Since when do leap years exist?

Leap year was introduced to synchronise our calendar and orbital movement in Rome, under the command of Julius Caesar. The dictator was advised by the mathematician and astronomer Sosígenes of Alexandria. Caesar decided that in the Julian calendar, one in four years would have 366 days, one day extra. He also ensured that the months of the year followed the rhythm of the seasons.  

Since the Earth does not reach the same point of its orbit in exactly an entire number of days, 365, but with an extra quarter of a day. Specifically, 44 minutes and 56 seconds are added every four years, that is, almost eight days per millennium. 

The difference accumulates in each revolution of the Earth around the Sun, and became important several centuries after Julius Caesar devised his calendar. Hence, in 1582 A.D., Pope Gregory XIII, advised by astronomers Christopher Clavius and Luigi Lilio, to introduce a reform consisting of adjusting leap years so that years divisible by one hundred but not by four hundred ceased to have 366 days. In this way the gap that was being produced by interspersing excessive leap years was avoided, since three days were suppressed every four centuries.

Thus, the year 1600 was a leap year and so was 2000 (all two are divisible by four hundred), and 1700, 1800 and 1900, and 2100 will be natural years.

Leap Day also observes another important day

Since February 29 is a "rare" date, it is also home to Rare Disease Day, which began in 2008 to raise awareness of diseases that affect less than 1 in 2,000 people. But don't worry: if it's not a leap year, the celebration is held on the last day of February.

Over the years, some intelligent members of the world's workforce realised that they were working an additional leap day each year without additional pay. This has led to a legitimate campaign to turn February 29 into a holiday. Makes sense, doesn't it?

An important group of literary characters does not observe leap years, for example.  While leap day helps keep our orbital timeline on track as we've seen, some literary characters don't seem to need it. Writer J.R.R. Tolkien's hobbits have a calendar that includes a February of 30 days each year. What if the weather works slightly differently in Middle-earth?