Science in Hindu calendar

Science in Hindu calendar
 
Hindu calendar system offers a multi-dimensional method of structuring time, combining information about lunar days, solar days, lunar months, solar months, the movements of the Sun and the Moon in relation to stellar constellations, and other astronomically defined time spans.  In the Hindu calendar, seasons follow the sun; months follow the moon; and days, both the sun and the moon.
 
The western or Christian calendar is solar calendar and the Islamic or Higri calendar is lunar calendar. But Hindu lunisolar calendar synchronizes both the solar and the lunar cycles. Hindu calendar has fixed the aberrations as under:

1. The year is determined by the earth's movement around the Sun in an elliptical orbit; it is a solar phenomenon with a period of 365.242189 days (the tropical year). A lunar year is equal to 354.2672 days (354 days 8 hours 48 minutes and 36 seconds). This creates a difference of about eleven days, which is offset every 2.71 years i.e. 32.5 months. In Hindu calendar, an extra month occurs after every 32.5 months to keep lunar and solar calendars aligned. This month is named as Purushottam or Adhik or Mala month. In Islamic or Hijri calendar, the year consists of 12 lunar months in a year of 354 or 355 days. In Western or Christian calendar, the common year is of 365 days and one day is added every fourth year called as leap year to make up the difference.
2. The month uses the rotation of the moon around the Earth as its unit; it is thus a lunar phenomenon. In Hindu calendar, the tithi (lunar day) is scientifically defined, so each month always has 30 tithis, and corresponds exactly to one cycle of the moon. In Western calendar, months have varying durations to 28, 30 & 31 days with no correlation with lunar cycle.
3. The day is the result of the Earth's rotation around its axis. In Hindu calendar, the solar day is from one sunrise to another. In western calendar, the day is from midnight to another which has no visible correlation.
4. The Moon orbits the Earth in 27.3 days and passes through 27 constellations of stars during the 360 degree orbit. This synergy and coincidence of the Moon and groups of stars is called Nakshatra. From one full moon to the next full moon, the moon must travel about 2.2 extra days before it appears again as a full moon, due to the curve of the earth's orbit around the sun. The mean length is around 29.53059 days (29 days 12 hours 44 minutes and 3 seconds). The constellation in which the Moon will be at the time of birth of any person or the group of stars passing through it is considered to be its birth constellation. In Hindu system, Astrology is aligned with Astronomy.
5. In Hindu system, From Makara Sankranti, the sun’s entrance into Capricorn – the year starting with it is divided into two halves and six seasons. It identifies the rainy season as the months of Sawan and  Bhadon.
6. The Hindu festivals typically are either on or the day after the full moon night or the darkest night (amavasya, अमावास्या), except for some associated with Shri Krishna, Ma Durga or Shri Rama. The lunar months of the hot summer and the busy major cropping-related part of the monsoon season typically do not schedule major festivals.

 
Hindu calendar systems:
All the Hindu calendars contain five parts of information: lunar day (tithi), solar day (diwas), asterism (nakshatra), planetary joining (yoga) and astronomical period (karana). This structure gives the calendar the name Panchangam.
 

1. Solar Years - Hindu rishis tracked the solar year by observing the entrance and departure of sun at sunrise and sunset in the constellation formed by stars in the sky. They divided it into 12 intervals of 30 degrees each.
2. Lunar Year - A lunar year with an adhika month has 13 amanta months. An adhika month occurs generally at intervals 2 years 4 months, 2 years 9 months, 2 years 10 months or 2 years 11 months, giving an average interval of about 2 years 8.4 months. The purimanta month starts about 15 days earlier and ends in the middle of the concerned amanta month. Although an amanta month may fall almost entirely outside its linked solar month, the purimanta month always covers at least half of that solar month. The purimanta lunisolar calendar is mainly used in the states of Uttar Pradesh, Bihar, Madhya Pradesh, Rajasthan, Punjab, Haryana, Himachal Pradesh, Orissa and Jammu and Kashmir.
3. Solar Months - If the transits of the Sun through various constellations (Rashis) are used, then we get solar months, which do not shift with reference to the Gregorian calendar. In practice, solar months are mostly referred as Rashi (not months).
4. Lunar Months - There are two types of lunar months being used in India. They are the new moon ending lunar month and the full moon ending lunar month, resulting in the Amanta and Purnimanta lunisolar calendars respectively. Amanta month runs from new moon to next new moon. The twelve months are named as under:

1. Chaitra, 2. Vaisakha, 3. Jyaishtha, 4. Ashadha, 5. Sravana, 6. Bhadra, 7. Asvina,  8. Kartika, 9. Agrahayana or Margasirsha, 10. Pausha, 11. Magha, 12. Phalguna.
When a solar month completely covers an amanta month, that is, when there are two new moons, one falling at the beginning and the other at the end of the solar month, the amanta month that begins from the first new moon is treated as a leap month and prefixed with the title ‘adhika’ or ‘mala’. We call the leap month adhika or mala month.

1. Fortnight - A month contains two fortnights called Paksha (पक्ष, literally "side").  One fortnight is the bright, waxing half where the moon size grows and it ends in the full moon. This is called "Gaura Paksha" or Shukla Paksha. The other half is the darkening, waning fortnight which ends in the new moon. This is called "Vadhya Paksha" or Krishna Paksha. 

6.    Lunar day - At the same time the lunar month (which has about 29.5 solar days) is divided into 30 lunar days called lunar day or tithi which are thus shorter (about 23 hours and 36 minutes) than the ordinary day and not tied to daylight and night; a tithi can begin at any time of day. To keep solar and lunar days together, occasionally a tithi is eliminated from the month.
7.    Karana - A karana is half of a tithi. To be precise, a karaṇa is the time required for the angular distance between the sun and the moon to increase in steps of 6° starting from 0°. There are only 11 such karaṇas which fill up the slots of 30 tithis. There are actually 4 "fixed" (sthira) karaṇas and 7 "repeating" (cara) karaṇas.

1. Muhurata - The solar day is divided into 30 muhurata (equivalent to 48 minutes), each muhurata into two ghati (24 minutes) and each ghati into 3600 vipala (0.4 seconds).
2. Prahar - 24 hours of day-night are divided into eight parts. Each part is of roughly three hours, called as ‘Prahar’. First Prahar starts with sunrise. Roughly sunrise is considered at 6 am and sunset at 6 pm. In day time, the four Prahars of the day are - 6 to 9 AM - forenoon (पूर्वान्ह), 9 AM to 12 PM - mid-noon (मध्यान्ह), 12 to 3 PM - afternoon (अपरान्ह) and 3 to 6 P.M - evening (सायंकाल). The four Prahars of the night are - 6 to 9 PM Pradosh (प्रदोष), 9 PM to 12 AM - Nishith (निशिथ), 12 to 3 AM - Triyama (त्रियामा) and 3 to 6 AM - Usha (उषा).
3. The all-famous Brahm Muhurat takes place between 4:24 and 5:12. Then there is the Sea-Muhurat. Both of them are in Usha Prahar.