the other Ages, as measured by the difference in the number of the feet of Virtue in each, is as follows:
17The tenth part of an Age multiplied successively by four, three, two, and one, gives the length of the Golden and the other Ages, in order: the sixth part of each belongs to its dawn and twilight.
18One and seventy Ages are styled here a Patriarchate (Manvantara); at its end is said to be a twilight which has the number of years of a Golden Age, and which is a deluge.
19In an Aeon (Kalpa) are reckoned fourteen such Patriarchs (Manu) with their respective twilights; at the commencement of the Mon is a fifteenth dawn, having the length of a Golden Age. The Mon is accordingly thus composed:
20The Aeon, thus composed of a thousand Ages, and which brings about the destruction of all that exists, is styled a day of Brahma; his night is of the same length.
21His extreme age is a hundred, according to this valuation of a day and a night. The half of his life is past; of the remainder, this is the first Mon.
22And of this Mon, six Patriarchs (Manu) are past, with their respective twilights; and of the Patriarch Manu son of Vivasvant, twenty-seven Ages are past;
23Of the present the twenty-eighth, Age, this Golden Age is past: from this point, reckoning up the time, one should compute together the whole number.
24One hundred times four hundred and seventy-four divine years passed while the All wise was employed in creating the animate and inanimate creation, plants, stars, gods, demons, and the rest.
25The planets moving westward with exceeding velocity, but constantly beaten by the asterisms, fall behind, at a rate precisely equal, proceeding each in its own path.
26Hence, they have an eastward motion. From the number of their revolutions is derived their daily motion, which is different according to the size of their orbits; in proportion to this daily motion they pass through the asterisms.
27One which moves swiftly passes through them in a short time; one which moves slowly, in a long time. By their movement, the revolution is accounted complete at the end of the asterism Revati.
28Sixty seconds (Vikala) make a minute (Kala); sixty of these, a degree (Bhaga); of thirty of the latter is composed a sign (Rasi); twelve of these are a revolution (Bhagana).
29ln an Age (Yuga), the revolutions of the sun, Mercury, and Venus, and of the conjunctions (Cighra) of Mars, Saturn, and Jupiter, moving eastward, are four million, three hundred and twenty thousand;
30Of the moon, fifty-seven million, seven hundred and fifty-three thousand, three hundred and thirty-six; of Mars, two million, two hundred and ninety-six thousand, eight hundred and thirty-two;
31Of Mercury’s conjunction (Cighra). seventeen million, nine hundred and thirty-seven thousand, and sixty; of Jupiter, three hundred and sixty-four thousand, two hundred and twenty;
32Of Venus’s conjunction (Cighra), seven million, twenty-two thousand, three hundred and seventy-six; of Saturn, one hundred and forty-six thousand five hundred and sixty-eight;
33Of the moon’s apsis (Ucca), in an Age, four hundred and eighty-eight thousand, two hundred and three; of its node (Pata), in the contrary direction two hundred and thirty-two thousand, two hundred and thirty-eight;
34Of the asterisms, one billion, five hundred and eighty-two million, two hundred and thirty-seven thousand, eight hundred and twenty-eight. The number of risings of the asterisms, diminished by the number of the revolutions of each planet respectively, gives the number of risings of the planets in an Age.
35The number of lunar months is the difference between the number of revolutions of the sun and of the moon. If from it the number of solar months be subtracted, the remainder is the number of intercalary months.
36Take the civil days from the lunar, the remainder is the number of omitted lunar days (Tithikshaya). From rising to rising of the sun are reckoned terrestrial civil days;
37Of these there are, in an Age, one billion, five hundred and seventy-seven million, nine hundred and seventeen thousand, eight hundred and twenty-eight; of lunar days, one billion, six hundred and three million, and eighty;
38Of intercalary months, one million, five hundred and ninety-three thousand, three hundred and thirty-six; of omitted lunar days, twenty-five million, eighty-two thousand, two hundred and fifty-two;
39Of solar months, fifty-one million, eight hundred and forty thousand. The number of risings of the asterisms, diminished by that of the revolutions of the sun, gives the number of terrestrial days.
40The intercalary months, the omitted lunar days, the sidereal, lunar, and civil days—these, multiplied by a thousand, are the number of revolutions, etc., in an Aeon.
41The revolutions of the sun’s apsis (Manda), moving eastward, in an Eon, are three hundred and eighty-seven; of that of Mars, two hundred and four; of that of Mercury, three hundred and sixty-eight;
42Of that of Jupiter, nine hundred; of that of Venus, five hundred and thirty-five; of the apsis of Saturn, thirty-nine. Farther, the revolutions of the nodes, retrograde, are:
43Of that of Mars, two hundred and fourteen; of that of Mercury, four hundred and eighty-eight; of that of Jupiter, one hundred and seventy-four; of that of Venus, nine hundred and three;
44Of the node of Saturn, the revolutions in an Eon are six hundred and sixty-two: the revolutions of the moon’s apsis and node have been given here already.
45Now add together the time of the six Patriarchs (Manu), with their respective twilights, and with the dawn at tin commencement of the Mon (Kalpa); farther, of the Patriarch Manu, son of Vivasvant,
46The twenty-seven Ages (Yuga) that are past, and likewise the present Golden Age (Krita Yuga); from their sum subtract the time of creation, already stated in terms of divine years,
47In solar years: the result is the time elapsed at the end of the Golden Age; namely, one billion, nine hundred and fifty-three million, seven hundred and twenty thousand solar years.
48To this, add the number of years of the time since past. Reduce the sum to months, and add the months expired of the current year, beginning with the light half of Caitra.
49Set the result down in two places; multiply it by the number of intercalary months, and divide by that of solar months, and add to the last result the number of intercalary months thus found; reduce the sum to days, and add the days expired of the current month;
50Set the result down in two places; multiply it by the number of omitted lunar days, and divide by that of lunar days; subtract from the last result the number of omitted lunar days thus obtained: the remainder is, at midnight, on the meridian of Lanka,
51The sum of days, in civil reckoning. From this may be found the lords of the day, the month, and the year, counting from the sun. If the number be divided by seven, the remainder marks the lord of the day, beginning
with the sun.
52Divide the same number by the number of days in a month and in a year, multiply the one quotient by two and the other by three, add one to each product, and divide by seven; the remainders indicate the lords of the month and of the year.
53Multiply the sum of days (Dinarasi) by the number of revolutions of any planet and divide by the number of civil days; the result is the position of that planet, in virtue of its mean motion, in revolutions and parts of a revolution.
54Thus, also are ascertained the places of the conjunction (Cighra) and apsis (Mandocca) of each planet, which have been mentioned as moving eastward; and in like manner of the nodes, which have a retrograde motion, subtracting the result from a whole circle.
55Multiply by twelve the past revolutions of Jupiter, add the signs of the current revolution, and divide by sixty; the remainder marks the year of Jupiter’s cycle, counting from Vijaya.
56The processes which have thus been stated in full detail, are practically applied in an abridged form. The calculation. Of the mean place of the planets may be made from any epoch (Yuga) that may be fixed upon.
57Now, at the end of the Golden Age (Krita Yuga), all the planets, by their mean motion—excepting, however, their nodes and apsides (Mandocca) are in conjunction in the first of Aries.
58The moon’s apsis (Ucca) is in the first of Capricorn, and its node is in the first of Libra; and the rest, which have been stated above to have a slow motion, their position cannot be expressed in whole signs.
59Twice eight hundred yojanas are the diameter of the earth: the square root of ten times the square of that is the earth’s circumference.
60This multiplied by the sine of the co-latitude (Lambajya) of any place, and divided by radius (trijiva), is the corrected, (Sphuta) circumference of the earth at that place. Multiply the daily motion of a planet by the distance in longitude (Decantara) of any place, and divide by its corrected circumference;
61The quotient, in minutes, subtract from the mean position of the planet as found, if the place be east of the prime meridian (Rekha); add, if it be west; the result is the planet’s mean position at the given place.
62Situated upon the line which passes through the haunt of the demons (Rakshasa) and the mountain which is the seat of the gods, are Rohitaka and Avanti, as also the adjacent lake.
63When, in a total eclipse of the moon, the emergence (Unmilana) takes place after the calculated time for its occurrence, then the place of the observer is to the east of the central meridian.
64When it takes place before the calculated time, his place is to the west: the same thing may be ascertained likewise from the immersion (Nimilana). Multiply by the difference of the two times in Nadis the corrected circumference of the earth at the place of observation.
65And divide by sixty, the result, in yojanas, indicates the distance of the observer from the meridian, to the east or to the west, upon his own parallel; and by means of that is made the correction for difference of longitude.
66The succession of the weekday (Vara) takes place, to the east of the meridian, at a time after midnight equal to the difference of longitude in Nadis; to the west of the meridian, at a corresponding time before midnight.
67Multiply the mean daily motion of a planet by the number of Nadis of the time fixed upon, and divide by sixty: subtract the quotient from the place of the planet, if the time be before midnight; add, if it be after: the result is its place at the given time.
68The moon is, by its node, caused to deviate from the limit of its declination (Kranti), northward and southward, to a distance, when greatest, of an eightieth part of the minutes of a circle;
69Jupiter, to the ninth part of that multiplied by two; Mars, to the same amount multiplied by three; Mercury, Venus, and Saturn are by their nodes caused to deviate to the same amount multiplied by four.
70So also, twenty-seven, nine, twelve, six, twelve, and twelve, multiplied respectively by ten, give the number of minutes of mean latitude (Vikshepa) of the moon and the rest, in their order.