In Search of Jyotish 13 SIDDHĀNTA 1: ASTRONOMY FUNDAMENTALS

SARAJIT PODDAR AN EARNEST JYOTIṢA SEEKER NOTION PRESS JULY 2022

IN SEARCH OF JYOTISH

NOTION PRESS India. Singapore. Malaysia. ISBN: __________________ This book has been published with all reasonable efforts taken to make the material errorfree after the consent of the author. No part of this book shall be used, reproduced in any manner whatsoever without written permission from the author, except in the case of brief quotations embodied in critical articles and reviews. The Author of this book is solely responsible and liable for its content, including but not limited to the views, representations, descriptions, statements, information, opinions, and references [“Content”]. The Content of this book shall not constitute or be construed or deemed to reflect the opinion or expression of the Publisher or Editor. Neither the Publisher nor Editor endorse or approve the Content of this book or guarantee the reliability, accuracy or completeness of the Content published herein and do not make any representations or warranties of any kind, express or implied, including but not limited to the implied warranties of merchantability, fitness for a particular purpose. The Publisher and Editor shall not be liable whatsoever for any errors, omissions, whether such errors or omissions result from negligence, accident, or any other cause or claims for loss or damages of any kind, including without limitation, indirect or consequential loss or damage arising out of use, inability to use, or about the reliability, accuracy or sufficiency of the information contained in this book.

FIRST EDITION July 2022 https://www.facebook.com/sarajit.poddar https://www.facebook.com/srivarahamihira https://www.facebook.com/insearchofjyotish email: [email protected] Disclaimer: Jyotiṣa (Vedic Astrology) strives to explain the effects of invisible forces on the lives of worldly affairs. The past life Karma manifests in the form of Grahas in specific positions in a Kuṇḍalī, which is used to decipher the effects of the past life Karma. Nothing stated in this book is absolute. It is about reflecting upon the symbols which are in the form of Grahas, Rāśis, Bhāvas, Nakṣatras and others. These reflections are only based on my interpretation and are for guidance only. What you decide to do, including any actions you take, with the information stated in this book, is based on your responsibility and choice. Nothing in this book should be considered a piece of advice, be it medical, legal, financial, or psychological, and subject to your interpretation and judgment. The content of this book is not a substitute for any advice or treatment that you may receive from a licensed professional such as a lawyer, doctor, financial advisor, or psychiatrist.

फलानि ग्रह चारे ण सूचयनति मिीनिणः। को वक्ता िारिम्यस्य िमेकं वेधसं नविा॥ phalāni graha cāreṇa sūcayanti manīṣiṇaḥ। ko vaktā tāratamyasya tamekaṃ vedhasaṃ vinā॥ For human beings, the fruits of their actions are indicated by the movement of Grahas. Who, except the creator Brahmā, can tell for sure what is about to happen! 10 JULY 2022

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ASTRONOMY FUNDAMENTALS

Dedicated to the lotus feet of Devī Sarasvatī the Goddess of Learning for being with me throughout writing this book

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IN SEARCH OF JYOTISH

DEVĪ SARASVATĪ PRAYER নম ো সরস্বতী হোভোমে বিমযে ক লমলোচমন । বিশ্বরূমে বিশোলোক্ষ্মী বিযেোাংমযহী নম োহস্তুমত ॥ জয়জয় দযিী চরোচর সোমর কুচযুেমশোবভত ুক্তোহোমর । িীনোরঞ্জিত েুস্তক হমস্ত ভেিতী ভোরতী দযিী ন হস্তুমত ॥ namo sarasvatī mahābhāge vidye kamalalocane । viśvarūpe viśālākṣmī vidyāṃdehī namohastute ॥ jayajaya devī carācara sāre kucayugaśobhita muktāhāre । vīnārañjita pustaka haste bhagavatī bhāratī devī namahastute ॥ যো কুমেেুতুষোরহোরধিলো যো শুভ্রিস্ত্রোিৃতো যো িীণোিরযণ্ড ঞ্জণ্ডতকরো যো দশ্বতেদ্মোসনো। যো ব্রহ্মোচু েত শাংকরপ্রভৃ বতবভমযেবিৈঃ সযো িঞ্জেতো সো োাং েোতু সরস্বতী ভেিতী বনৈঃমশষজোড্েোেহো॥ yā kundendutuṣārahāradhavalā yā śubhravastrāvṛtā yā vīṇāvaradaṇḍamaṇḍitakarā yā śvetapadmāsanā। yā brahmācyuta śaṃkaraprabhṛtibhirdevaiḥ sadā vanditā sā māṃ pātu sarasvatī bhagavatī niḥśeṣajāḍyāpahā॥ শুক্োাং ব্রহ্মবিচোর সোর ের ো োযেোাং জেদ্ব্েোবেনীাং িীণো-েুস্তক-ধোবরণী ভযযোাং জোড্েোন্ধকোরোেহো । হমস্ত স্ফটিক োবলকোাং বিযধতীাং েদ্মোসমন সাংবিতো িমে তোাং েরম শ্বরীাং ভেিতীাং িুঞ্জিপ্রযোাং শোরযো ॥২॥ śuklāṃ brahmavicāra sāra paramāmādyāṃ jagadvyāpinīṃ vīṇā-pustaka-dhāriṇīmabhayadāṃ jāḍyāndhakārāpahām। haste sphaṭikamālikāṃ vidadhatīṃ padmāsane saṃsthitām vande tāṃ parameśvarīṃ bhagavatīṃ buddhipradāṃ śāradām॥2॥

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ASTRONOMY FUNDAMENTALS

ॐ गणािां त्वा गणपतिं हवामहे कतवं कवीिामुपमश्रवस्िमम् । ज्येष्ठराजं ब्रह्मणाम् ब्रह्मणस्पि आ िः शृण्वन्नूनिन ःसीदसादिम् ॥ ॐ महागणानधपिये िमः ॥ ॐ सह नाववतु। सह नौ भुनक्तु । सह वीर्यं करवावहै। तेजस्वव नावधीतमवतु मा स्वस्िषावहै। ॐ शास््तिः शास््तिः शास््तिः॥ om saha nāvavatu। saha nau bhunaktu। saha vīryaṁ karavāvahai। tejasvi nāvadhītamastu mā vidviṣāvahai। om śāntiḥ śāntiḥ śāntiḥ॥ OM! May He protect us! May He nourish us! May we work together with great energy! May our intellect be sharp and study effective! Let there be no animosity between us! OM! Let there be Peace in me! Let there be Peace in the world! Let there be Peace in the forces that act on me!

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IN SEARCH OF JYOTISH

PREFACE Jyotiṣa is dependent on the precise position of Grahas in the sky. Therefore, understanding of Jyotiṣa is incomplete without adequate knowledge of astronomy. While in modern times, there is a tendency to jump to the Phalita (horoscopy) section of Jyotiṣaśāstra, studying the classical texts reveals that this is not the traditional approach. The Jyotiṣa classical texts state that Jyotiṣa has 3 important segments, called the Skandhas, and among them, Gaṇita, the mathematical portion of Jyotiṣa is an important Skandha. An understanding of astronomical mathematics helps understand the movement of the Grahas in the sky and helps draw parallels between such movement and worldly affairs. This book introduces the fundamentals of astronomy, which should help one visualise the Grahas’ movement in the sky. It starts with understanding the Celestial Sphere and the Coordinate system. What is a Celestial Sphere? The Celestial Sphere is an imaginary sphere, with an arbitrarily large radius, with Pṛthvī at its centre. The objects in the sky are projected upon the Celestial Sphere's inner surface. This sphere helps mark the position of various celestial objects, called the celestial or the Spherical Coordinate system. We shall start the study of astronomy with the fundamentals such as the measurement of time and then the Coordinate systems. That is followed by the computation of the mean and True Positions of the Grahas. In the chapter, I have covered the fundamentals of computing the planetary Coordinates based on both modern and Siddhānta methods. This area of Jyotiṣa and mathematics always attracted me. However, as destiny had it, I didn’t get an opportunity to study this in school, college or university. But my desire remained intact to understand and learn this. My search led me to several wonderful astronomical treaties, both Modern astronomy and Siddhānta astronomy. Notable ones are Mr Jean Meeus’s Astronomical Algorithms and Mr Peter Duffet Smith’s Practical Astronomy with your Calculator. Complementing this is the wonderful website of Mr Paul Schlyter https://stjarnhimlen.se, which gave a practical demonstration of the computation, which anyone can follow. Among the Siddhānta Texts, the ones that helped me immensely are Sūryasiddhānta, the books that I found to be helpful are Sūryasiddhānta English translations by Rev. Ebenezer Burgess and Śrī Bapu Deva Śāstrī, and Hindi translation by Śrī Mahavir Prasad Srivastava. I am also helped by Pañcasiddhāntikā by Śrī TS Kuppanna Śāstrī and Ancient Indian astronomy by Śrī S Balachandra Rao. I am immensely grateful to these authors. Suppose we consider a recent epoch for computation of the Graha positions, the Epoch of Caitra Śukla Pratipada of Gregorian year 2022. The Epoch is 2nd April 2022, 6 am LMT, Śanivāra, Caitra Śukla Pratipada. [6]

ASTRONOMY FUNDAMENTALS

Kalidina = 1871206, JD 2459671.54. The computations of the Graha positions based on this Epoch is as follows: Madhyagraha: 1. Sūrya = mod(346.061 + 0.985609 * d, 360) 2. Candra = mod(351.760 + 13.176355 * d, 360) 3. Maṅgala = mod(270.024 + 0.524033 * d, 360) 4. Budha Śig = mod(4.906 + 4.092339 * d, 360) 5. Bṛhaspati = mod(325.661 + 0.083091 * d, 360) 6. Śukra Śig = mod(217.705 + 1.602130 * d, 360) 7. Śani = mod(298.079 + 0.033460 * d, 360) 8. Prajāpati = mod(25.529 + 0.011732 * d, 360) 9. Varuṇa = mod(328.900 + 0.005981 * d, 360) 10. Yama = mod(247.359 + 0.003975 * d, 360) Mandocca: 1. Sūrya = mod(78.648 - 0.000030 * d, 360) 2. Candra = mod(64.419 + 0.111365 * d, 360) 3. Maṅgala = mod(131.87 - 0.000026 * d, 360) 4. Budha = mod(233.273 - 0.000034 * d, 360) 5. Bṛhaspati = mod(170.063 - 0.000033 * d, 360) 6. Śukra = mod(287.487 - 0.000037 * d, 360) 7. Śani = mod(248.721 - 0.000023 * d, 360) 8. Prajāpati = mod(328.121 - 0.000036 * d, 360) 9. Varuṇa = mod(202.452 - 0.000038 * d, 360) 10. Yama = mod(19.834 - 0.000039 * d, 360) The Rāhu and Ketu are Pāta of Candra, and their coordinates are 11. Rāhu = mod(30.431 - 0.052992 * d, 360) 12. Ketu = mod(210.431 - 0.052992 * d, 360 The Mandaparidhi and Śīghraparidhi of the Grahas are Sūrya 12.047 - 0.00, Candra 39.513 - 0.00, Maṅgala 67.150 - 236.609, Budha 147.276 - 138.363, Bṛhaspati 34.936 - 69.223, Śukra 4.870 - 260.396, Śani 39.950 - 37.744, Prajāpati 33.728 - 18.774, Varuṇa 6.447 - 11.977, Yama 177.786 - 9.218. There are no Śīghraparidhi of Sūrya. Let us find the coordinates of Sūrya, Candra, Śukra, Bṛhaspati and Rāhu in the Kuṇḍalī of Svāmi Vivekānanda. The computation of Śukra applies to Budha, and that of Bṛhaspati applies to Maṅgala, Śani, Prajāpati, Varuṇa and Yama. Therefore, if we can compute the positions of the 5 Grahas, we can compute for others. The first step in computing Graha positions is determining the time elapsed from the epoch (CSP 2022, 6:00 LMT Ujjain, Kalidina “KDe” 1871206). To do that, we must find the Kalidina. [7]

IN SEARCH OF JYOTISH

Kalidina is the continuous day count from Kali (23 Jan -3101, 06:00 LMT, Ujjain). Kalidina = (Year - 2000) * 365.2422 + 1863444. Year = yyyy + mm/12 + dd/365.25 - 1.086. We must perform the Vāra correction on Kalidina. Vāra correction “vc” = mod(Kalidina, 7) - Vāra + n. The Vāra is the Vāra of the concerned day where 1 is Śukravāra, 2 is Śanivāra, 3 is Ravivāra, 4 is Somavāra, 5 is Maṅgalavāra, 6 is Budhavāra, 7 is Bṛhaspativāra. “n” is 1 when the time is between 06:00 and Sūryodaya. Svāmi Vivekānanda was born on January 12, 1863, 6:17 LMT (6.283), tz = +5.89, Ravivāra, Sūryodaya 6:42:35 (6.709). Year = yyyy + mm/12 + dd/365.25 - 1.086 = 1863 + 1/12 + 12/365.25 - 1.086 = 1862.030. Kalidina = (year - 2000) * 365.2422 + 1863444.22 = (1862.030 - 2000) * 365.2422 + 1863444.22 = 1813051.75 = 1813052. Let us perform the Vāra correction. For Svāmiji, “n” is 1, because the birth is between 06:00 and Sūryodaya (6.709). Vāra correction “vc” = mod(Kalidina, 7) - Vāra - n = mod(1813052, 7) - 3 - 1 = -1. Kalidina “KD” = Kalidina - vc + (time - tz - 0.95)/24 - 1 = 1813052 + 1 + (6.283 - 5.89 - 0.95)/24 - 1 = 1813051.977. d = KD - KDe. The Kalidina of the CSP 2022 “KDe” is 1871206 and that of the given DateTime “KD” is 1813051.977. Therefore, d is 1813051.977 - 1871206 = -58154.023. SŪRYA:

Sūrya’s computation is simple as we need to do only one operation called the Manda operation. Spaṣṭa = Madhya + Mandaphala. Mandaphala “mph” = R * (MP/360) * dsin (MK)/60, where mph is Mandaphala, MP is Mandaparidhi, MK is Mandakendra and R is Trijyā 3438. MK = mod(Mandocca - Madhya, 360). For the given date and time, Sūrya’s Madhya is mod(346.061 + 0.985609 * d, 360) = mod(346.061 + 0.985609 * 58154.023, 360) = 268.933. Sūrya’s Mandocca is mod(78.648 - 0.000030 * d, 360) = mod(78.648 - 0.000030 * -58154.023, 360) = 80.393. MK = mod(Mandocca - Madhya, 360) = mod(80.393 - 268.933, 360) = 171.46. Sūrya’s MP is 12.047. mph = 3438 * (12.047/360) * dsin (171.46)/60 = 0.285. Therefore, Sūrya is Spaṣṭa = Madhya + Mandaphala = 268.933 + 0.285 = 269.218 CANDRA:

Candra’s computation is like Sūrya, where only Manda correction is needed. For the given date and time, Candra’s Madhya is mod(351.760 + 13.176355 * d, 360) = mod(351.760 + 13.176355 * -58154.023, 360) = 173.708. Candra’s Mandocca is mod(64.419 + 0.111365 * d, 360)= mod(64.419 - 0.111365 * -58154.023, 360) = 60.742. MK = mod(Mandocca Madhya, 360) = mod(60.742 - 173.708, 360) = 247.034. Candra’s MP is 39.513. mph = 3438 * (39.513 /360) * dsin (247.034)/60 = -5.79. Therefore, Candra is Spaṣṭa = Madhya + Mandaphala = 173.708 - 5.79 = 167.918 [8]

ASTRONOMY FUNDAMENTALS

ŚUKRA:

Like any other Tārāgrahas, Budha’s computation is a four step process, which involves the following operation in succession Śīghra1 → Manda1 → Manda2 → Śīghra2. For Budha and Śukra, their Madhyas are their Śīghras “Śīg” and Sūrya’s Madhya is their Madhya “mg”. Śukra’s Śighrocca = mod(217.705 + 1.602130 * d, 360) = mod(217.705 + 1.602130 * -58154.023, 360) = 287.400. Śukra’s Mandocca = mod(287.487 - 0.000037 * d, 360) = mod(287.487 - 0.000037 * -58154.023, 360) = 289.639. Śukra’s Madhya “mg” = Sūrya’s Madhya = 268.933. Śukra’s Mandaparidhi and Śīghraparidhi are 4.870 and 260.396. SK1 = mod(Śig - mg, 360) = mod(287.400 - 268.933, 360) = 18.467. Bhujāphala “BPh” = R * dsin(SK1) * SP/360 = 3438 * dsin(18.467) * 260.396/360 = 787.709. Rectified Koṭiphala “rKPh” = R * (1 + dcos(SK1) * SP/360) = 3438 * (1 + dcos(18.467) * 260.396/360) = 5796.728. Śīghrakarṇa “Śkar” = sqrt(BPh^2 + rKPh^2) = sqrt(787.709^2 + 5796.728^2) = 5850.004. sph1 = dasin(BPh / Śkar) = dasin(787.709 / 5850.004) = 7.738. mg1 = mod(mg + sph1 / 2, 360) = mod(268.933 + 7.738 / 2, 360) = 272.802. MK1 = mod(man - mg, 360) = mod(289.639 - 268.933, 360) = 20.706. mph = R * (MP/360) * dsin(MK1)/60 = 3438 * (4.870/360) * dsin(20.706)/60 = 0.274. mg2 = mod(mg1 + mph / 2, 360) = mod(272.802 + 0.274/ 2, 360) = 272.939. MK2 = mod(man - mg2, 360) = mod(289.639 - 272.939, 360) = 16.700. mph = R * (MP/360) * dsin(MK1)/60 = 3438 * (4.870/360) * dsin(16.700)/60 = 0.222. msg = mod(mg + mph, 360) = mod(268.933 + 0.222, 360) = 269.155. SK2 = mod(Śig - msg, 360) = mod(287.400 - 269.155, 360) = 18.245. Bhujāphala “BPh” = R * dsin(SK2) * SP/360 = 3438 * dsin(18.245) * 260.396/360 = 778.564. Rectified Koṭiphala “rKPh” = R * (1 + dcos(SK2) * SP/360) = 3438 * (1 + dcos(18.245) * 260.396/360) = 5799.762. Śīghrakarṇa “Śkar” = sqrt(BPh^2 + rKPh^2) = sqrt(778.564^2 + 5799.762^2) = 5851.786. sph2 = dasin(BPh / Śkar) = dasin(778.564 / 5851.786) = 7.646. sg = mod(msg + sph2, 360) = mod(269.155 + 7.646, 360) = 276.801. BṚHASPATI:

Bṛhaspati’s computation is like Budha, but here Sūrya’s Madhya is considered his Śighrocca. Bṛhaspati’s Madhya “mg” = mod(325.661 + 0.083091 * d, 360) = mod(325.661 + 0.083091 * -58154.023, 360) = 173.585. Bṛhaspati’s Śighrocca “Śig” = Sūrya’s Madhya = 268.933. Bṛhaspati’s Mandocca “man” = mod(170.063 - 0.000033 * d, 360) = mod(170.063 0.000033 * -58154.023, 360) = 171.982. Bṛhaspati’s Mandaparidhi “MP” and Śīghraparidhi “SP” are 34.936 and 69.223 SK1 = mod(Śig - mg, 360) = mod(268.933 - 173.585, 360) = 95.348. Bhujāphala “BPh” = R * dsin(SK1) * SP/360 = 3438 * dsin(95.348) * [9]

IN SEARCH OF JYOTISH

69.223/360 = 658.202. Rectified Koṭiphala “rKPh” = R * (1 + dcos(SK1) * SP/360) = 3438 * (1 + dcos(95.348) * 69.223/360) = 3376.384. Śīghrakarṇa “Śkar” = sqrt(BPh^2 + rKPh^2) = sqrt(658.202^2 + 3376.384^2) = 3439.942. sph1 = dasin(BPh / Śkar) = dasin(658.202 / 3439.942) = 11.031. mg1 = mod(mg + sph1 / 2, 360) = mod(173.585 + 11.031 / 2, 360) = 179.101 MK1 = mod(man - mg, 360) = mod(171.982 - 173.585, 360) = 358.397. mph = R * (MP/360) * dsin(MK1)/60 = 3438 * (34.936/360) * dsin(358.397)/60 = -0.156. mg2 = mod(mg1 + mph / 2, 360) = mod(179.101 - 0.156/ 2, 360) = 179.023 MK2 = mod(man - mg2, 360) = mod(171.982 - 179.023, 360) = 352.959. mph = R * (MP/360) * dsin(MK1)/60 = 3438 * (34.936/360) * dsin(352.959)/60 = -0.682. msg = mod(mg + mph, 360) = mod(173.585 0.682, 360) = 172.903 SK2 = mod(Śig - msg, 360) = mod(268.933 - 172.903, 360) = 96.03. Bhujāphala “BPh” = R * dsin(SK2) * SP/360 = 3438 * dsin(96.03) * 69.223/360 = 657.422. Rectified Koṭiphala “rKPh” = R * (1 + dcos(SK2) * SP/360) = 3438 * (1 + dcos(96.03) * 69.223/360) = 3368.554. Śīghrakarṇa “Śkar” = sqrt(BPh^2 + rKPh^2) = sqrt(657.422^2 + 3368.554^2) = 3432.107. sph2 = dasin(BPh / Śkar) = dasin(657.422/3432.107) = 11.043. sg = mod(msg + sph2, 360) = mod(172.903 + 11.043, 360) = 183.946 RĀHU:

The computation of Rāhu is straightforward. Rāhu = mod(30.431 0.052992 * d, 360) = mod(30.431 - 0.052992 * -58154.023, 360) = 232.129. The Sphuṭas of the Grahas arrived through our computations are Sūrya, Candra, Budha, Bṛhaspati, and Rāhu are 269.218, 167.918, 276.801, 183.946 and 232.129. According to Swiss Ephemeris (with Sṛṣṭi Ayanāñśa), the values are 269.303, 167.193, 276.98, 183.904 and 232.139. The objective of this volume is to explore the Modern and Siddhānta computations of Graha positions and provide the corrected values of the Orbital Elements (Bīja corrected values). I hope this will trigger new interest among the Jyotiṣa enthusiasts to take this subject seriously. Sarajit Poddar (Varāhamihira)

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ASTRONOMY FUNDAMENTALS

ABOUT ME I am an earnest seeker of Jyotiṣa, having an unquenching thirst for learning this discipline. I was born in Dhanu Lagna, Vṛścika Rāśi and Anurādhā Nakṣatra, on a Navamī Tithi, when Bṛhaspati was in Kumbha, Śani, in Mithuna, and Sūrya, in Siṅha. In my thirteenth year, I stepped into the world of Jyotiṣa in 1988, and after that, guided by divine providence, to study it seriously. I was guided by my paternal uncle and my first Jyotiṣa Guru, Śrī Manoj Kānti Poddar, an accomplished Jyotiṣaśastri and a Śakti Sādhaka. My father was also a Śakti Sādhaka and an accomplished Palmist. Therefore, I was born into a family of Jyotiṣīs and Śakti Sādhakas, and Jyotiṣa is running down my family lineage. I studied palmistry from 1988 to 1993, and eventually, in 1993, I got introduced to Jyotiṣa through Dr BV Raman’s astrological magazine. I commenced my learning through the astrological magazine for months. After that, it continued through a Bengali edition of Bṛhatparāśara and Sarvārtha Cintāmaṇi that my uncle gave me. During my initial years, I learned immensely from Dr Raman’s books, Hindu Predictive Astrology and How to Judge a Kuṇḍalī Vol I and II. In 1999, Pt Sanjay Rath accepted me as his student, an event I always cherish. It was the beginning of learning advanced Jyotiṣa. From him, I learned several advanced topics, including Āruṛhas, Argalās, Vargas, Tithi Praveśa Cakra etc. His books, Crux of Vedic Astrology: Timing of Events and Jaimini Maharṣi’s Upadeśa Sūtras, remained my constant companion for several years. In my studies over thirty-three years, I always endeavoured to uncover the hidden meaning behind the ślokas and sūtras and reconcile the principles across several classical texts. My search slowly took the shape of this book, which is why I named it “In Search of Jyotiṣa”. I started penning down my thoughts and experiences in a blog, “http://varahamihira.blogspot.com/” in 2004, and later continued to write in other mediums such as Facebook, Medium.com, and LinkedIn.com. I kept my pen name as Varāhamihira in honour of the great Jyotiṣaśastri, who adorned the court of king Vikramāditya as one of his Navaratnas (nine jewels). Who am I? It is difficult to say who I am. Different people see me in so many different ways. From my viewpoint, I am a soul trapped inside the world of illusion! I am not a Pundit, Ācārya, or Guru, who claims to be a master of this discipline. I am merely a seeker who wishes to share his observations and experiences with like-minded seekers. I encountered numerous challenges navigating the arduous path of Jyotiṣa. In this book, I am narrating my reflections with a sincere prayer so it could be of some help to others in their journey. Sarajit Poddar (Varāhamihira)

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IN SEARCH OF JYOTISH

ACKNOWLEDGMENT Many thanks to Śrī Senthil Ananth, my good friend who is always more than willing to edit my books. Without his help, bringing out so many volumes in a short time would not have been possible. Many thanks to my wife and children for actively supporting my writing. I appreciate all my readers and those who inspire me without comments, feedback and appreciation. I appreciate those authors actively disseminating the knowledge of Siddhānta and Modern Astronomy and bringing the subject to new heights. My appreciation and gratitude to the invisible Guru who is constantly with me and is blessing me to continue unceasingly. Sarajit Poddar (Varāhamihira)

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ASTRONOMY FUNDAMENTALS

Contents 13 SIDDHĀNTA 1: ASTRONOMY FUNDAMENTALS ......................... 1 13.1 MODERN ASTRONOMY ....................................................................... 16 13.1.1 Measurement of Time ................................................................. 19 13.1.2 The Coordinate Systems ............................................................ 24 13.1.2.1 Ecliptic Coordinate System ............................................................27 13.1.2.2 Equatorial Coordinate System .......................................................28 13.1.2.3 Coordinate Conversion ...................................................................30

13.1.3 The Coordinates ......................................................................... 47 13.1.3.1 Kepler’s Law ....................................................................................48 13.1.3.2 Definitions .......................................................................................51 13.1.3.3 Approach I .......................................................................................64 13.1.3.4 Approach II......................................................................................90

13.1.4 Higher Accuracy ....................................................................... 102 13.1.5 Sidereal Computations ............................................................ 110 13.1.6 The Fixed-Stars ........................................................................ 115 13.1.7 Obliquity and Nutation ........................................................... 122 13.2 SIDDHĀNTIKA ASTRONOMY ............................................................. 124 13.2.1 The Astronomers ...................................................................... 126 13.2.2 Hindu Astronomy ..................................................................... 133 13.2.3 Sūryasiddhānta ....................................................................... 144 13.2.4 The Fundamentals ................................................................... 146 13.2.4.1 Trigonometry .................................................................................146 13.2.4.2 The Quadrants ..............................................................................151

13.2.5 The Madhyagraha.................................................................... 154 13.2.5.1 The Quality of Time ......................................................................159 13.2.5.2 Mahāyuga and Yuga .....................................................................169 13.2.5.3 Manvantara and Kalpa.................................................................170 13.2.5.4 Time Elapsed from Sṛṣṭi ...............................................................174 13.2.5.5 The Mean Motion of Grahas .........................................................175 13.2.5.6 The Subdivision of THE Zodiac ....................................................177 13.2.5.7 Mahāyuga Bhagaṇa ......................................................................178 13.2.5.8 The Derived Elements of Time .....................................................185 13.2.5.9 The Apsis and Nodes ....................................................................193 13.2.5.10 Sṛṣṭi Ahargaṇa ............................................................................196 13.2.5.11 Abda, Māsa, Vāra and Horā Lords .............................................213 13.2.5.12 Mean Positions ............................................................................221 13.2.5.13 Tretā Ahargaṇa ...........................................................................231 13.2.5.14 Mean Positions at Other Places .................................................234 13.2.5.15 Distance from Prime Meridian ...................................................237 13.2.5.16 Vāreśa for the World ...................................................................238 13.2.5.17 Mean Position..............................................................................240 13.2.5.18 Mean Greatest Latitude .............................................................241 13.2.5.19 Ācārya Varāhamihira .................................................................243

13.2.6 The Spaṣṭagraha ...................................................................... 250 [13]

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13.2.6.1 The Epicyclic Theory .................................................................... 250 13.2.6.2 Śīghrocca, Mandocca and Pāta .................................................... 258 13.2.6.3 Hindu Concept of Gravitation ..................................................... 258 13.2.6.4 Forward and Backward Motion ................................................... 259 13.2.6.5 Pāta and Latitude ........................................................................ 260 13.2.6.6 The Antargrahas .......................................................................... 261 13.2.6.7 The Deflections of a Graha .......................................................... 262 13.2.6.8 8 Kinds of Motions ....................................................................... 263 13.2.6.9 The Observed Positions ............................................................... 269 13.2.6.10 1st and 2nd Sine ........................................................................... 271 13.2.6.11 Versedsine .................................................................................. 274 13.2.6.12 The Declination .......................................................................... 276 13.2.6.13 The Kendras ............................................................................... 279 13.2.6.14 Interpolation............................................................................... 285 13.2.6.15 The Paridhis ............................................................................... 286 13.2.6.16 The Phalas .................................................................................. 293 13.2.6.17 Prakāśa vs Tārā Grahas ............................................................ 298 13.2.6.18 The Spaṣṭagraha ........................................................................ 299 13.2.6.19 The Application .......................................................................... 302 13.2.6.20 Leading Scholars ........................................................................ 309 13.2.6.21 Illustration ................................................................................. 325 13.2.6.22 The Bhujāntara Correction........................................................ 334 13.2.6.23 True Position of Candra ............................................................. 335 13.2.6.24 Mean Daily Motion..................................................................... 335 13.2.6.25 True Daily Motion ...................................................................... 338 13.2.6.26 The Cause of Vakragati ............................................................. 340 13.2.6.27 Vakrī and Margi ......................................................................... 340 13.2.6.28 The Latitudes ............................................................................. 343 13.2.6.29 True Declination ........................................................................ 345 13.2.6.30 Graha Ahorātra .......................................................................... 345

13.2.7 The 9 Time Measures............................................................... 348 13.2.7.1 The Types of Time Measures ....................................................... 348 13.2.7.2 1_The SauraMāna ........................................................................ 350 13.2.7.3 2_The Sāvanamāna ...................................................................... 352 13.2.7.4 3_The Nākṣatramāna .................................................................. 353 13.2.7.5 4_The CāndraMāna ..................................................................... 355 13.2.7.6 5_The Bārhaspatya Māna ........................................................... 357 13.2.7.7 The Ayana and the Seasons......................................................... 361 13.2.7.8 The Month Names ........................................................................ 362

13.2.8 Indian Calendars .................................................................... 365 13.2.8.1 The Year Name ............................................................................ 366 13.2.8.2 The Samvatsara Name ................................................................ 368

13.2.9 The 60 Jovian Years ................................................................ 370 13.2.9.1 Sūryasiddhānta ............................................................................ 371 13.2.9.2 Computation ................................................................................. 373 13.2.9.3 At Kaliyuga .................................................................................. 374 13.2.9.4 The Samvat Start ......................................................................... 374 13.2.9.5 The Pañcasamvatsara Yuga ........................................................ 376 13.2.9.6 The Mean Rāśi ............................................................................. 380 [14]

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13.2.9.7 The Mean Nakṣatra ......................................................................381 13.2.9.8 From Kaliyuga ..............................................................................383

13.3 BĪJA SAṄSKĀRA ................................................................................ 390 13.3.1 Fundamentals .......................................................................... 392 13.3.2 Current Time ............................................................................ 398 13.3.3 Longer-Term ............................................................................. 418 13.4 APPENDIX ........................................................................................ 427 13.4.1 Q&A .......................................................................................... 428 13.4.2 References ................................................................................. 437 13.4.3 Glossary .................................................................................... 470 13.4.4 About “In Search of Jyotiṣa” .................................................... 485

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