(The below includes extracts from: wikipedia.)
Trepidation (from Lat. trepidus, “trepidatious”), in now-obsolete medieval theories of astronomy, refers to hypothetical oscillation in the precession of the equinoxes. The theory was popular from the 9th to the 16th centuries. Trepidation was the mainstay of Hindu astronomy and was used to compute ayanamsha for converting sidereal to tropical longitudes.
In Suryasiddhanta
The third chapter of the Suryasiddhanta, verses 9-10, provides the method for computing it, which E. Burgess interprets as 27 degree trepidation in either direction over a full period of 7200 years, at an annual rate of 54 seconds. This is nearly the same as the Arab period of about 7000 years. Brahma Siddhanta, Soma Siddhanta and Narada Purana describe exactly the same theory and magnitude of trepidation as in Suryasiddhanta, and some other Puranas also provide concise references to precession, esp Vayu purana and Matsya Purana.
- The zero date according to the Suryasiddhanta was 499 AD, after which trepidation is forward in the same direction as modern equinoctial precession.
- The vernal equinox of the Surya Siddhanta librated 27° in both directions from the sidereal epoch. Thus the equinox moved 54° in one direction and then back 54° in the other direction. This cycle took 7200 years to complete at a rate of 54″/year. The equinox coincided with the epoch at the beginning of the Kaliyuga in −3101 and again 3600 years later in 499. The direction changed from prograde to retrograde midway between these years at −1301 when it reached its maximum deviation of 27°, and would have remained retrograde, the same direction as modern precession, for 3600 years until 2299.
- For the period before 1301 BCE, Surya-siddhantic trepidation would be opposite in sign to equinoctial precession. For the period 1301 BCE to 2299 AD, equinoctial precession and Suryasiddhantic precession would have the same direction and sign, only differing in magnitude.