Kalamana (कालमानम्)

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Kalamana (Samskrit: कालमानम्) broadly refers to the measurement of time (Kala). Bharatiya shastrajnas have explained the various macrocosmic and microcosmic time systems and depending on the needs of particular topics in astronomy, different scales and units of time are used. On the macrocosmic scale, the Yuga system has been described, whereas on the microcosmic scale, a small unit of time Truti (1/33750 of a second) has been mentioned by Bhaskara II. We mention the macrocosmic time scales (Svetavaraha kalpa, Vaivasvata Manvantara etc) only in the samkalpa of our daily puja rituals.

Introduction

On the day to day basis, however, we use the classic Panchanga (5 elements namely, Tithi, Vara, Nakshatra, Karana and Yoga) which measures time on a working scale, on a daily basis, to perform any activity of importance in our lives such as to determine Muhurta or auspicious times as well as to determine time for Shraddha and other Pitr karmas. The present article Kalamana discusses the aspects of Suryodaya, Suryastamaya or sunrise and sunset timings, Chandrodaya timings, Tithi, Nakshatra, Paksha (fortnight), Vara (day of the week), Samvatsara (year) and their determination. It may be noted that while some factors such as sunrise and sunset, moon-rise, rashis, sankramanas are common in all parts of India, some calculations such as of the day or a year are set variously by people of different cultures of India.

Many of these factors are based on simple natural observations, earth, moon and planetary motions and seasons - all of which are pratyaksha pramanas (visible evidence) in the nature around us manifesting the environmental changes. It is common knowledge that it is a day with sunrise, a night with sunset, high and low tides with lunar movements, rashis associated with the movement of moon in nakshatras, formation of new leaves and leaf shedding indicates seasonal change with Vishvat (equinoxes) so on and so forth.

It is only with deep respect for the intellect and keen observation of our ancient maharshis, rsis and later day ganita and jyotisha shastrajnas that we can appreciate the systematic work done by them - not requiring huge telescopes or light measuring instruments - to leave a legacy of astronomical wealth for us.

Here we discuss a few important astronomical concepts, briefly, that are in use in our present day calendars, without delving deep into the mathematical calculations used to arrive at them.

नवमानानि ॥ Nine Kinds of Time

Surya Siddhanta is one of the oldest and accepted by many scholars as an authentic source of information regarding the astronomical calculations and specifications. Manadhyaya (14th Adhyaya) of Surya Siddhanta is referred here.

ब्राह्मम् दिव्यम् तथा पित्र्यम् प्राजापत्यम् गुरोस् तथा । सौरम् च सावनम् चान्द्रम् आर्क्षम् मानानि वै नव ॥

चतुर्भिर्व्यवहारोऽत्र सौरचान्द्रार्क्षसावनैः।बार्हस्पत्येन षष्ट्यब्दा ज्ञेया नान्यैस्तु नित्यशः॥ (Sury. Sidd. 14.1-2)

There are nine Manas or measurements of time (kinds of time). They are

1. ब्राह्मम् ॥ Braahmam (Of Brahma)
2. दिव्यम् ॥ Divyam (Of Devatas)
3. पित्र्यम् ॥ Of Pitrs
4. प्राजापत्यम् ॥ Of Prajapati
5. गुरोः (बार्हस्पत्यम्) ॥ Of Guru (Brhaspati)
6. सौरम् ॥ Of Surya
7. सावनम् ॥ Of Savana
8. चान्द्रम् ॥ Of Chandra
9. आर्क्षम् (नाक्षत्रम्) ॥ Aarksham (Of Nakshatra)

The Manas which are used in daily activities are four in number - सौरचान्द्रार्क्षसावनैः । Solar, Lunar, Sidereal, and the Savana (Civil). The Mana of Jupiter (Barhaspatya) is used for determining the Shasthtyabda (60 Samvatsaras) or attaining 60 years of age while the remaining four are not used on a daily basis.

दिननिर्नयम् ॥ Dina Nirnaya

It is long known to our ancient seers that it is the earth that revolves around the sun in an ecliptic path. However, the time is calculated based on using the earth as a reference, and thus we say sun is revolving around the earth. We see in the sky that due to diurnal motion, the Sun rises in the eastern horizon, moves up in the sky westward and sets in the western horizon. From the sunset to the next sunrise, it will be below the horizon during the night. It is common knowledge all over the world that this period of time between the sunrise and sunset is called a Day. However, our seers have calculated and defined a Day, not just with respect to the Earth but also with other cosmic references and specified where such a measure of time is to be used.

सौरदिनम् ॥ Saura Dina (Solar Day)

सौरेण द्युनिशोर्मानं षडशीतिमुखानि च। अयनं विषुवच्चैव सम्क्रान्तेः पुण्यकालता॥ (Sury. Siddh. 14.3)

With reference to Earth the Sun's motion along the ecliptic path, in the rashi, is about 1° per day. This is called a Solar Day.

षडशीतिमुखानि ॥ Shadasheeti Mukhas

तुलादि षडशीत्यह्नाम् षडशीतिमुखम् क्रमात् । तच्चतुष्टयम् एव स्याद् द्विस्वभावेषु राशिषु ॥

षड्विम्शे धनुषो भागे द्वाविम्शे निमिषस्य च । मिथुनाष्टादशे भागे कन्यायास् तु चतुर्दश॥

Vishuvats

ततः शेषाणि कन्याया यान्य् अहानि तु षोडश । क्रतुभिस् तानि तुल्यानि पितृऋणाम् दत्तम् अक्षयम् ॥

1 Saura Dina (Solar Day) = Movement of Sun in a Rashi by 1 degree in ecliptic path

Purpose of Saura Dina

1. Determining the length of the day and night
2. Shadashiiti Mukhas
3. Determine Uttarayana and Dakshinayana (the northern and southern paths of the Sun)
4. Equinoxes and Vishuvats
5. Sankrantis (the time of entry of Sun into a new rashi)

सावनदिनम्॥ Savana Dina (Civil Day)

उदयाद् उदयम् भानोः सावनम् तत् प्रकीर्त्यते । सावनानि स्युरेतानि यज्ञकालविधिस्तु तैः ॥

सूतकादिपरिच्छेदो दिनमासाब्दपास्तथा । मध्यमा ग्रहभुक्तिस्च सावनेन प्रकीर्त्यते ॥ (Sury. Siddh. 14.18)

The duration between two successive risings of the Sun is called a Savana Dina or Civil Day.

Observations of sunrise over a very long time has revealed that the duration of a day is not constant but varies from day to day although very slightly. An average calculated based on the observations is referred to as the Mean Solar Day or Mean Civil day. Savana Dina is divided into 60 equal parts called Ghatikas or 24 equal parts called Hora (hours). Thus the 24 hour day that is used for our regular daily activities is the Savana Dina.

1 Savana Day (Civil Day) = 24 Hours

Purpose of Savana Dina

1. Savana days are used to determine the time of to perform yajnas.
2. Determine Asoucha or Sutaka due to birth and death
3. Limits of Chandraayana and other vratas
4. Determine the rulers of the day, month and year
5. To calculate the mean motion of planets.

तिथिः ॥ Tithi (Lunar Day)

अर्काद्विनिस्सृतः प्राचीं यद्यात्यहरहश्शशी। तच्चान्द्रमानम् अम्शैस्तु ज्ञेया द्वादशभिस्तिथिः॥

तिथिः करणम् उद्वाहः क्षौरम् सर्वक्रियास् तथा। व्रतोपवासयात्राणाम् क्रिया चान्द्रेण गृह्यते॥ (Sury. Siddh. 14.12-13)

The time in which the Moon being separate from the Sun (after a conjunction) moves daily to the east is the measurement for the moon (चान्द्रमानम्) Chandra Mana. The time taken by the Moon to cover exactly an amount of 12° relative to the Sun, is defined as Tithi or Lunar Day.

Since the moon moves faster than the sun, starting from a new moon, the moon gains about 12° per day over the Sun, i.e., one Tithi per day, thus the chandra masa has 30 tithis. The half-lunar month from a new moon to the succeeding full moon is called Shukla Paksha (the bright fortnight) and the other half-lunar month from the full moon to next new moon is called Krshna Paksha (dark fortnight). The lunar month is a natural unit for a month. It is important to note that the beginning and end of a lunar month are naturally marked by two successive new moons.

Purpose of Chandra Mana

1. Determination of Tithi, Karana (half of Tithi)
2. Determine the time for samskaras like marriage
3. Determine the appropriate time for activities such as shaving, tonsure
4. To determine the time for Vratas, Upavasas, Yatras

नाक्षत्रदिनम् ॥ Nakshatra Dina (Sidereal Day)

भचक्रभ्रमणम् नित्यम् नाक्षत्रम् दिनम् उच्यते। नक्षत्रनाम्ना मासास् तु ज्ञेयाः पर्वान्तयोगतः ॥ (Sury. Siddh. 14.15)

The time taken for one revolution of the sphere of stars is called a sidereal day.

The time taken by the fixed stars to go around the earth is called a Nakshatra Dina or Sidereal Day; and this time is equal to the period of the rotation of the Earth. Sidereal is a term used to refer to stars. It is important to note that the time taken by the fixed stars to go round the Earth once is not the same as that taken by the Sun. While all the celestial bodies appear to move from the east to west due to the diurnal motion, the Sun would have moved from west to east along the ecliptic by about 1°, relative to the stars. Therefore, the fixed stars take a little less than 24 hours (mean civil day) to complete a rotation around the Earth. As a natural consequence if a particular star rises in the eastern horizon at a particular time today, it will rise about two hours earlier after 30 days, 4 hours earlier after 60 days, and so on.

It is found that the fixed stars take about 3 minutes 56 seconds less than the Sun to go round the Earth once.

1 Nakshatra Dina = 1 Savana Dina - 3 mins 56 secs = 23 Hrs 56 Mins 4 Secs

Purpose of Nakshatra Dina

1. Naming of lunar months is from the Nakshatras; the name of a lunar month is determined from the nakshatra in which moon is present at the time of Purnima (15th day of full moon) tithi (with a few exceptions).

Summary

1 Saura Dina (Solar Day) = Movement of Sun in the Rashi by 1 degree

1 Tithi (Lunar Day) = 

1 Savana Dina (Civil Day) = 24 hours

1 Nakshatra Dina (Sidereal Day) = 23 Hrs 56 Mins 4 Secs

Masa and Varsha Nirnaya

Once we understand how the day is determined under each Mana - kind of measurement - we proceed to make the Masa (month) and Varsha (year) calculations in this section.

Saura Masa and Varsha

The time taken by the Sun to complete a revolution around the Earth, as observed from the Earth, is defined as a Saura Varsha (Solar Year)

Four Other Manas

पितृमानम् ॥ Pitr Mana

त्रिम्शता तिथिभिर्मासश्चान्द्रः पित्र्यमहः स्मृतम्। निशा च मासपक्षान्ते तयोर्मध्ये विभागतः॥ (Sury. Siddh. 14.14)

Thirty tithis make a lunar month (mentioned under Tithis) which constitutes one day and night for the Pitrs. The end of Chandramasa (lunar month) i.e., the end of the New moon day (Amavasya) corresponds to the noon time for the Pitrs and the end of the Full moon day (Purnima) corresponds to the midnight time for the Pitrs. Thus the middle of Shukla Ashtami tithi corresponds to the start of the day for Pitrs and the middle of Krshna Ashtami tithi corresponds to the start of the night for the Pitrs. The Bhugola Adhyaya of Surya Siddhanta further discusses this topic establishing Amavasya as the noon time and Purnima as midnight for Pitrloka (Page 767-768 of Reference).

Purpose of Pitr Mana

1. Determine the Masikas (performing monthly Pitr kriyas upto one year of death).
2. Determine the time of annual Shraddha