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The time of beginning of life or the time of birth is not under the control of person. Similarly all entire the good or bad person has to face, just because his life started at a particular time, is not under his control. The study of Muhurta is the study of that 'time of commencement.'
'Muhurta' is a moment created by various positions of planet containing certain vibrations or promises for any action, process or life starting at that time. To study Muhurta is to study those effects and to decide the suitability or unsuitability of that moment first for a particular action, and then for the particular individual. From user's point of view Muhurta means a time which is auspicious for a particular activity. Relevance of Muhurta also lies in its being a means through which one can adapt to nature. Instead of going against natural forces it is better to being when the cosmic power is favorable.

Tithi is the name given to various angles formed by Sun and Moon.When Sun and Moon are together at same degree it is called New Moon or Amayasya. As moon moves away from the Sun and fifteen in the dark half (Krishna Paksha)- when moon moves towards the Sun.
From the starting point of Nirayana Zodiac if we divide the Zodiac in to 27 equal parts then one part will be of 13'20' and is called a Nakshatra.Starting from the 1st point of Nirayana Aries the names of 27 Nakshatras in order are as follows.
1. Ashwini            10. Megha                    19. Moola    
2. bharani            11. Poorva Falguni            20. Poorvashada
3. Kritika            12. Uttara Falguni            21. Uttarashada
4. Rohini            13. Hasta                    22. Abhijit
5. Mrigshira            14. Chitra                    23. Shravana
6. Ardra                15. Swati                    24. Dhanishta    
7. Punarvasu            16. Vishakha                    25. Shatbhisha
8. Pushya            17. Anuradha                26. Poorva Bhadrapad
9. Ashlesha            18. Jyeshtha                    27. Revati
When Moon transits in a particular division of 13'20' (called Nakshatra) it is called Nakshatra of that moment. In Muhurata when we say Nakshatra at a particular time is Mrigshira we mean that Moon at that particular time is placed in Mrigshira

Day os from one sunrise to another sunrise. Each day is alloted to a planet e.g. Sunday to Sun, monday to Moon, Tuesday to Mars, Wednessday to Mercury, Thursday to Jupitar, friday to venus and Saturday to Saturn.
Out of these Tuesday and Saturday are wholly malefic and Sunday is partially malefic. These are also like classified like nakshatra as follws.
Sunday            -    Dhruva-Sthira ( Fixed and Constant)
Monday            -    Char-chal (Movale)
Tuesday            -    Ugra-Kroora (Aggressive and Cruel)
Wednesday        -    Mishra (Mixed)
Thursday        -    Kshipra-Lagun (Short & dynamic)
Friday            -    Mridu Mraitra(Gentle and Friendly)
Saturday        -    Tikshna-Darun (Volatile)
The days are suitable for all acts which the Nakshtras of the same category are suitable like Sunday for fixed nature, Monday for Acts requiring movement or motion and so on.

Yoga is formed by relative position of Sun and Moon in the Zodiac. To put it mathematically
Yoga = (Moon's Longitude + Sun's Longitude)/ 13'20'
This will give us the Yoga number. The yogas are 27 in number. These number and names are below.
1. vishkumbha        10. ganda            19. parigha    
2. preeti                11. vriddhi            20. shiva
3. ayushmaaana        12. dhruva            21. siddha
4. subhagya            13. vyaghata            22. sadhya
5. shobhana            14. harshana            23. shubha
6. atiganda            15. vajra                24. shykla    
7. sukarma            16. siddhi            25. brahma
8. dhriti                17. vyatipaata        26. indra
9. shoola            18. variyana            27. vaidhriti

The names are suggestive of their nature. malefic yogas no. 1. (Vishkumbha), 6. (Atiganda), 9. (Shoola) 10. (Ganda) 13. (Vyaghata) 15. (Vajra) 17. (Vyatipaata) 19. (Parigha) and 27. (Vaidhriti) are particularly avoided in elections.

Karana is one-half of tithi. There are eleven Karanas out of which four are fixed and seven are movable. Four fixed Karanas are (i) Shakuni (ii) Chatuspada (iii) Naga and(iv) Kintughna. Second half of 14th tithi in dark half (Krishna Chaturdashi) is shakuni karana.Ist half of Amavashya is Chatuspada abd 2nd half is Nega Karana First half of first tithi of bright half (Shukla pratipada) is allocated to Kintughna. These four Karanas are considered inauspicious.
Seven movable karanas are (i) Bava, (ii) balava, (iii)kaulava, (iv) Taitila, (v)Gara, (vi) Vanija and (vii)Vishti. starting from the 2nd half of 1st tithi in the bright half they come in order and each karana comes eight times in a lunar month. Various karanas and parts of tithis ruled by them.

There are four kinds of months which are generally used
(A)Solar month - This is based on Sun's entry in to various Nirayana signs.
(B)Lunar month - Two types of lunar months are in use in India. One is Shukladi-from one new moon to another new moon, another is Krishnadi-from one full moon to another full moon.
(C)Sawana month- Taking one day equal to time from one sunrise to another sunrise a Sawana month consists of 30 days. It is used for deciding age, period of pregnancy.
(D)Nakshatra month - it is based on moon's transit over 27 Nakashatras and is used for "nakshatara shanti", specific yagnas and for certain mathematical relating to nakshatras.

Ascendant is one of the most important components of Muhurata even where other favorable conditions are not present a properly chosen where will remove the defects created by other components of muhurata or by presence of malefic yogas. Thus lagna rising at the time of beginning of an act, with position of planets in various house needs due attention, as it rightfully deserves.
Choice of proper lagna and placement of planets will differ with change in the nature of activity to be started.