Celestial Arithmatic

Hindu Astrology 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 excercise 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 Arithmatic
2. Understanding Date & Time of birth in various calenders & 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 Arithmatic as given below will make you familiar with the basic operations on degrees or hours and their corelation.

1. Notation:
Time is measured in days, hours, minutes and seconds and is represented as 1^d, 1^h, 1^m or 1^s respectively.

Angle is measured in signs degrees, minutes and seconds and is represented as 1^s,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

1^s = 1 sign
1⁰ = 1 degree
1' = 1 arc minute
1" = 1 arc second

and,
1^d = 1 day
1^h = 1 hour
1^m = 1 minute
1^s = 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, repectively). For minutes and seconds of time use the symbols m and s respectively.

2. Conversion Scale:
We know it very well that

1^m = 1 minute of time = 60^s = 60 seconds
1^m = 1 hour of time = 60^m = 60 minutes of time
1^d = 1 day = 24^h = 24 hours

Similarly,
1' = 1 minute of arc = 60" = 60 seconds of arc
1⁰ = 1 deg. of arc = 60' = 60 minutes of arc
1^s = 1 sign = 30⁰ = 30 degrees
1^c = 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'

3. Coordinate System:
The world is normally on a map with GMT in the centre.

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

(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"
_______________

21^h 25^m 30^s
9^h 30^m 25^s
_______________
11^h 55^m 5^s
____________________

(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 :-

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

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

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

5. 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 hours
or 15⁰ = 1^h
or 15' = 1^m
or 15" = 1^s
or 24 hours = 360⁰
or 2^h = 30⁰ =1^s
or 4^m = 1⁰
or 4^s = 1'

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

        1⁰ = 4^m
or 1 = 4^s
that 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
_____
32^m 120^s
_______
= 5^h 30^m 0^s

For Delhi longitude is 77⁰ 13'

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

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