CHAPTER 7 HELIACAL RISING AND SETTING AND CIRCUMPOLARITY OF SOME BRIGHT STARS

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1 109 CHAPTER 7 HELIACAL RISING AND SETTING AND CIRCUMPOLARITY OF SOME BRIGHT STARS Many cultures have featured heliacal phenmenn prminently in their astrnmy fr calendrical purpses. The imprtance f the heliacal rising and setting f heavenly bdies was realized in tw cntexts: (i) the inferir planets Mercury and Venus visible in the eastern and western hrizn respectively as mrning star and evening star. (the Mayans divided their calendar int fur intervals based n this phenmenn); (ii) the brightest star Sirius (Lubdhaka) heralding the famus flds in the Nile river in Egypt annually at its heliacal rising made Egyptians base their calendar n the heliacal rising f Sirius; and (iii) the first day f the Islamic lunar mnth is defined by the helical rising f the Mn. The visibility f the star Canpus has been given great imprtance in Indian Astrnmical literature. 7.1 DEFINITION Heliacal Rising and Setting Stars and planets underg perids f invisibility when it is clse t the Sun, within the prescribed limit. The cncerned heavenly bdy is then said t be cmbust r asta, and it is nt visible due t the Sun s effulgence. This is called the Heliacal setting f the cncerned star r planet. This invisibility f the heavenly bdy cntinues fr a few days until the bdy cmes ut f the prescribed range f the Sun s brightness.

2 110 After a few days when the heavenly bdy is utside the prescribed angular distance frm the Sun it becmes visible and remains s fr quite a few days. This visibility is called Heliacal rising [Heliacal: related t the Sun]. A heavenly bdy is said t be heliacally rising if it rises in the eastern hrizn a few minutes befre the sunrise i.e. in the mrning twilight. Similarly, a star r planet is heliacally setting a few minutes after the sunset i.e. in twilight f dusk Csmic Rising and Setting Since the cncerned star is clse t the Sun in this interval f its heliacal setting and heliacal rising, the Sun and the star set r rise tgether within a small interval f time. Apart frm these there are real but nt bservable, phenmenn. These definitins are thse published by Delambre in his histry f astrnmy, qutes as (i) The csmic rising r true mrning rising: it is the day when the star rises in the mrning at the same time as the Sun. (ii) The csmic setting r true evening setting: is the day when the star sets in the evening at the same time as the Sun. 7.2 RISING AND SETTING OF STARS IN INDIAN ASTRONOMY The phenmenn f heliacal rising and setting f stars and planets is an imprtant phenmenn discussed in all classical siddh ntas under the chapter Uday st dhik ra. Even in mdern astrnmy great imprtance is given t this tpic. Over thusands f years f bservatin the ancient and medieval astrnmers have estimated the altitudinal distance between the Sun and any

3 111 particular star fr the phenmenn f heliacal rise and set. The great Greek astrnmer Ptlemy (c.150 C.E.) called this altitudinal (vertical) distance as arcus visinis. This interesting phenmenn has been well studied and used in classical Indian astrnmy. The star f particular interest fr heliacal rising and setting is Canpus ( Carinae). In almst all siddh ntic texts the celestial lngitudes f the Sun fr the heliacal rising and setting f Canpus are prescribed. These tw pints are referred t as uday a and ast a respectively. The uday a and ast a differ fr different heavenly bdies and even fr particular star these vary with the terrestrial latitude. Further, due t the precessin f the equinxes the rising and setting pints fr any given place change, thugh slwly, ver centuries Canpus s Rising in Indian Texts The brightest suthern star knwn as Agastya in India has all the fur visible phenmenn namely heliacal rise, csmic rise, csmic set and heliacal set. This star has a magnitude f As mentined earlier the Indian classical astrnmical texts refer t Canpus s heliacal rising since the phenmenn was cnsidered imprtant fr religius bservances besides astrnmical curisity. The rising f Canpus is given imprtance in Suth India particularly in Tamil Nadu. We mentin a few f these references Varahamihira s prcedure In his encyclpedic text hat Sa hit Var hamihira gives the apprximate day f the slar year when Canpus becmes visible in the eastern hrizn just befre the sunrise as fllws:

4 112 The time f rising f Canpus fr each cuntry shuld be determined by calculatin and annunced by an astrnmer. Nw, fr Ujjayini, it takes place when the Sun s true psitin is 7 shrt f sign Virg (Kany ). A better and mre explicit prcedure is given by Var hamihira in his famus astrnmical wrk Pañcasiddh ntik as fllws (Sastry 1993). Multiply the square f 5 (i.e. 25) by half the equinctial midday shadw; (treating it as the Rsine f an arc) find the crrespnding arc (in terms f degrees) and add 15(degrees) t that. Multiply that by 10 and add 21 times the equinctial midday shadw. These are vin s. Assuming these vin s as the time elapsed since sunrise and taking the Sun at the first pint f Cancer, calculate the lngitude f the rising pint f the ecliptic. When (the lngitude f) the Sun happens t be equal t that then the sage Agastya (i.e. the star Canpus) that lks like the special red tilaka-mark n the frehead f the lady-like suthern directin shines frth and delights the minds f men. Such is the divine knwledge based n time. Figure 7.1 represents the celestial sphere fr a place with latitude. SEN is the hrizntal and Z the zenith; RET is the equatr and P and Q are its nrth and suth ples; GSD is the ecliptic. A is Canpus at the time f its heliacal rising and S the Sun at that time. PGAQ is the hur circle f Canpus, and G the pint where it intersects the ecliptic. Assuming that the celestial lngitude f Canpus is 90 and the celestial latitude S, we have G = 90, AG = and AA = = Therefre R sin E = R sin (asc. diff. f Canpus A) = R tan tan,

5 113 Figure 7.1 Rising f Canpus where is the declinatin AA f Canpus and the latitude f the place, sin sin R = cs cs sin 51 20' = 12 palabh 120 cs 51 20' since Var hamihira takes, R=120 we btain 25 palabh 2 a E=arc (in terms f degrees) crrespnding t Rsine equal t 25 palabh 2 a EG the accessinal difference fr G 21xpalabh, vin s

6 114 because fr unit palabh, the accessinal difference fr G (the first pint f Cancer) is 21 vin s. Als, assuming 15 t be the time-degrees fr the visibility f Canpus, S 15 degrees = E + EG + degrees = [10( E + 15) + 21 palabha] vin s, where E + 15 is in degrees and palabh in digits. Degrees multiplied by 10 are vin s. Nw GS is the arc f the ecliptic which rises abve the hrizn (f Lank ) in the time given by the arc f the equatr. Hence it is bvius that Canpus A will rise heliacally when the Sun is at S, i.e., when Sun s lngitude = lngitude f G + arc GS = lngitude f G (i.e., 90 ) + arc f the ecliptic which rises (at Lank ) in the time given by the arc f the equatr Hence the rule. Obviusly, the rule is very crude. It was discarded by the later astrnmers wh replaced it by better rules Bhaskara II and Grahal ghava prcedure fr rise and set f Canpus Multiply the Palabh by 8 and subtract frm and add t 78 and 98 respectively. These values crrespnd respectively t the setting and rising f the Canpus star when the (true) Sun is at thse pints.

7 115 Example 7.1: Latitude f Varanasi=25 19', Lngitude f Varanasi=83 01' Palabh =12xtan(25 19')= =5 40'35''.92 (i) 78 8xpalabh = 32 35'12''.64 (ii) 98 +8xpalabh =143 24'47''.36 This means the lpa and dar a f Agastya in Varanasi take place when the Sun s true lngitudes are respectively 32 35'12''.64 and '47'' MODERN PROCEDURE FOR HELIACAL RISING AND SETTING Accrding t mdern investigatins the phenmenn f heliacal rise set depends n the fllwing factrs: (i) the light pllutin (ii) the altitude f the star abve the hrizn, (iii) the depressin f the star, (iv) the brightness (magnitude) f the star, (v) the clr f the star, and (vi) the transparency ( extinctin ) f the air. All these factrs cntribute t fixing the arcus visinis, the vertical angular distance between the Sun and the star. Cnsidering the abve factrs, it is estimated that fr the heliacal rising and setting f Canpus the star shuld be 3 abve the hrizn while the Sun is 5 belw the hrizn. Similarly fr the star Sirius the respective altitudes are 5 and 4. Incidentally, it must be nted that Sirius is the brightest star and Canpus is the secnd brightest star amng thse visible t the naked eye. Fr example, the Sun s altitude ( 4 ) which makes the star Sirius visible is quite smaller than the altitude ( 11 ) that allws Antares ( Scrpii)

8 116 t be visible in the early dawn r twilight sky. This is because Sirius is brighter than Antares. Arcus visinis (arc f visibility) is defined as the altitudinal distance between the star and the Sun fr heliacal rising and setting. This altitudinal difference is different fr different stars. Fr a star risen abve the eastern hrizn, fr its visibility there shuld be a crrespnding amunt f darkness in the sky which means that the Sun shuld be crrespndingly belw the hrizn. If the altitude f the Sun is dented by h, and that f the star is H, bth in degrees, then the arcus visinis is H + h =. Here h is belw the hrizn while H is abve the hrizn. While the famus Greek astrnmer Ptlemy (2 nd cent C.E.) takes as a cnstant, in mdern investigatins nt nly is taken a variable, but even the altitudes f tw bdies H and h are taken differently depending n the stars magnitude and als the atmspheric and visibility cnditins, In case the trpical lngitude f the Sun is knwn, then it is transfrmed t the equatrial c-rdinates, by using the expressins (7.1) 1 sin (sin sin ) (7.2) 1 tan (cs tan ) where is the bliquity f the ecliptic, taken apprximately as It is t be nted that the expressins Equatin (7.1) and Equatin (7.2) fllw frm the mre general frmulae in which the latitude f the Sun 0.

9 117 Then in terms f, and the terrestrial latitude f the places, the crrespnding hur angle H is given by H 1 cs 97 sin sin cs cs cs (7.3) Here the zenith distance f the Sun is taken as 97 i.e. altitude 7 belw the hrizn as a standard case. Hwever, this value changes slightly fr different stars, depending n their magnitude. The hur angle frm Equatin (7.3), is taken negative fr the heliacal rising in the mrning twilight and psitive fr the heliacal setting in the evening twilight. Then the sidereal time (ST) at the time f the abve event is given by ST = H (7.4) Nw cming t the heliacal rising f the star, under the abve cnditins, fr a place f latitude, the hur angle is given by H cs (7.5) R 1 tan tan And the crrespnding ST at that time is given by HR ST = s (7.6) where s is the right ascensin f the star. With the data frm the abve expressins, we can find the crrespnding trpical lngitude f the Sun and hence the calendar dates fr the heliacal rising.

10 118 Similarly, by taking the psitive value fr H in Equatin (7.3) we get the ST, trpical lngitude and hence the calendar dates fr the heliacal setting f the star. Table 7.1 Heliacal Rising and Setting f Sme Imprtant Stars Star Heliacal set Csmic set Csmic rise Heliacal rise Agastya May 25 June 4 July17 July 27 Citra September 26 Octber 12 April 13 April 26 Lubdhaka January 10 January 21 July 8 July 19 Rhini May 20 May 30 June 2 June 12 Jyesta Nvember 11 Nvember 27 Nvember 29 December 14 Kratu April 13 April 3 August 11 September 1 Mula Nvember 21 December 9 December 17 January 4 Table 7.1 gives the rising and setting dates f sme imprtant stars fr Bangalre latitude fr the year Table 7.2 Heliacal Rising and Setting f Agastya fr Different Latitudes fr the Year 2014 Latitude Place Heliacal set Csmic set Csmic rise Heliacal rise 8 04' Kanyakumari June 2 June 12 July 9 July ' Bangalre May 25 June 4 July 17 July ' Varanasi April 30 May 11 August 9 August ' Jaipur April 26 May 8 August 12 August ' Srinagar March 26 April 18 September 1 September24

11 119 Helical rising and setting dates fr different latitudes f India is shwn in Table 7.2. In places f higher latitude Canpus sets early in the year than in the places f lesser latitude. Figure 7.2 Evening Sky Picture at Bangalre fr 25 th May with Canpus nt Visible in Western Sky Figure 7.3 Evening Sky Picture at Bangalre fr 22 nd May with Canpus Visible in Western Sky

12 120 The visibility perid f Canpus fr different latitudes in India listed in Table 7.3. It is bserved that as the latitude increases the date f setting f Agastya is earlier and as the date f rising is later. Table 7.3 Heliacal Rising and Setting f Agastya fr Different Centuries and Different Places Latitude Place Heliacal set Csmic set Csmic rise Heliacal rise 500 C.E. 8 04' Kanyakumari May 25 June 4 June 30 July ' Bangalre May 16 May 26 July 8 July ' Varanasi April 22 May 4 July 31 August ' Srinagar 1000 C.E. 8 04' Kanyakumari May 24 June 2 June 28 July8 13 0' Bangalre May 15 May 25 July 7 July ' Varanasi April 21 May 2 July 29 August ' Srinagar March 21 April 10 August 21 September C.E. 8 04' Kanyakumari May 22 June 1 June 27 July7 13 0' Bangalre May 14 May 24 July 5 July ' Varanasi April 19 May 1 July 28 August ' Srinagar March 18 April 8 August 20 September C.E. 8 04' Kanyakumari June 2 June 12 July 8 July ' Bangalre May 24 June 3 July 16 July ' Varanasi April 29 May 11 August 8 August ' Srinagar March 26 April 17 August 31 September 23

13 CIRCUMPOLARITY Stars rise and set heliacally fr a given place n different dates in a year. In between the heliacal setting and rising dates the star will nt be visible. On the ther hand, in between the heliacal rising and setting the star will be visible in the sky. In the case f sme stars, nce it is set heliacally n sme day, fr a lng perid it will nt be visible at all. This perid f invisibility can be fr several hundreds r thusands f years, depending n the declinatin ( ), f the star and the terrestrial latitude f the place. Then, the star is said t be Circumplar. Similarly, after a star has risen heliacally it may nt set, again fr hundreds r thusands f years in which case als the star is said t be circumplar. Figure 7.4 The Mtin f the Stars as Viewed by a Nrthern- Hemisphere Observer Circumplarity in Bh skara s Wrks Bhaskara in his Siddh nta shirmani explains abut circumplar stars r the Saddita stars as fllws:

14 122 Stars that are circumplar visible in ne hemisphere are circumplar invisible fr crrespnding latitudes in the ppsite hemisphere. Fr a star f nrth declinatin t becme circumplar fr the place f latitude in the nrthern hemisphere shuld be greater than 90 (i.e. > 90 ) it will be always abve the hrizn, als if the suthern declinatin is greater than 90 such a star will never be seen in a nrthern latitude, be it Lubdhaka r Agastya r even a planet fr that matter. Bhaskara gives tw examples here namely (i) if the latitude is greater than 37 (i.e., with greater nrth plar distance), there Agastya will nt be visible. (ii) if the latitude is greater than 52 (i.e. with small nrt plar distance), there Abhijit is always abve the hrizn. Fr the year 2013 Canpus s declinatin is abut Suth. Therefre = Since we take int cnsideratin the prescribed arcus visinis f the star, Canpus becmes circumplar fr even latitudes greater than 35 as mentined earlier. It is t be nted that n star is circumplar fr places n the earth s equatr. On the ther hand at the nrth ple r suth ple all star s are circumplar since ne half f the celestial sphere can never be seen. Table 7.4 gives the visibility duratin f star Canpus fr Ujjayini and places nrth f Ujjayini. The calculatins are dne taking altitude f the star 3 and that f the Sun 5 belw hrizn. It is clear that fr the places f nrthern latitude Canpus is visible fr a lesser perid. At latitude it is circumplar.

15 123 Table 7.4 Circumplarity f Canpus fr Places Nrth f Ujjayini Latitude( ) Lwer limit (years) Upper limit (year) Duratin f visibility (years) 23 11' , , , , ' , ' ' ' ' ' Table 7.5 Circumplarity f star Canpus fr latitude Year Heliacal Rising Heliacal Setting 667 Never abve the hrizn September 19 March September 16 March September 31March 2034 Never abve the hrizn Cnsidering altitude f star 1 abve hrizn and that f the Sun 7 belw the hrizn fr a place f latitude the visibility duratin is shwn in Table 7.5.

16 124 Canpus star becmes circumplar prgressively fr decreasing terrestrial latitude, ver thusands f years f interval until it reaches lwest terrestrial latitude. Then the behavir f the star reverses by becming circumplar during different increasing years as its declinatin prgresses nrthward. In ther wrds the phenmenn is peridic.

Heliacal Rising of Canopus in Indian Astronomy

Indian Journal of History of Science, 51.1 (2016) 83-91 DOI: 10.16943/ijhs/2016/v51i1/48379 Heliacal Rising of Canopus in Indian Astronomy S Balachandra Rao*, Rupa K** and Padmaja Venugopal*** (Received