Vimśottari Daśa: the Numbers Behind It

As I have recently been reading Jyotisha literature more intensively. I would like to share some of the material I find of interest, particularly as not every book is easily obtainable. I was fortunate in coming across a copy of ‘Astrology and Jyotirvidya’ by Viswanath Deva Sarma (published in 1973 and never reprinted it seems). He provides a wonderful overview, complete with tables, on the division of Vimśottari into its Daśas or periods and also provides a unique insight into how the periods came to have the divisions that they have.

In a later article I want to look more closely at how this fascinating system is applied.

First, Vimśottari literally means ‘120’. So Vimśottari Daśa simply means the divisions of 120. Quite straight forward. These are the divisions and also their order:

Sun 6 years
Moon 10 years
Mars 7 years
Rahu (North Node) 18 years
Jupiter 16 years
Saturn 19 years
Mercury 17 years
Ketu (South Node) 7 years
Venus 20 years

If you add everything up you arrive at 120. But just why Venus should have 20 years and the Sun only 6 is much more mysterious. But be assured. There is a logic behind it. First where does the number 120 come from? Hindu astrology uses 27 lunar mansions known as Nakśatra. Each Nakśatra is 13 1/3 degrees long.  (13 1/3  × 27 = 360). There are nine ‘planets’ (including Rahu and Ketu). 13 1/3 × 9 = 120.

You might already have noticed that the lunar month, roughly 27 days, is brought in relation to the solar year, 360 days. This is the first clue as to how the divisions are arrived at. We have an interaction between two major divisions of time, that of the Sun (360) and that of the Moon (13 1/3) with the planets (9).

The solar year is composed of 12 months which each have 30 days.  Now if we convert to the lunar month each day is equal to 1 nakśatra which can be divided into 60 danda. (the danda is equal to 60 pala which are equal to 6 prāna which are equal to 10 guru-aksara which are equal to 27 nimeṣa which is equal to one blink of the eye which is roughly a second.) 😉

The crucial step is to bring into relation the time it takes the Sun to make a complete circle of the ecliptic and the time it takes for the Moon to make a complete circle. You could say that a lunar ‘year’ is equal to a solar month. V.K. Sarma describes it thus:

solar period lunar period
1 year 360 ‘years’
1 month 30 ‘years’
1 day 1 ‘year’
1 danda 6 days

and the reverse:

lunar period solar period
1 year 1 day
1 month 5 danda
1 day 10 pala

The last two numbers are the ones we want. 6 defines the length of the Sun’s Daśa and 10 that of the Moon. Now all that is left is to determine the periods for the rest of the planets. V.K. Sarma describes it thus: the inclination of the Moon to the axis of the earth is 24 degrees (cosmologically) or 23 1/2 degrees (astronomically). If we subtract the solar and lunar periods from 24 the difference is 14 and 18. 14 and 18 divided in half gives us 7 and 9. So the basic numbers we can work with are 7 and 10 for the Moon; 6 and 9 for the Sun.

I’m going to put the results in tabular form as I think it is easier to understand what happens:

As you can see there are some interesting interactions going on. The two outermost planets make use of the Moon’s major number (10) and the major and minor number for the Sun while the inner planets only use the Moon’s major and minor numbers. Rahu doubles the Sun’s minor number and Ketu uses the Moon’s minor number as does Mars.

Saturn 10 + [(24 – 6) ÷ 2] = 10 + 9 = 19 years 10
Jupiter 10 + 6 = 16 years 10
Mars (24 – 10) ÷ 2 = 14 ÷ 2 = 7 years 7 Moon
Rahu 18 years 18 Sun
Ketu 14 ÷ 2 = 7 years 7 Moon
Sun 6 years 6 Sun
Moon 10 years 10 Moon
Mercury 10 + [(24 – 10) ÷ 2] = 10 + 7 = 17 years 10
Venus 10 + 10 = 20 years 10

3 thoughts on “Vimśottari Daśa: the Numbers Behind It

  1. Hello – thanks for this very fascinating analysis. But I’m a bit confused when you say “V.K. Sarma describes it thus: the inclination of the Moon to the axis of the earth is 24 degrees (cosmologically) or 23 1/2 degrees (astronomically).” Surely this 23.5/24° figure is the inclination of th earth to the ecliptic, not the the moon’s inclination to the earth. Cf; Wikipedia “Axial tilt”:
    The Earth currently has an axial tilt of about 23.5°
    The Earth’s axial tilt varies between 22.1° and 24.5°, with a 41,000 year period.
    6.688° = Moon’s tilt to its orbit in the Earth-Moon system (Moon’s tilt to ecliptic is 1.5424°).
    Do you think Sarma has confused things, or have I not understood something?
    Thanks for any help.

  2. Hello Graham

    Well spotted. Sarma’s description is then fuzzy and one would indeed have to ask why he makes a distinction between ‘cosmological’ and ‘astronomical’. I’ll look the passage up in detail, in case I’ve missed something…

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