Some serious commentators have noted that the siddhāntic solar year is believed to be sidereal by moderners, but it is nearer to the modern anomalistic year rather than to modern sidereal year. Due to the stubborn insistence of moderners of treating ancient siddhāntas as texts of materialist physical astronomy based on observations, no serious attempt is made either to test ancient siddhāntas astrologically, which was their purpose, or to understand the deeper mechanisms of ancient siddhāntas. Here is one graring example :

The article Evidence of Modern Value of Precession in Bhāskaracharya's Work based on Suryasiddhānta brings to light some neglected and distorted aspects of ancient astronomy. As shown in that article with details, Bhāskara-ii cites 30000 revolutions of sampāta per Kalpa of 4320 million years, which he used with Munjāla's ayana-chalana to get a figure which is surprisingly near to modern value of period of equinoctial precession of Earth's orbit. In that article, I showed that as in the case with modern physical astronomy, this sampāta motion moves in opposite direction to that of precession, and is therefore nearly same as the anomalistic motion of apparent orbit of the Sun, i.e, motion of apogee or perigee of the apparent geocentric orbit of the Sun. The magnitude of this anomalistic year is about 365.259 now, which is surprisingly near to Suryasiddhāntic solar year of 356.2587565 . Let us examione it more closely.

Suryasiddhānta uses a long term anomalistic motion whose rate is 387 revolutions per Kalpa. But Bhāskara-talks of a similar motion which is much quicker : 30000 revolutions per Kalpa. The difference is of 29613 revolutions per Kalpa. It gives a periodicity of one revolution in 145881.876 years. Suppose this is the correction needed to convert the Suryasiddhāntic anomalistic (i.e., nirayana) year to sidereal. Divide the number 356.258756481481 with 145881.876 and substract the result from 356.258756481481, the final outcome is 365.2562527 days, which ought to be the length of Suryasiddhāntic sidereal year provided the siddhāntic nirayana year is assumed to be anomalistic year. Now, this sidereal year of 365.2562527 is short of modern value by only 9 seconds only.

On page 108 in the section "Indian Luni-Solar Astronomy" in the 344 page long Introduction (writted by Dr Satya Prakash, D.Sc.) to Brahmagupta's Brahma-sphuta-siddhānta by Brahmagupta edited by a board of editors headed by Acharya Ram Swarup Sharma, the following passage was reproduced from P.C. Sengupta's Appendix-i of the Khandakakhādyaka : "Though we take that Indian year was designed to be the sidereal year, it approached most closely the anomalistic year' and its excess over the sidereal year was about 3 minutes. From this consideration it appears that the Indian astronomers were justified in taking the Sun's apogee to be fixed".

"The Indian astronomers were justified in taking the Sun's apogee to be fixed" , a very important (approximate) conclusion which was arrived at by PC Sengupta long ago, then reproduced by Dr Satya Prakash in 1966 edition of Bhahmashutasiddhanta's Introduction published by Indian Institution of Astronomical and Sanskrit Research, Delhi. But the mainstream historians of astronomy followed the footsteps of Otto E Neugebauer (who was active then and died in 1990) and David Pingree who turned a blind eye to such facts, because the Greek and Babylonian year-length was much erroneous than the India one which was noted by the same authors PC Sengupta and Satya Prakāsh just below the afore-cited statement. PC Senguptā , Satya Prakāsh and Rām Swarup did not paid attention to the statement of Bhāskar-ii made in Siddhānta Shiromani about 30000 revolutions per Kalpa of a sampāt, which was a tangible evidence for the idea proposed by P C Sengupta. Let us examine this idea more closely.

Sidereal Year in a Geocentric system means Sun's one complete revolution round the Earth with respect to the stars (if the stars are fixed, then sidereal system is same as Nirayana system).

Anomalistic Year in a Geocentric system means one complete revolution of Sun's apogee (uchcha) or perigee (neecha) round the Earth with respect to the stars.

Harmonic difference of these two quantities, i.e., reciprocal of the difference of their reciprocals, gives the period of revolution of apogee with respect to stars.

Sun's path is called the ecliptic. The points of intersection of the ecliptic with Nādi Vritta (projection of Earth's equatorial plane into sky) is called vishuva sampāt ; vishuva means "equal". Hence, day is equal to night at these two sampāt points which are known as equinoxes.

But there is another type of sampāt of the ecliptic and the Nādi circle : when apogee of the Sun's orbit touches the nādi circle at the first point of nirayana Mesha. Such an event takes place once every 144000 years according to the Suryasiddhāntic value cited by Bhāskara-ii.

Thus, what PC Sengupta and Dr Satya Prakash wanted to say was that this apogee was taken to be fixed, which means the nirayana system of Indians was actually not with reference to the stars as fixed, but as Sun's apogee taken to be fixed. Its implication is that according to PC Sengupta, Sun's orbit of its apparent revolution round the Earth, with its apogee and perigee, was taken to be Fixed in the Nirayana system. In other words, Earth's real orbit of its revolution round the Sun is assumed to be Fixed. It means motions are to be measured not with respect to stars assumed to be fixed as in the sidereal system, or as equinoxes assumed to be fixed as in the tropical system, but as solar ecliptic plane or at least its apogee assumed to be fixed. Any frame of reference can be assumed to be the fixed frame for measuring the motions of other objects.

There are finer tunings of Drik (physical) motions with respect to siddhāntic. Take the above value 365.2562526834 and add its 4320000th part to it because there is one extra revolution in Drik frame with respect to the Saura (siddhāntic). We get the result 365.2563372335 days. Then, there is the Saura anomalistic motion of 387 revolutions per Kalpa or one revolution per 11162791 years. Therefore, divide 365.2563372335 with 11162791 and add the result to 365.2563372 to get 365.2563699544 days, which is less than one second in time away from modern average value of sidereal year. There are finer motions of manvantara and kalpa but they are insignificant.

Thus, the siddhāntic solar year is not the sidereal year, but anomalistic year, with siddhāntic value of sidereal year to be only 0.754 seconds longer than modern sidereal year, while anomalistic year having slightly more than one minute variance with modern value, and siddāntic sāyana year having 115 seconds of difference with modern value. Sidereal value being more accurate suggests siderealism and not tropicalism was used for measurements.

The above is a rational explanation. Actual siddhāntic method was not observation, but revelation.

Vinay Jha