This link gives an idea of the rites and festivals in which Epicurus may have participated. It's an Ancient Greek neo-pagan website, but they give a good description of each of the festivals. This is also my preferred source for a reconstructed Ancient Greek calendar for determining Epicurus's birthday. Enjoy.
Ancient Greek Festivals and Rites
I found this on summer solstice festivals:Quote
According to certain iterations of the Greek calendar—they varied widely by region and era—the summer solstice was the first day of the year. Several festivals were held around this time, including Kronia, which celebrated the agriculture god Cronus. The strict social code was temporarily turned on its head during Kronia, with slaves participating in the merriment as equals or even being served by their masters. The summer solstice also marked the one-month countdown to the opening of the Olympic games.
In the days leading up to the summer solstice, ancient Romans celebrated the Vestalia festival, which paid tribute to Vesta, the goddess of the hearth. Rituals included the sacrifice of an unborn calf remove from its mother’s womb. This was the only time of the year when married women were allowed to enter the sacred temple of the vestal virgins and make offerings to Vesta there.
Apollo, Helios, and the Solstices in the Athenian, Delphian, and Delian CalendarsApollo, Helios, and the Solstices in the Athenian, Delphian, and Delian Calendarswww.academia.edu
Looks like Eratosthenes did his experiment on the summer solstice:Eratosthenes of Cyrene (article) | Khan Academywww.khanacademy.org
AlsoAncient Greek CalendarsAncient Greek Calendarswww.academia.edu
Adding for future reference: