

Laghu Maanas
Note 
The following text has been taken from Laghu Maanas, written by
Manjulaachaarya  This book which
contains the knowledge about planets, has been written in 60 Shlok in
Anushtup meter. Soorya Dev Yajvaa explains the text as follows: “In other
works on astronomy, the treatment of the subject matter being extensive
(and the rules being lengthy) calculation is not possible mentally; for
this reason, I have written this Karan work (a handbook on astronomy)
entitled Maanas (= mental calculation), a means of acquiring knowledge
of planetary motion, in 60 Shlok only. The number of verses has been
mentioned here to emphasize that the present work though dealing with many
topics is really small in size. Those who will produce the counterfeit
work in imitation of this work shall earn infamy. For, nobody can know the
rationales etc. of the rules given in this Karan work written by me, and
therefore, the learned people will easily know that suchandsuch person
has forged another work on the same subject by stealing the contents of
this work. Thus, such authors shall certainly earn a bad reputation. They
shall be called counterfeiters only.”
So also explains Yallaya: “The work,
which is called Mānasa (mental), as it enables one to know the planetary
motion mentally also without taking recourse to laborious computation, has
been composed in 60 verses in Anushtup meter. What is meant is that
whatever was stated by Soorya and others in voluminous works has been told
by me in a small work. Thus, all astronomy has been summarized by me in 60
verses, and as compared to others, I have produced a more accurate work
agreeing with observations and involving lesser calculation. Those
counterfeiters who want to imitate this work shall earn ill reputation. By
(saying) this, the intention is that this science should be taught to a
worthy pupil after having tested him in various ways. Otherwise, there
will be counterfeiters. To impart knowledge to one who is liable to
imitate is a fault.”]
Here the topics have been separated by colors.
Without special corrections
due to attraction of Sun on Moon, 1 Tithi will vary from 54 to 65 Dand,
i.e. it can be 5 more or 6 less than the mean of 60 Dand in a Solar day.
But Smriti like that of Gautam gives rules which indicate that Tithi can
be of 51 Dand also. The rule is: if the Tithi just touches the start of
Saayaahn and is over before Kutap Muhoort (24 minutes before and after
local true noon), then Shraaddh should be done next day. Here, 1 Tithi =
Saayaahn (6 Dand) + night (30 Dand) + half day(15 Dand) = 51 Dand.
Panchaang Committee of 193031
under Pandit Dinanath Shastri Chulet of Indore set up by king Yashavanta
Rao Holkar has also indicated several quotes from Smriti to show Tithi
variation from 50 to 69 Dand. It had also indicated a rule of variation of
Tithi in a fortnight quoted by Kamalaakara Bhallaa in his Nirnayasindhu
from Skand Puraaan. As it indicated accurate calculation in ancient India,
it was removed by William Jones from printed edition of Skand Puraan. Half
month of 13 or 17 days means that 1 Tithi is of 13 or15 days = 52 Dand, or
17 or 15 days = 68 Dand. This is average, a particular Tithi can be from
50 to 69 Dand.
All astronomy texts give location of towns on globe separated by 90 deg
longitude with reference at Ujjain  Yamakoti Pattan 90 deg East (SouthWest
tip of New Zealand with same south latitude as Yam star, It is nearest to Yam
Dweep (Yamala = 2) which is Antarctica with 2 land masses. In cylindrical
projection of map, or pyramid projection, its scale will be infinite, so it
was called Anant), Siddha Pur 180 deg East (a gate was constructed here by
Brahmaa to mark the end of East direction  Vaalmeeki Raamaayan, Kishkindhaa
Kaand, 40/54, 64), Romak Pattan 90 deg West (where MayaAsura revised the text
of Vivaswaan, father of Vaivasvat Manu). This is not possible without accurate
survey of the whole globe. Only after the survey of the whole lobe, we can find
the distance of Moon by parallax from 2 places whose distance can be known only
by global survey. That is by sighting Nakshatra, so it is called Nakshaa.
All Puraan tell triangular
shape of India in south, but reek authors thought it to be rectangular
which shows lack of their knowledge. All astronomy, works of Greeks were
written at Egypt only. Appolonius and Herodotus had come to India for
study. But no outsider has ever gone to Greece for study, they could go
only as a slave. Measures of solar system, galaxy abound in Vedas and
astronomy texts which indicate accurate global measurements in astronomy
in past. Puraan give 4 cardinal towns  of Indra  Vaswaukasaaraa, of Som
 Vibhaavaree (90 deg East), of Varun  Sukhaa (180 deg East), and of Yam
 Sanyamanee Puree (90 deg West) separated by 90 deg longitude. These
could be at the junction of Talas or could be earlier division at time of
Svāyambhuva Manu.
References(a) Megasthenes: Indika
http://projectsouthasia.sdstate.edu/docs/history/primarydocs/Foreign_Views/GreekRoman/MegasthenesIndika.htm
India, which is in shape
quadrilateral, has its Eastern as well as its Western side bounded by the
great sea, but on the Northern side it is divided by Mount Hemodos from
that part of Skythia which is inhabited by those Skythians who are called
the Sakai, while the fourth or Western side is bounded by the river called
the Indus, which is perhaps the largest of all rivers in the world after
the Nile. The extent of the whole country from East to West is said to be
28,000 stadia, and from North to South 32,000.
Kendra and Signs of Bhuj and Koti
The longitude of a planet diminished by the longitude of its Uccha, (Mandochcha
or Śīghrochcha), is its Kendra. The Bhuj thereof is positive or negative
according as the Kendra is greater or less than six signs; whereas the Koti (i.e.
the complement of the Bhuj) is positive, negative, negative, and positive in the
four quadrants (of the Kendra), (respectively).
That is,
Mandkendra = Planet – Mandochcha
Sheeghrakendra = Planet – Sheeghrochcha
The Bhuj corresponding to the Kendra is defined as follows: When the
Kendra is less than 3 Signs, the Kendra itself is the Bhuj;
when the Kendra is greater than 3 Signs and less than 6 Signs, Bhuj = 6 Signs – Kendra;
when the Kendra is greater than 6 Signs and less than 9 Signs, Bhuj = Kendra – 6 signs; and
when the Kendra is greater than 9 Signs but less than 12 Signs, Bhuj = 12 signs – Kendra.
That is, the Bhuj is the arcual distance of the planet from its Uchcha or
Neecha, whichever is nearer.
The Bhuj is negative,
negative, positive, and positive, and Koti is positive, negative,
negative, and positive, according as the Kendra is 0 to 3 signs, 3 signs
to 6 signs, 6 signs to 9 signs, and 9 signs to 12 signs respectively. The
rule is based on the fact that the Bhuj Phal is negative, negative,
positive, and positive and Koti Phal is positive, negative, negative, and
positive in the first, second, third, and fourth quadrants, respectively.
Shape of India in Matsya Puraan, Chapter 114
Cardinal Towns in Soorya Siddhaant, 12/3842
Vishnu Puraan, 2/8  In Rath (body or extent) of solar system, Eeshaa Dand
is 9,000 Yojan.
Puraan give measure of the size of the Solar system as  Rath of Sun of
157 Laakh Yojan (Sun diameter).
Vishnu Puraan, 1/8/3 
Soorya Siddhaant, 12  gives the Size of Galaxy  This is 1.87 x 10^{16} Yojan,
Here it is BhaYojan = 27 x Bhoo Yojan = 214 kms.
This is about 13,000 light years diameter.
Kathopanishad gives 1/2 X 1017 Dhaam Yojan (half degree of Equator = 55.5
kms) as circumference, or 9700 LY diameter.
NASA's estimate was 100,000 LY in 1995 and 95,000 in 2005.
The
equatorial circumference of the Earth has been assumed to be 4,800 Yojan.
The Hindu Prime Meridian, by
common consent, is the Meridian that passes through Avantee or Ujjayinee
(modern Ujjain). According to the commentator Prashastidhar, these places
are situated on it  Lankaa, Kumaarikaa, Kaanchee, Paatalee, Siddhapuree,
Vatsagulm, Ujjayinee, Lohitak, Kuru, Yamunaa, and Meru. Lankaa is a hypothetical
place in 0 latitude and 0 longitude. Kumaarikaa is the same as Kanyaa Kumaaree
(modern Cape Comorin). Kaanchee is also called Kaanjeevaram. Vatsagulm is Basim.
Lohitak is Rohatak. Kuru is Kurukshetra. Yamunaa is Yamunaa Nagar. Meru is North
Pole. Paatalee and Siddha Puree are unidentified.
How to Calculate Panchaang Parts
There are 5 parts in a a
Panchaang that is why it is called PanchAng, they are 
Tithi, Karan, Nakshatra, and Yog  Compute
the Tithi and the Karan  from Moon’s longitude minus Sun’s longitude,
the Nakshatra from the planet’s longitude, and
the Yog from Moon’s longitude plus Sun’s longitude; and
the time of their beginning and end from their own daily motions, by
applying proportion.
Comments 
The Tithi, Vaar (day), Nakshatra, Karan, and Yog constitute the five
elements of the Hindu Panchaang.
Let S be the Sun’s longitude and M the Moon’s longitude. Also let d be the
difference and s the sum of daily motions of the Sun and Moon.
Then the Tithi, Karan, Nakshatra and Yog and their computation may be
described as follows 
Tithi 
A Lunar Month, which is defined in Hindu astronomy as the period from one
new moon to the next, is divided into 30 parts called Tithi (or lunar
days). Of these 30 Tithi, 15 fall in the Bright fortnight (Shukla Paksh)
and 15 in the dark fortnight (Krishn Paksh).
When M – S = 0, it is the New Moon and the beginning of the first Tithi;
When M – S = 120, the first Tithi ends and the second begins;
when M – S = 240, the second Tithi ends and the third begins; and so on.
The fifteen Tithi of the Bright fortnight are numbered as 1, 2, 3, ……., 14, 15
and the fifteen Tithi of the dark fortnight are numbered as 1, 2, 3, ……., 14, 30.
The first Tithi of each fortnight is called Pratipad or Pratipadaa, the 15
tithi of the Bright fortnight is called Poornimaa or Poornmaasee, and
The thirtieth tithi of the month is called Amaa, Amaavasyaa, or Amaavaasyaa.
To compute the Tithi, reduce M – S to minutes of arc and divide by 720
(720’ = 120 being the measure of a Tithi). The quotient of the division
gives the number of Tithi elapsed since the beginning of the Lunar Month.
The remainder of the division, multiplied by 60 and divided by d gives the
Ghatee etc elapsed time since the beginning of the current Tithi. The same
remainder subtracted from 720, when multiplied by 60 and divided by d
gives the Ghatee etc to elapse before the end of current Tithi.
Karan 
A Karan is half of a tithi and likewise there are 60 karaṇas in a lunar
month. The measure of a karaṇa is 360’ minutes of arc. The first Karan
begins when M – S = 0; the second when M – S = 60, the third when M – S =
120; and so on. The first Karan is called Kinstughna, then a cycle of 7
Karan called Bava (or Baba), Baalav, Taitil, Gar, Vanij, and Vishi (respectively)
repeats itself 8 times. These 7 Karan are called movable Karan. Of these Karan,
Vishti Karan (also called Bhadraa) is considered to be inauspicious and no
auspicious deed is done in its duration. Then the 58th Karan is called Shakuni,
59 Naag, and the last 60 is Chatushpad.
To compute the Karan, reduce M
– S to minutes of arc and divide by 360. The quotient gives the number of
Karan elapsed. The remainder multiplied by 60 and divided by d gives the
Ghatee etc elapsed since the beginning of the current Karan. The same remainder
subtracted from 360, when multiplied by 60 and divided by d gives the Ghatee
etc. to elapse before the end of current Karan.
Nakshatra 
Beginning with the first point of Nakshatra Ashwinee (or star Zeta Piscicum),
the ecliptic is divided into 27 equal parts, each equal to 800 minutes of arc.
These parts are called Nakshatra and are named as – (1) Ashwinee, (2) Bharanee,
(3) Krittikaa, (4) Rohinee, (5) Mrigashiraa, (6) Aardraa, (7) Punarvasu, (8)
Pushya, (9) Aashleshaa, (10) Maghaa, (11) PoorvaaPhaalgunee, (12) UttaraaPhaalgunee,
(13) Hast, (14) Chitraa, (15) Swaati, (16) Vishaakhaa, (17) Anuraadhaa, (18)
Jyeshthaa, (19) Mool, (20) PoorvaaAashaadhaa, (21) UttaraaAashaadhaa, (23) Shravan,
(24) Dhanishthaa, (25) Shatabhishaa, (25) PoorvaBhaadrapadaa, (26) UttaraaBhaadrapadaa,
and (27) Revatee.
To compute the Nakshatra,
reduce the longitude of the desired planet to minutes and divide it by
800’. The quotient gives the number of Nakshatra passed over by the
planets. The remainder divided by the daily motion of the planet gives the
day etc. elapsed since the planet entered into the current Nakshatra. The
same remainder subtracted from 800, when divided by the daily motion of
the planet, gives the days etc to elapse before the planet enters into the
next Nakshatra. The Panchaang give the Moon’s Nakshatra.
Yog 
The Yog are also 27 in number and are named as  (1) Vishkambha, (2)
Preeti, (3) Aayushmaan, (4) Saubhaagya, (5) Shobhan, (6) Atigand, (7)
Sukarmaa, (8) Dhriti, (9) Shool, (10) Gand, (11) Vriddhi, (12) Dhruv, (13)
Vyaaghaat, (14) Harshan, (15) Vajra, (16) Siddhi, (17) Vyateepaat, (18)
Vareeyaan, (19) Parigh, (20) Shiv, (21) Saadhya, (22) Siddha, (23) Shubh,
(24) Shukla, (25) Brahmaa, (26) Indra, and (27) Vaidhriti.
The measure of each Yog is 800’ minutes of arc. The first Yog begins when
S + M = 0, the second when S + M = 800’, the third when S + M = 1600’, and
so on. To compute the Yog, reduce S + M to minutes of arc and divide by
800. The quotient gives the number of Yog elapsed since the beginning of
the current Yog, and the remainder multiplied by 60 and divided by 800
gives the Ghatee etc. The same remainder subtracted from 800, when multiplied
by 60 and divided by 800, gives the Ghatee etc to elapse before the end of
the current Yog.
The term Palabhaa means the
equinoctial midday shadow of a gnomon of 12 Angul (digits).
The term Vishuv Chhaayaa used in Sanskrit text is synonym of Palabhaa.
The term ViNaadee is a unit of time equal to 1/60th of a Naadee or Ghatee,
or 24 seconds. ViNaadee is also called Chashak.
Day Length and Nat Kaal (Hour angle)
The ViNaadee of the Sun’s Char (i.e., twice the Sun’s ascensional difference),
being applied reversely to 30 Naadee, give the length of the day.
The difference between the semiduration of the day and the day elapsed
since sunrise gives the Naadee of the Sun’s hour angle from midday.
When the Sun is in the Northern Hemisphere:
Length of day = 30 Naadee + twice the Sun’s ascensional difference (in ViNaadee),
Length of night = 30 Naadee  twice the Sun’s ascensional difference (in ViNaadee).
When the Sun is in the Southern Hemisphere:
Length of day = 30 Naadee  twice the Sun’s ascensional difference (in ViNaadee),
Length of night = 30 Naadee + twice the Sun’s ascensional difference (in ViNaadee).
The term ‘reversely’ in the text is meant to say that the ViNaadee of the Sun’s
Char should be added when the sign of the Sun’s Chara is negative, and subtracted
when the sign of the Sun’s Char is positive, the sign of the Sun’s Char being the
same as the sign of Sun’s Bhuj. That is, addition of the ViNaadee of the Sun’s
Char should be made when the Sun is in the Northern Hemisphere and subtraction
when the Sun is in the Southern Hemisphere.
The hour angle is measured from midday. Before midday, it is east; after
midday, it is West.
Diameter of the Planets
The diameters (in terms of minutes) of the planets beginning with Mars are
6, 11, 20, 12, and 22, each multiplied by 10, and divided by the sum of
the planet’s own Sheeghra divisor.
That is, Diameter of Mars = (6 × 10)/(D+10) mins.
Diameter of Mercury = (11 × 10)/(D+10) mins.
Diameter of Jupiter = (20 × 10)/(D+10) mins.
Diameter of Venus = (12 × 10)/(D+10) mins.
Diameter of Saturn = (22 × 10)/(D+10) mins.
Where D = Sheeghra divisor of that planet (given in chapter 3verses 56).
These rules are empirical.
We can calculate Yojan for the
Sun and star planets from present measures in kms. That comes to about 216
kms. which is 27 times the Yojan used for EarthMoon (= 8 kms). Bha = Nakshatra
and number 27 also, so this can be called BhaYojan = 27 x BhooYojan. Angular
diameters of planets are much bigger as they are calculated for distance in 8 kms.
Calculating that in 27 x 8 kms unit, it will be approximately correct.
AngulDegree Relation
At the end of the Yashti (radius) of 56 Angul from the centre of the
directions (Dinmadhya), one Angul is equal to one degree. The value of a
radian has been assumed here as equal to 560. The correct value is 57017’45”.
What is meant by the above rule is that if a circle is drawn with a radius
equal to 56 Angul, the circumference will contain 360 Angul approx.
Then 10 of the circumference of circle will be equal to 1 Angul.
The rule is intended to be used
for finding the number of degrees between two planets in conjunction in longitude.
Parameshwar says: “Having constructed a Yashti measuring 56 Angul in length, attach
at its end, at right angles to it, a scale graduated with the marks of Angul.
Keeping (the other end of) the Yashti between the eyes, observe the two planets
in such a way that they lie along the vertical scale. Then as many Angul are there
between the planets, so many degrees lie between them.”
Sit and Asit
The number of Karan elapsed since the beginning of the (current) fortnight
diminished by 2 and then (the difference obtained) increased by 1/7th of
itself, gives the measure of the Sit  if the fortnight is Bright or the
Asit if the fortnight is dark.
That is, in the Bright fortnight,
Sit = (K  2) (1 + 1/7) Angul
Where K is the number of Karan elapsed since the beginning of the Bright
fortnight; and in the dark fortnight, Asit = (K  2) (1 + 1/7) Angul
Where K is the number of Karan elapsed since the beginning of the dark
fortnight.
The Karan
is obtained as follows: Let S and M be the longitudes of the Sun and Moon
in terms of degrees, then the quotient obtained by dividing M – S by 6
gives the number of Karan elapsed since the beginning of the Bright fortnight,
and the quotient obtained by dividing M – (S + 1800) by 6 gives the number of
Karan elapsed since the beginning of dark fortnight.
In the Bright fortnight, the
Moon is first visible when it is at a distance of 12 degrees from the Sun,
i.e., when 2 Karan have just elapsed, so the proportion is made here with
180 – 12 = 168 degrees instead of 180 degrees.
If M and S denote the longitudes of the Moon and the Sun in terms of
degrees, the proportion implied is:
“When (M – S – 12 deg) amount to 168 deg the measure of the Sit is 32 Angul,
what will be the measure of the Sit when (M – S – 12 deg) has the given value?”
The result is Sit = ((MS12) × 32)/168 Angul = ((MS)/6 2) ( 1+ 1/7)
Angul = (K – 2) (1 + 1/7) Angul,
Where K denotes the number of of Karan elapsed since the beginning of the Bright
fortnight.
In the dark fortnight, the Moon becomes completely invisible when the moon is
12 degrees behind the Sun, i.e., when 2 Karan are yet to elapse of the
dark fortnight. So the proportion implied in this case is:
“When M – (S + 180 deg) – 12 deg amount to 168 deg the Asit amounts to 32 Angul,
what will be the measure of the Sit when (M – (S + 180 deg) – 12 deg has
the given value?”
The result is: Asit = ([M (S + 180°)  12°] × 32)/168 = [(M (S + 180))/6  2] (1 + 1/7) =
(K – 2) ( 1 + 1/7) Angul,
Where K denotes the number of of Karan elapsed since the beginning of the
dark fortnight. Hence the rule.
