Siddhanta

GRAHĀNAYANĀDHYĀYA

Verse 1. To Compute the Ahargana the collection of days from the beginning of Kalpa ie from the beginning of creation. Multiply the number of sidereal solar years from the beginning of Kalpa by 12; add the number of elapsed lunar months; multiply by thirty; add the number of elapsed tithis. Let this number be x.

Then $\lfloor \frac{x \times A}{s} \rfloor$ the integral number obtained by dividing the product of x and A the number of Adhikamasas in a Kalpa by s the number of solar days thereof gives the number of elapsed Adhikamasas. Multiply this number of Adhikamasas by 30 and add to x. The result gives the number of elapsed tithis, Let this be y.

Then $\lfloor \frac{y \times K}{T} \rfloor$ the integral number obtained by dividing the product of y and K the number of Kshayahas in a Kalpa by T the number of Tithis in a Kalpa, gives the number of Kshayahas. Subtracting this number from y, we have the Ahargana ie the number of the elapsed civil days from the beginning of Kalpa. This Ahargana has its beginning on Sunday and is itself constituted of mean solar days. While computing the Adhikamasas or Kshayahas, the integral numbers of the quosients alone should be taken rejecting the remainders.

Verse 4. Computation of the planetary positions.

The Ahargana multiplied by the number of sidereal revolutions of a planet and divided by the number of civil days in a Kalpa gives the planet ie its number of revolutions upto the day concerned both integral and fractional.

Verse 5. To obtain the position of the mean Moon, when the mean Sun is known from what is called Avama-Sesa.

The Avama Sesa divided by 13149000000 in degrees is to be added to twelve times the elapsed tithis and the result added to the Sun’s position gives the position of the Moon. Conversely the position of the Sun can be had from the position of the Moon.

Verses 6, 7. Computation of the positions of the Sun and the Moon from the Adhimāsa-Sesha and Avama-Sesha.

The Avama-Sesha divided by 2711000000 is termed an additive constant in minutes of arc to the Sun’s position; the same Avama-Sesha multiplied by 13 and divided by 35 is termed such an additive constant to the position of the Moon;

Construe that the Sun’s position is given by as many degrees as there are elapsed tithis after the beginning of Chaitra and that the Moon’s position is given by Thirteen times the same. Let these positions of the Sun and the Moon be diminished by a number of degrees equal to what is obtained by dividing the Adhimāsa-Sesha by the number of lunations in a Kalpa.

Then add the respective additive constants to the positions of the Sun and the Moon so obtained. The results will be the positions of the Mean Sun and the Mean Moon.

Verses 8, 9. Another way of computing the planetary positions.

The mean position of the Sun in Rasis minus A×G131493037500 131493037500A×G

Rasis where A stands for the Aharghaṇa, G stands for the Sāvana days of the planet concerned in a Kalpa gives the position of the planet in Rasis. Let pandits find out other similar methods.

Verses 10, 11. Proof of other methods of computing planetary position. Even as the sums or differences of two or more of the numbers of Adhimāsas, Kṣhayāhas, lunations etc give the number of sidereal revolutions of the planets the sums or differences of two or more of the positions of the imaginary planets which go by the names Adhimāsa-graha, Kṣhayāhagraha etc computed out of the numbers of those Adhimāsa Kṣhayāhas etc. give the respective planetary positions.