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I. Celestial Sphere is an imaginary projection of the earth in all direction up to infinity.
II. Celestial Equator is the extension of the plane of terrestrial equator into space.
III. Celestial Poles are the points cutting the celestial sphere by extension of the axis of the earth to infinity.
IV. Meridian: Any great circle joining the celestial north and south poles is called a meridian. The meridian corresponds to the terrestrial longitude. Angular distance between the principal (or standard) meridian and meridian of a place is the longitude of the place.
V. Midheaven: The Sun crosses the meridian of a place at mid day. The intersection of ecliptic (Sun’s apparent path around the earth) with the meridian of a place is the midheaven (this corresponds to the cusp of 10^{th} house of a horoscope). The meridian of a place thus passes around the earth, through North Pole, midheaven (10^{th} house cusp), South Pole, nadir (4^{th} house cusp) and back to North Pole.
VI. Location co ordinates of a planet or a star in heaven:
 Method I
 Ecliptic Celestial longitude and latitude: Celestial longitude and latitude are measured along and perpendicular to the ecliptic (different from terrestrial longitude and latitude which is measured from equator).
 Method II
 Equatorial Declination and right ascension: Angular distance between the principal (or standard) meridian and meridian passing through a planet or a star (i.e. angular distance, measured eastwards along the celestial equator from vernal equinox to the point of perpendicular from planet to equator) is the right ascension of the planet or star. It corresponds to the terrestrial longitude. Declinationcorresponds to the terrestrial latitude. of a planet is the angle subtended by it and the celestial equator. The declination of a planet exactly
 Method III
Alt azimuth:
Ø The horizon is the great circle that represents the meeting line of earth and the sky. It varies according to the position of the observer on the surface of the earth, for example for an observer at the North Pole of the earth; the horizon corresponds with the equator while southern hemisphere remains out of view. For one standing at equator, the great circle passing through poles represents the horizon; the two poles are on horizon in this case. For any intermediary positions, the horizon varies according and corresponds to great circle perpendicular to the meridian for the place of the observer.
Ø The point of celestial sphere that is directly overhead an observer is called Zenith. Its opposite is called as the Nadir. The great circle that passes north south direction through the Zenith, the nadir and celestial north & South Pole (i.e. the north and south poles of equator) is also the meridian for the observer’s place.
Ø Let O – the observer on the surface of the earth (supposed spherical) – is the center of the celestial sphere. Let Z (the zenith) be the point on the celestial sphere vertically overhead its direction can be defined by means of a plumb line. OZ is thus continuation of the straight line joining earth’s center to O. Plane through O at right angles to OZ is the plane of horizon, cutting the celestial sphere in the great circle NAS, called the celestial horizon or horizon. The upper part is visible hemisphere and the lower part is hidden from the observer by the earth. Thus if the altitude or zenith distance of a star is given, the parallel of attitude on which it lies can be definitely specified. To define its position completely on the celestial sphere, the particular vertical circle on which it lies must also be specified. This is done as follows.
Ø Let OP be parallel to the axis about which the earth spins. If the latitude of the observer is north, as in fig above the position P is the north celestial pole or simply the North Pole. Due to rotation of the earth, the stars appear to travel across the sky and their altitudes and directions continually changing. However, in northern hemisphere, there is a star Polaris or North Pole star whose direction change very little and its direction is given by OP. If there happen to be a star at P on the celestial sphere, its altitude and direction will be invariable throughout the night. The vertical circle through P is ZPN (which cuts the horizon at N), as the principal vertical circle and the point N as the north point of the horizon. The point S on the horizon opposite to N is the south point; the west (W) and the east (E) points (taking observer if facing north) have direction at right angles to N and S (E is not shown in the fig.). The points N, E, S and W are called the cardinal points.
Ø Now the position of a star X on celestial sphere is given with reference to the horizon and the principal vertical circle ZPN. If the star is in western part of the celestial sphere , the spherical angle PZX (which is formed by the principal vertical circle and the vertical circle through X) or the great circle arc NA is the azimuth (W). Azimuth is measured 0º to 360º N for unidirectional azimuth or 0º 180º E or 0º 180ºW for bi directional azimuth. Altitude of Sun at sunrise is 0º and when it cross meridian plane or vertical planes at noon (at meridian cusp) its altitude will be 90º.
Ø The altitude of the pole P is equal to the latitude of the observer on earth. PZ = 90°  Latitude; and altitude of pole PN = 90°  PZ= Latitude of the observer.
Ø Let X is the position of a star on the celestial sphere at a given moment. Any great circle (i.e. circle passing through center of the earth) is called a vertical circle; in particular the vertical circle in figure passing through X is ZXA. In the plane of ZXA, the angle AOX or great circle arc AX is called the attitude, which will be denoted by a. Since OZ is perpendicular to the plane of horizon, the circle arc ZA is 90°; hence ZX = 90° a. ZX is the zenith distance by z. Thus
Z= 90° a.
Ø LXM, a small circle through X parallel to the horizon; it is called a parallel of altitude and is such that all heavenly bodies, whose position at a given time lie on this small circle have the same altitude and also same zenith distance (z = ZX).
VII. Equator and Ecliptic and formation of seasons:
1. The earth rotates on its axis in 24 hours. Along with its rotation, it also revolves around the Sun in one year or 365.2422 days (365 days 5 hours 48 minutes 46 seconds). This span of time is called a tropical year. The ecliptic is the apparent path of Sun around earth. The equator divides the earth in two equal parts – northern and southern hemispheres. The ecliptic is inclined to the equator at an angle of 23° 28’. It crosses the equator at two points, the vernal equinox (when Sun is in northerly course around 21 march) and autumnal equinox (when Sun is in southerly course – around 23 September).
On these two occasions, the day and night all over the globe are of equal duration and the Sun is vertically above the equator at this time. The declination of Sun is zero as it corresponds to the terrestrial equator that has zero degrees latitude.
2. After vernal equinox, the Sun progressively attains north declination until it reaches a maximum of 23° 28’. This is around 21^{st} June and is known as summer solstice. Sun is vertically above the Tropic of Cancer at this time. The northern hemisphere experiences the longest day and shortest night (summer season) and opposite (winter season) in southern hemisphere.
3. After the autumnal equinox, the Sun pursues the southward course and attain a maximum south declination of 23°28’ at the time of winter solstice around 22^{nd} December. The Sun is vertically above the Tropic of Capricorn. The southern hemisphere experience longest day and shortest night (summer) and opposite (winter) in northern hemisphere. Thus the obliquity of ecliptic to the equator results in the formation of seasons.
VIII. Rashimaan Ascension or Oblique
Ascension:
1. As earth complete its rotation around its axis in 24 hours from west to east, all the signs, nakshatras and heavenly bodies appear to successively ruse in the eastern horizon and set at the western horizon once in 24 hours. Time taken to traverse 30° of a sign is the rashimaan or ascension. Since this time varies from sign to sign and latitude to – latitude, it is called oblique ascension.
2. Six of the signs appear at the eastern horizon during daytime and the remaining six at the nighttime. The following points are of importance:
Ø The sign rising at the eastern horizon is the ascendant or the Lagna. It is the sign where the ecliptic cuts the western horizon. It represent 1^{st} house.
Ø The sign 7^{th} from the ascendant is the descendant or the setting sign. It is the sign where the ecliptic cuts the western horizon. It represent 7^{th} house in a horoscope.
Ø
The points where the meridian cuts the ecliptic are the zenith (above the earth) and nadir (below the earth opposite zenith). The zenith (mid heaven) represents the 10^{th} house in a horoscope, while the nadir represents the 4^{th} house.
Ø Depending upon their rising periods (rashimaans), signs are divided in three groups.
Groups

Signs

A

1, 6, 7, 12

B

2, 5 , 8, 11

C

3, 4, 9, 10

Ø All signs of a group take same time to rise at equator. For any given latitude the rising time of different signs is fixed. The period six signs 4, 5, 6, 7, 8, 9 lengthen (i.e. they remain longer on the horizon) and of 1, 2, 3, 10.11.12 signs shorten as one proceeds from the equator to the North Pole and vice versa as one proceed from equator to the South Pole.
Ø Six signs rise during daytime (from sunrise to sunset) and remaining six rise during nighttime. During winters when days are shorter, six signs rise in shorter time (short ascension) and remaining six signs during night take longer time (long ascension). In northern hemisphere, signs of short ascension are 10, 11, and 12,1,2,3 and of long ascension are 4, 5, 6,7,8,9 and vice versa in southern hemisphere.
Ø As one nears the poles certain signs fail to rise.
IX Sidereal time:
1. The Earth rotates around its axis and when writ (with reference to) Sun measured, it takes 24 hrs. To complete one rotation (time between two successive sunrise or from one vernal equinox to the other etc.) This is mean solar day. When measured wrt affixed star it takes approximately 23 hrs. And 56 mins. (23 hrs. 56 min. and 4.09 sec.). This is called sidereal day. As Sun is also moving and during earth’s one rotation it would move by 1° of longitude and earth has to rotate 1° extra (equal to additional rotation time of 4 min. by earth) to achieve same position wrt to Sun. Whereas sidereal time is wrt a star which remains fixed during the rotation of earth and achieve same position 4 minutes earlier. In the course of full revolution around the Sun, earth has to make one additional revolution so that it may acquire same position writ Sun.
2. A sidereal day is the time interval between two successive transits of a fixed star over the meridian of a place. A sidereal day consists of 24 hours. 0 sidereal hour at 1^{st} crossing of the meridian by a fixed star to 24 sidereal hour at the next crossing of the meridian by the star. Time reckoned according to this method is called the sidereal time. Since the sidereal time consider the rotation of earth wrt the fixed star of the zodiac, the earth will attain the same position wrt zodiac every day at the same time. This means for any location the position of rising sign, the setting sign, the 10^{th} house sign, 4^{th} house sign etc. will be same at sidereal time. Therefore it is essential to obtain correct sidereal time casting a horoscope for any given moment of solar time as provide by the watch.
X Precession of equinoxes:
1. The earth revolves around the Sun once in 365d 5h 48m 46s. Considered from earth, the Sun appears to complete one round of ecliptic during this period and earth regains its original angular position with the Sun. This is called tropical year year of seasons. It is equivalent to time taken by Sun from vernal equinox to the next crossing of the vernal equinox.
2. When considered the position of earth wrt a fixed star, at the end of a tropical year from one vernal equinox to the next, the earth appears to lie 50.20’ of celestial longitude to the west of the vernal equinox i.e. original position of the earth. In order to attain same position of the earth. In order to attain same position wrt to the fixed star (i.e. to reach the vernal equinox), the earth has to move additional 50.26” of celestial longitude equal to about 20m longer than tropical year. The total span becomes 365d 6h 9m 9.5s known as sidereal year.
Note:
{(365d 48m 46s) x 50.26”} / (360ox 60x60) = 20m (Approx.)
3. Thus each year, the vernal equinox fall short by 50.36” of along zodiac (or ecliptic) reckoned from the fixed stars. This continuous receding if the vernal equinox along the zodiac is called the precession of the equinoxes.
4. Cause of the precession: The earth rotates around its axis like a spinning top. In doing so, it’s North Pole (and hence, the celestial pole), describe a circle of about 47° around the pole of the equator intersects the plane of ecliptic. Therefore, the plane of the equator intersects the plane at a constantly shifting point. This point, the first point of Aries or vernal equinox, goes on receding westward at a rate of about 50.26” of arc per year. The result of this precession of equinox is a slow increase in right ascensions of almost all fixed stars in zodiac. This precession takes about 25, 785.91 yrs i.e. about 26,000yrs.) to complete one circle. An appreciation of this precession is of paramount importance in the understanding of the basic concept of Vedic Astrology.
XI Fixed and Movable zodiac: The fixed or the sidereal or niryana zodiac is based on fixed star (nakshatra). his fixed star is Spica in the Chitra nakshatra and 180° from this star is 1^{st} degree or point of Aries in the fixed (niryana) zodiac. The movable or the tropical or sayana zodiac is reckoned from the vernal equinox, i.e. the 1^{st} point of Aries beings from the vernal equinox. Movable zodiac continues to recede westward @ 50.26” per year.
XII The Sayana and Niryana systems and Ayanamsha:
1. Due to precession of equinoxes @ 50.26” per year, the distance between the vernal equinox (1^{st} point of Aries of movable zodiac) and the1st point of Aries on fixed zodiac has been progressively increasing. This distance at any given epoch (time) is called the Ayanamsha. The system that uses the fixed zodiac is called the Niryana (without Ayanamasha) system and the one that uses movable zodiac is called the Sayana (with Ayanamsha) system.
2. The Niryana and planetary longitude can br derived by subtracting Ayanamsha from the Sayana longitudes.
3. The Niryana and Sayana zodiacs coincided in the year 285 AD when the ayanamsha was zero. The annual rate of precession varies slightly due to complex interplanetary motions and influences on our universe. According to new determination of the location of equinoxes, the value of Ayanamsha as on 21^{st} March 1956 is 23°15’. Adding to this yearly precession as above @ 50.26” per year (actually this also varies with time), current (as on 21^{st} March 2004 AD) Ayanamsha come to 23° 55’ 12.48” (Actual Ayanashma as on 1^{st} January 2004, after taking more detailed and latest astronomical data is 23° 54’ 37”).
4. The equinoctial precession completes one round in about 26,000 years and the fixed and movable zodiac coincide regularly after this period. The ayanamsha reckoned on the basis of considering the year 285 AD as the year when Sayana and Niryana zodiacs coincided is known as Chitrapaksha ayanamsha. There are others ayanamshas taking different years of coincidence 397 AD by Dr. BV Raman; 361 AD, 394 AD, 498 AD, 559 AD etc. by others. However, Chitrapraksha ayanamsha ahs found to give most accurate timing of events and hence is used most commonly.
XII Concept of Time:
1. Vedic measure of time:
Time

Sub
division

Years

Yugas

Years

Yugas

1 Asu
(pranaone
Respiration)

= 4
(sidereal)
Sec.

17, 28,000
Sidereal yrs.

= 1 Sat yuga
(1^{st} Yuga)

14 Manu

= 1 Kalpa (or 1008
Mahayuga)

6 Asu

= 1 sidereal
Pala (or Vighati)

12, 96,000
Sid. yrs

= Treta Yuga
(2^{nd} Yuga)

2 Kalpa

= One day & night of Brahma

60 Pala

=1 Ghati
(24 mts.)

8, 64, 000
Sid. yrs.

= Dwaper yuga
(3^{rd} Yuga)

30 day night of Brahma

= 1 month of Brahma

60 Ghati

= 1 day

4, 32, 000
Sid. yrs.

= Kali yuga (4^{th}
Yuga)

12 months of Brahma

= 1 year of
Brahma

30 days

= 1 month

43, 20.000
Sid yrs.

=1 Mahayuga
(total of 4 Yugas)

100 years of Brahma

= Life of brahma (1 Mahakalpa)

12 months

= 1 year
(sidereal)

72 Yuga

= 1 Manvantar
Or Manu

1 prahar

=3 hrs.

1 day &
night

= 1 ahoratra =
30 muhuratas

1 dinmaan

= 15 muhurata

1
muhurat

= 1/ 2 yamardha

There are many methods of reckoning the time. One standard method is given above.
2. Vedic measure of angles:
Angle

Sub division

Angle

Equivalent
Time

1 zodiac (360°)

= 12 signs (Rashis)

1” of longitude

= 1/ 15 sec.

1 sign

= 30° (Lavas)

1’ of longitude

= 4 sec.

1 degree

= 60’ (Lipta or Kala)

1° of longitude

= 4 minutes

1 minute

= 60” (Vilipta or Vikala)

15° of longitude

= 1 hour

1 second

= 60 tatpatra

360° of longitude

= 24 hour

1 Tatpatra

= 60 pratatpatra

3. Other Vedic Methods of time for astrological purposes:
S.No.

Item

Definition

1.

Sidereal day

Time interval between one star rises to the next.

2.

Civil day

Time interval between one Sunrise and the next.

3.

Lunar month

One new Moon to the next new Moon.

4.

Solar year

Interval between entry of Sun from one sign to the next.

5.

Solar year

Period of one solar revolution.

6.

Jupiterian (or Jovian) year (Brahaspatya)

Period of Jupiter’s motion through a sign.

4. Modern measure of time: The length of an astronomical year is 365. 25 days (365d 5h 48m 45.2s). A common year has 365 days and once in four years a day is added to the year making it a leap year with 366 days. The modern division of time is an follows:
Item

Division

Item

Division

1 century

=100 yrs.

1 week

= 7 days

1 leap yr.

= 366 days

1 day

=24 hours

1 year

= 365 days

1 hour

= 60 minutes

1 calender month

=30 days (varies)

1 minute

= 60 seconds

5. Greenwich Mean Time GMT (or Universal Time UT): The earth’s motion is not perfect circle but elliptical and that too is not uniform. The inclination of earth’s axis of rotation also creates complications in adopting Sun as uniform reference point for measure of time. Therefore a fictitious means Sun is adopted, moving over the equator and giving us a mean solar time. A mean solar day is equal to 24 hours irrespective of varying factors of motion Sun Earth system. GMT or UT is the mean solar time on the prime meridian of Greenwich meridian, it is 12:00 noon. Almost all countries follow the time which is + or  of GMT.
6. Local Mean Time (LMT): LMT is the time elapsed from mid night of a place. Due to rotation of earth from west to east, one rotation (360°) in 24 hrs. (i.e., 4 minutes per degree of longitude), the Sunrise 4 minutes earlier at a place 1° east of any place And vice versa. This time of 4 minutes per degree of longitude is not uniform and will from latitude to latitude due to tilt of earth etc. Time of each place, different from longitude to longitude roughly 4 minutes per degree, is called LMT.
7. Standard time: As the local mean time of place varies from place to place. Within one country or a state, different town will have different times depending upon the longitude. Therefore each country has chosen by law or practice a uniform time, + or – some hours from GMT, called standard Time for that country. In India, we have + 5: 30 hrs. time form GMT as Indian Standard Time. It relates to 82° 30’ E meridian or time zone of + 5: 30 E (82. 5x 4 min. = 5:30 hrs.), being E of prime meridian it is 5: 30 hrs. ahead of GMT. This time is used for all civil purpose and watches would show this time. But in Vedic astrology, as sunrise and sunset varies from place to place according to longitude, it the local time, which is of importance and used for all calculations.
8. Zonal Standard Time (ZST): In large country like the USA, there is large variation of longitude across the country. Therefore standard time will don’t serve the purpose. So the country is divided in four official standard of time, the Eastern, Central, Mountain and the Pacific corresponding to LMT of 75°, 90°, 105° and 120° of west meridians. The standard meridian of a country or zone is called Time Zone. Time corresponding to that meridian is called ZST.
XIV Retrogreeion and direct motion: Planets move along the zodiac from west to east, around the Sun. However, when seen from the earth, something there motion appears top occurring in reverse direction against the background of star.
This apparent reverse motion is called retrogression of planets and has importance in predictive astrology.
XV Combustion of planets: Planets too close to Sun become invisible and are called as combust. They lose their strength and behave adversely in predictive astrology.
XVI Moon’s Nodes Rahu and Ketu:
1. The moon’s apparent path cuts the elliptic, obliquely at two point called nodes. This is similar to Sun’s path or ecliptic cutting the equator at an cblique angle. The point where the Moon crosses the ecliptic from south to north is called ascendind node or Rahu (dragon’s mouth) and where it crosses the ecliptic from north to south it is called the descending node or Ketu (dragon’s tail). These are two points 180° apart. Just as the equinoctial point shofts westward on ecliptic, so also the Moon’s orbit intersect the ecliptic at a constantly shifting point. Thus their motion is always retrograde. They complete one around of zodiac in 18 yrs. and 10 days.
2. They are mathematical sensitive points having special importance in predictive astrology.
Shanker Adawal
www.shankerstudy.com, www.shankarsastro.com
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