Celestial Arithmetic

Future Point | 01-Jan-2014

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FuturePointIndia.com is starting a series of lessons on mathematics of astrology. These lessons will give you insight about the calculations and will be useful to beginners as well as the learned. To the beginners it will teach the computations in an easy way and to the learned it will be a good review exercise while adding certain techniques of computations to their knowledge bank. We are listing below some of the lessons which will form part of the series. Further list shall be announced as it proceeds.

  1.  Celestial Arithmetic

  2.  Understanding Date & Time of birth in various calendars & clocks.

  3.  Place of birth & its co-ordinates.

  4.  Calculation of Sidereal Time.

  5.  Calculation of Ascendant & 10th house.6. Calculation of Planet degrees.

The first lesson on Celestial Arithmetic as given below will make you familiar with the basic operations on degrees or hours and their correlation.

NOTATION:Time is measured in days, hours, minutes and seconds and is represented as 1d, 1h, 1m or 1s respectively.Angle is measured in signs degrees, minutes and seconds and is represented as 1s,10, 1' or 1" respectively.

There stands a confusion in words minute and second, each representing time as well as angle.

Both have been well distinguished in their notation, but to be explicit in speech, it is suggested to use the word minute for angle. Similarly second should be used for second of time and arc second for second of angle. Thus

    1s = 1 sign10 = 1 degree1' = 1 arc minute1" = 1 arc second

    and,1d = 1 day1h = 1 hour1m = 1 minute1s = 1 second

Note:- Do not use the symbols ' and " for minutes and seconds of time; they are used for minutes and seconds of a degree (or arc minutes and arc seconds, respectively). For minutes and seconds of time use the symbols m and s respectively.

CONVERSION SCALE:We know very well that

1m = 1 minute of time = 60s = 60 seconds1m = 1 hour of time = 60m = 60 minutes of time1d = 1 day = 24h = 24 hours

Similarly,1' = 1 minute of arc = 60" = 60 seconds of arc10 = 1 deg. of arc = 60' = 60 minutes of arc1s = 1 sign = 300 = 30 degrees1c = 1 circle = 3600 = 12 signs

Note that minute, second and arc minute & arc second all are to a scale of 60 and not 100. Hence do not use "." to distinguish between degree, arc minute & arc second or hour, minute & second. For example 1.50 hour is not 1hour 50 minutes but 1 hour 50 hundredth of an hour, or 1 hour and 30 minutes. Similarly 25 degrees 35 arc minutes should never be written as 25.350 but 250 35'

COORDINATE SYSTEM:The world is normally on a map with GMT in the center.

If we place the origin of the coordinate system at 00 longitude & 00 latitude then it's longitude becomes +ve in East and -ve in West whereas latitude becomes +ve in North & -ve in south. We shall be following the above notation of + and - for all computations later in the book.


(i) Addition: To add hours, minutes and seconds or degrees, arc minutes and arc seconds, add the seconds to seconds, minutes to minutes and hours to hours respectively. If seconds are 60 or more subtract multiples of 60 & carry to the minutes. Similarly extract multiples of 60 from minutes & carry to hour or degree. e.g.

700 55' 38'Add 1200 45' 40" _______________ 1900 100' 78"or 1910 41' 18"

Similarly, 10h 35m 48s 13h 40m 30s _________________ 23h 75m 78s or 1d 0h 16m 18s ----------------------

(ii) Subtraction :To subtract two values in hours or degrees, first substract seconds fom seconds. If seconds to subtract are more than the value to subtract from take carry from minute and add 60 to seconds. Next subtract minutes from minutes, take a carry of 60 minutes from hours, if required. For example:

620 35' 48'530 40' 52"_______________80 54' 56"_______________

21h 25m 30s9h 30m 25s_______________11h 55m 5s____________________

(iii) Multiplication :To multiply a figure in degrees or hours by a constant, multiply seconds, minutes and degrees by the constant respectively. Extract multiples of 60 seconds to add to minutes & extract multiples of 60 minutes to add to degrees. If degrees are more than 3600, discard multiples of 3600. For example

410 25' 30" X 10______________ 4100 250' 300"= 540 15' 0" (Discarding 3600)______________

In case of hours, discard mutiples of 24hours or retain as days, if required :-

10h 25m 38s X 10 ___________________= 4d 8h 16m 20s ______________

(iv) Division:To divide a value in degree by a constant extract multiples of divisor from degrees to get degree part of quotient, convert remainder degrees into minutes and add minute value of dividend to it; extract multiples of divisor from minutes to get minute value of quotient, convert remainder minutes into seconds and add second value of dividend; extract multiples of divisor again from seconds to get second value of quotient.

For example

16)1200 38' 47"(70 112 8X60 = 480 +38 16)518(32' 512 6X60 = 360 +47 16) 407(25" 400 7

Similarly hour value is divided by a constant

7)6h 25m 30s(oh 6X24 144 +25 7)169(24m 168 1X60 = 60 +30 7) 90(12s 84 6

Since the remainder is 6s which is more than 50% of divisor 7, 1 can be added to 12s to round off the result as 0h 24m 13s.

ANGLE - HOUR RELATIONSHIP:The earth moves around its axis to complete a circle in 24 hours. That is, it rotates by 360 degrees in 24 hours. This gives us a relationship between angle and time as follows:

3600 = 24 hoursor 150 = 1hor 15' = 1mor 15" = 1sor 24 hours = 3600or 2h = 300 =1sor 4m = 10or 4s = 1'

CONVERSION:Time zone of a country or longitude of a city can be converted into time by the simple rule

10 = 4mor 1 = 4sthat is multiply longitude by 4 to get the value in time. East should be taken as "+" and West as "-". For example, for India time zone is 820 30'.

Multiplying by 4

    820 30' x 4_____32m 120s_______= 5h 30m 0s

For Delhi longitude is 770 13'

    multiplying by 4 770 13' x 4 _______ 308m 52s