Samvatsara
Samvatsara (संवत्सर) is a Sanskrit term for a "year" in Vedic literature such as the Rigveda and other ancient texts. In the medieval era literature, a samvatsara refers to the "Jovian year", that is a year based on the relative position of the planet Jupiter, while the solar year is called varsha. A jovian year is not equal to a solar year based on the relative position of Earth and Sun.
A samvatsara is defined in Indian calendars as the time Brihaspati (Jupiter) takes to transit from one sign of the Hindu zodiac (i.e. rashi) to the next relative to its mean motion. The ancient text Surya Siddhanta calculates a samvatsara to be about 361 days, marginally short of a solar year. Hence, one complete orbit of Jupiter through all the twelve signs of the zodiac will approximately equal twelve solar years. Five such orbits of Jupiter (i.e. 12 times 5 = 60 samvatsara) are referred to as a samvatsara chakra. Each samvatsara within this cycle has been given a name. Once all 60 samvatsara are over, the cycle starts over again.
This cycle of 60 samvatsara is based on the relative positions of Jupiter and Saturn in the sky. The orbital periods of Jupiter and Saturn are approximately 12 and 30 solar years respectively. The least common multiple of these two orbital periods is ~60 solar years. Every sixty years, both planets will be positioned at nearly the same sidereal coordinates where they started off sixty years before, thus forming a sixty year cycle.