We 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.The first lesson on Celestial Arithmetic as given below will make you familiar with the basic operations on degrees or hours and their correlation.
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.
1. 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,1°, 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 sign
1° = 1 degree
1' = 1 arc minute
1" = 1 arc second
and,
1d = 1 day
1h = 1 hour
1m = 1 minute
1s = 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.
2. Conversion Scale:
We know it very well that
1m = 1 minute of time = 60s = 60 seconds
1h = 1 hour of time = 60m = 60 minutes of time
1d = 1 day = 24h = 24 hours
Similarly,
1' = 1 minute of arc = 60" = 60 seconds of arc
1° = 1 deg. of arc = 60' = 60 minutes of arc
1S = 1 sign = 30° = 30 degrees
1C = 1 circle = 360° = 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 25.35° but 25° 35' .
3. Coordinate System:
The world is normally on a map with GMT in the center.
If we place the origin of the coordinate system at 0° longitude & 0° 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.
4. Arithmetic:
(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.
(ii) Subtraction : To subtract two values in hours or degrees, first subtract seconds from 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:
(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 :
{ discarding 360° }
In case of hours, discard multiples of 24hours or retain as days, if required :-
=
(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 :-
Similarly hour value is divided by a constant
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.
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:-
6. Conversion: Time zone of a country or longitude of a city can be converted into time by the simple rule
or
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 82° 30'.
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.
1. 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,1°, 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 sign
1° = 1 degree
1' = 1 arc minute
1" = 1 arc second
and,
1d = 1 day
1h = 1 hour
1m = 1 minute
1s = 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.
2. Conversion Scale:
We know it very well that
1m = 1 minute of time = 60s = 60 seconds
1h = 1 hour of time = 60m = 60 minutes of time
1d = 1 day = 24h = 24 hours
Similarly,
1' = 1 minute of arc = 60" = 60 seconds of arc
1° = 1 deg. of arc = 60' = 60 minutes of arc
1S = 1 sign = 30° = 30 degrees
1C = 1 circle = 360° = 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 25.35° but 25° 35' .
3. Coordinate System:
The world is normally on a map with GMT in the center.
If we place the origin of the coordinate system at 0° longitude & 0° 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.
4. Arithmetic:
(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.
(ii) Subtraction : To subtract two values in hours or degrees, first subtract seconds from 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:
(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 :
{ discarding 360° }In case of hours, discard multiples of 24hours or retain as days, if required :-
=
(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 :-
Similarly hour value is divided by a constant
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.
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:-
6. Conversion: Time zone of a country or longitude of a city can be converted into time by the simple rule
or
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 82° 30'.
