I noticed in Kala there is an option for GC mid-Mula as well as Dhruva GC mid-Mula, which also has equatorial and ecliptic longitude options. I believe I understand the difference; can someone tell me if I have done so properly?
1) GC mid-Mula
Divide the ecliptic into 27 equal portions such that 6:40 of Mula coincides with the ecliptic longitude of the Galactic Center
2) Dhruva GC mid-Mula
Divide the (celestial) equator into 27 equal portions such that 6:40 of Mula coincides with the equatorial longitude of the Galactic Center
2a) equatorial option
to find the nakshatra of a planet, find that planet's equatorial longitude. the nakshatra of the planet is the one that contains the planet's equatorial longitude
2b) ecliptic option
project the equatorial nakshatra boundaries onto the ecliptic. to find the nakshatra of planet, find which ecliptic-projected nakshatra contains that planet's ecliptic longitude
so GCmid-Mula divides the ecliptic equally, whereas DhruvaGCmid-Mula divides the equator equally. with 2b) the equal division of the equator creates an unequal division of of the ecliptic, so each of the Dhruva nakshatras projected on the ecliptic will not be the same size
@ernst So, with the Dhruva GC Middle of Mula with equatorial coordinates , if some of the nakshatras are more than 13'20 and some are less than 13'20, are some actually 13'20 of arc?
Also, with that method would the nakshatras change size due to precession over the longterm cycle?
I'm going to take a try answering due to my interest in the topic, and hopefully Ernst will correct me or add what is necessary.
I think you meant to write ecltipic coordinates, since with equatorial coordinates all the nakshatras are 13'20.
I'm pretty sure the dhruva ecliptic nakshatras wouldn't change size due to precession itself. They do however change size due to the change in ecliptic obliquity, i.e., the angle between Earth's axis of rotation and the ecliptic. To get the eclptic boundaries, we take the equatorial boundaries and transform the coordinates onto the ecliptic, but when ecliptic changes places, then the boundaries will change.
The obliquity of the ecliptic changes very slowly though, wikipedia says 0.013 degrees over 100 years, so the boundaries won't change drastically.
EDIT: I had included some information here that was wrong, so I deleted it; fyi in case you saw it.
Here is the right information I think...I had not been calculating the ecliptic obliquity correctly, as I did not realize swisseph had its own function for that.
Find below the boundaries that exist at present:
0 is the beginning of ashvini
>>> dhruvecl2025
[0.0, 12.268, 24.739, 37.591, 50.943, 64.819, 79.121, 93.632, 108.072, 122.181, 135.799, 148.891, 161.534, 173.879, 186.121, 198.466, 211.109, 224.201, 237.819, 251.928, 266.368, 280.879, 295.181, 309.057, 322.409, 335.261, 347.732, 360]
and the sizes of these nakshatras
>>> naksize2025
[12.268, 12.471, 12.852, 13.352, 13.876, 14.302, 14.511, 14.44, 14.109, 13.618, 13.092, 12.643, 12.345, 12.242, 12.345, 12.643, 13.092, 13.618, 14.109, 14.44, 14.511, 14.302, 13.876, 13.352, 12.852, 12.471, 12.268]
13'20 is 13.3333333, so none are exactly that size.
The attached text file contains this information for a period of 4000 years, from 2100 bc to 2100 ad, just in case your curious; the boundary points and sizes mostly seem to change maybe like .2-.3 degrees over 4000 years.
@j0sh4rp3
Thanks for the details. I thought that when we coordinate nakshatras to the celestial equator then project that to the ecliptic, then the nakshatras change size.
I think you might enjoy these videos of Ryan interviewing Ernst on these topics, in case you haven't seen them:
"I thought that when we coordinate nakshatras to the celestial equator then project that to the ecliptic, then the nakshatras change size."
Yes, that is exactly right. That is what this is showing:
>>> naksize2025
[12.268, 12.471, 12.852, 13.352, 13.876, 14.302, 14.511, 14.44, 14.109, 13.618, 13.092, 12.643, 12.345, 12.242, 12.345, 12.643, 13.092, 13.618, 14.109, 14.44, 14.511, 14.302, 13.876, 13.352, 12.852, 12.471, 12.268]
So if you use dhruva ecliptic coordinates, then ashivini is 12.286 degrees in size, bharani is 12.471 degrees in size, krittika is 12.852 degrees in size, etc.
If you use dhruva equatorial coordinates, then all the nakshatras are the same size.
So, in this case, what does the word 'dhruva' mean here?
My understanding is that dhruva means, "constant, not changing".
"ध्रुव - fixed, firm, immovable, unchangeable, constant, lasting, permanent, eternal"
says Monier-Williams, so yes that is it.
I wasn't very precise in my wording:
I said the nakshatra sizes change if you use dhruva ecliptic.
That is not correct.
What changes is the degrees that the nakshatra take up on the reference plane.
The nakshatras don't actually change size. It is just that since the ecliptic is tilted with respect to the equator, thus the same boundaries will have a different length of eclitpic.
The image from the Ayanamsha and Rashis class is really helpful to visualize this. I attached it.
The nakshatras are the cylinder and its divisions...so they don't actually change size. They take up 13'20 of the equator, but since the ecliptic is tilted, a different length of the ecliptic passes through each nakshatra.
Well done, I always found this confusing though I have 'gotten' it a couple of times when really tuning into it.
Dhruva means fixed. Its the term that the hindus applied to the pole star, believing it to be fixed. Its really not and its another bit of information that shows they did not know about precession of the equinoxes which causes the pole to move through the stars. In astronomy, dhruva calculations refer to polar coordinates, so using the poles as an axis instead of the ecliptic poles as an axis in the calculations.