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Disagreement about the date for Easter goes back to the very earliest years of Christianity. Pope Anicetus and Polycarp are said to have disagreed about the correct date, as early as the middle of the second century, both finally agreeing that they could not convince each other to change. Irenaeus, bishop of Lyons in what is now France, mentioned this in a letter to Pope Victor, as a precedent to press Pope Victor to allow Eastern Christians to continue their tradition when they were in Rome.
Easter continued to be celebrated on different days in the east and in the west, but this was almost the least of the issues that divided Christianity. What today would seem to be a trifling issue, the insertion of the filioque clause into the Nicene Creed was to be the major issue that finally sealed the division of the eastern and western branches of Christianity, in the Great Schism of 1054. Pope Leo XI insisted on inserting the filioque clause, providing a subtle change in the definition of the Trinity, into the Nicene Creed in spite of a requirement that no change could be made to the Nicene Creed other than by a council of the bishops. Another trigger was that the western churches insisted on celibacy for the clergy, whereas the eastern churches regarded marriage by the clergy as acceptable.
While the disagreement about the date of Easter may be about genuine, firmly held views on proper theology, many of the other divisions that occurred in the Christian Church have been about power. Pope Leo was arguably more concerned to assert his authority over the entire Christian Church than whether priests could marry. The secular world talks of the division between Roman Catholic and Greek Orthodox as the 'Great Schism', but more often, when the Catholic Church talks of the 'Great Schism', it is the western schism of 1378-1418, in which various claimants vied for the power and wealth that came with the papacy. This western schism was called the 'Great Schism' in order to differentiate it from the several other papal schisms in the Catholic Church, with John W. OβMalley SJ saying in A History of the Popes, page 150 that the schism was certainly not the first papal schism, nor would it be the last.
The earliest Christian writings, from the epistles of St Paul and the apocryphal Gospel of Thomas demonstrate that the Christian Church has never been united. Differences over theology, such as the date of Easter or the providence of GThomas are arguably more noble than the disunity over power and access to the vast wealth of the Church.
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The Orthodox Church celebrates Pascha (Easter) on the first Sunday following the first full moon after Passover. This naturally means that we, unlike others, never celebrate it before the annual Jewish holiday of Passover.
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Following the Julian Calendar which currently places the vernal equinox on April 3 is how it differs from western calculations. You also have the 19 year metonic cycle used in the paschal tables devised millenia ago. I believe the Latins use a different mathematical cycle.
The thing about christian "unity" makes absolutely no sense in an Orthodox context as we dont include those outside our borders into the equation. Anyone can adopt the Nicene formula of the Alexandrian Paschalion if they so wish to but it has no bearing for the Orthodox. And even then eikonomia (leniency) can be employed for unusual circumstances that a specific local church may face.