I've spent the last several months trying to decipher an 1860 English translation of the #SuryaSiddhanta, which was originally written in #Sanskrit and published in its final form in KY 3606 (505 AD). After tracing multiple errors and bugs, I've finally gotten a pretty accurate algorithm which agrees with the methods of late Classical Indian #astronomy as well as observations...

And it looks like modern Indian Solar New Year is actually synched to the #GregorianCalendar.

#Programming

I've spent the last few months trying to work out how the epicyclic system of classical Indian astronomy works.

Today I realised I've been completely misunderstanding the sources. In fairness, the #SuryaSiddhanta is pretty vague in the name of maintaining a classical poetic form and was probably intended as a complement to in-person instruction. Ebeneezer Bugess' translation and commentary are hard to follow and riddled with cluttered, confusing diagrams and tangents.

I've done it!

Since I had some #Covid-related downtime, I've been teaching myself to program, and I've finally managed to implement #Python functions to compute the time of #sunrise and #sunset according to traditional #Indian methods.

Admittedly, I don't think my method is the same as the one described in the #SuryaSiddhanta, but the translation and commentary I was able to find are really vague and unclear about what to actually do. Mine at least is consistent with what was known at the time

#SuryaSiddhanta verses 3:9-12 describe the Precession of the Equinoxes, but assumes that the northward equinox osscilates around Revati rather than moving east (relative to the zodiac) at a constant rate.

But the numbers give, if read correctly, can be interpreted as giving a tropical year of 365 days 5 hours 50 minutes 41.7 seconds, which is less than 2 minutes longer than the actual tropical year.

#Jyotish #Jyotisha #Astronomy

I've gone over and over the #SuryaSiddhanta's passages regarding the precession of the equinoxes, and I think I've figured out what' going on.

Now I just need to figure out when the ayana is going east and when it's going west.

The #SuryaSiddhanta's methods for calculating the positions of the sun and moon at times specify that the absolute value of the jya of an arc must be added to some value in some cases, and subtracted in others.

Since the jya is the predecessor to the modern sine, in this we see the earliest inklings of negative values of trigonometric functions. It's interesting how ideas develop.

#Jyotisha #Trigonometry #Maths #HistoryOfMaths #MathHistory

I managed to get it into my head that my #algorithm to calculate the #Sun's true position as per the #SuryaSiddhanta was just a #kludge that seemed like it gave the right answer, but then I read the relevant passage and it turns out I was right all along.

To a large extendt, Burgess' commentary is necessary to understand the Surya Siddhanta, but Burgess keeps making vague, meandering, unclear explanations coupled with incredibly cluttered, unreadable diagrams.

The first few verses of chapter 3 of the #SuryaSiddhanta is the only place in the book to use the Roman custom of taking the ecliptic as fixed and the zodiac as mobile; the entire rest of the siddhanta treats the zodiac as the fixed reference frame, and considers the ecliptic to just be a line along the zodiac.

#Jyotisha #IndianAstronomy

Chapter 3 of the #SuryaSiddhanta describes the precession of the equinoxes, but in such a way that the ecliptic sort of oscillates relative to the zodiac. This appears to be because early Indian astronomers did not notice the tiny difference between the tropical and sidereal years, but eventually the differences built up. To avoid making the number of years in a mahayuga ambiguous, the solution was a libratory model of precession, so the mean tropical year could match the sidereal. #jyotish