The 10th House or MidHeaven And Ascendant

The point of intersection of the ecliptic of the given time with the meridian of the place is the tenth house for that moment. If A is the sidereal time expressed in degrees and B is the tenth house, then tenth house can be computed as, tan B = tan A Sec w , where w is the inclination of earth's equatorial plane to the ecliptic.

Ascendant : The ascendant is the point of intersection of the ecliptic with the eastern horizon of the place, if A is the sidereal time in degrees + 90° then tan B = tan A cos w ....(1)
From A & B, we can evaluate D the declination & q =90 - angle between meridian & ecliptic, as: sin D = sin A sin w ....(2)
sin q = sin w cos b ....(3)
From D & q, we compute the ascendant as : 
tan E = sin D tan(j + q) ...(4)
where j is the latitude of the place. Ascendant = B + E ....(5) 
The value of the ascendant as calculated above is the sayan value. Subtracting ayanamsa we get nirayana ascendant. The above formulae gives accurate values of ascendant. In absence of scientific calculators, the ascendant & the tenth house can be computed using tables of ascendant by N.C. Lahiri. However, calculation of ascendant using tables gives rise to errors because of tables not available for the given place or for the given sidereal time. This error some times goes up to many minutes of arc.

Calculation of Sidereal Time and Ascendant

In this lesson we are describing sidereal time and are listing the formulas to derive 10th house and ascendant degree accurately using sidereal time. Oral computation of ascendant is also described. Attention is drawn towards the common error committed by most of the fellow astrologers in the computation of ascendant or planet degrees. 
 One Solar day is the time between two successive passages of the sun across the meridian as observed at a particular place. In astrology, we are interested in motion of stars. We want to know the time period of earth when any star is observed to return to the same position. Such a clock is called a sidereal clock and its time, being regulated by stars is called sidereal time.
 There are 365.2422 days in the year. During this period, the earth makes one revolution around the Sun. If we look from remote stars, we see that the earth has made 366.2422 circles about its axis in 365.2422 days. Each sidereal day is thus : Duration of one sidereal day ->
  
 
(shorter by 3 min 55.91 seconds than the mean solar day of 24 hours.)
GMT and Greenwich sidereal time coincide at one instant every year at the autumnal equinox (around September 22). Thereafter, the difference increases until half a year later it is 12 hours (around March 23). After one year, the times again coincide. To compute sidereal time manually, please refer to "Tables of Ascendants" by N.C. Lahiri.

Longitude and Time Summary

Sun is the best time-keeper throughout the world. It Sun regularly rises and sets every day. Local time can be measured by the shadow cast by the sun. All the places on a meridian have midday at the same moment. If the earth rotates from West to East, places East of Greenwich are ahead of Greenwich time and those in the West behind it. Since the earth rotates 360° in 24 hours, every 15° there is a difference of 1 hour.

      -: Standard Time :- 
Local time of places which are on different meridians differ. In India there will be a time difference of about 1 hour and 45 minutes in the local time of Dwarka in Gujarat and Dibrugarh in Assam. It will be difficult to prepare a time-table of trains which move from one corner to another. It is therefore necessary to adopt the local time of some central meridian of a country as the standard time for the country. In India 82°30'E is treated as the standard meridian. The local time at this meridian is taken as the standard time for the whole country. Some countries have a great longitudinal extent and so they adopt more than one standard time. For example USA has as many as 5 standard times. The earth has been divided into 24 time zones of one hour each. A few countries like India adopt a time zone in between the two, like 5½ hour zone.

     -: Time Correction :- 
In countries with high latitudes, day duration changes drastically from say 6 hours in winters to 18 hours in summers. At poles this difference becomes so large that there is day for six months and night for six months. In Northern latitude May, June are longer, whereas in Southern latitude December January are longer and they have summer at this time. In summer the sun rises very early. To take the advantage of sun light, the clocks are advanced by one hour during summer for about six months and it is set back to original position during winter. This advanced time is called "summer time" or "day light saving time". At some places the correction is done for 2 hours and it is called as "double summer time". Similarly sometimes it is only half an hour correction. Since this adjustment is only to save light, it is subtracted before we do any astronomical calculation.

      -: Summary :-
For astrological purposes we need date, time and place of birth. City of birth is normally sufficient as place of birth. Along with this one should know the standard time zone and the day light saving time correction to know exactly and correct the time of birth. With the knowledge of coordinates we can even determine the distance between two points. Longitudinal distance play vital role in time gap compared to latitude.