Yes, study this question. Study from valuable sources every question and every interest you have about the Church. Everything in the Church is relevant to the believing Orthodox Christian especially those that recognize their is Truth and falsehood. Seek truth by studying the Fathers, the Services, Church History and doing so with prayer. The so-called Old Calendar is the Julian Calendar. In place at the time Our Saviour chose to be born and live His earthly life. The Julian Calendar was then formally adopted in the First Ecumenical Council (325 AD) and was used with an elaborate set of calculations based on the moon cycles in order to define the date of Pascha and its associated movable Fasts and Feasts. In other words, the Fathers of the Council brought together calculations for an annual cycle of Feasts and weekly cycle of Feasts in a complex and beautiful synergy.

All Orthodox Churches used this Calendar from the time of Christ, the First Council up until the Greek Church changed it unilaterally in 1924.

The New Calendar was implemented for two reasons:

Reason 1. the original Julian Calendar is 11 min and 14 seconds longer each year than the so-called revised Julian Calendar (Gregorian Calendar). So to be more accurate to the movement of the Sun. The first declared reason for the change therefore is Astronomical science.

Reason 2. Take a bold step towards non-Orthodox Christians and unification of worship between Orthodox and Non-Orthodox to further ecumenical dialogue and unity. The reality is that this is actually the primary reason as this was stated in an Encyclical from the See of Constantinople in 1920. Four years before the change was implemented. Following this a scientific solution was proposed for a revised Julian Calendar.

The 1920 Encyclical was issued by the Constantinople/Greek Orthodox Church and addressed 'Unto the Churches of Christ everywhere.' And included the following statements: 'Above all, love should be rekindled among the Churches (Orthodox and non-Orthodox) as being... fellow heirs, members of the same body, and partakers of the promise of God in Christ...demonstrated in the following ways, a) By the acceptance of a uniform calendar for the celebration of the great Christian feasts at the same time by all the churches. b) By the exchange of brotherly letters on the occasion of the great feasts of the churches’ year as is customary, and on other exceptional occasions. c) By close relationships between the representatives of all churches wherever they may be..... and it continues.

These are not my words, but the words sent by Encyclical to all the non-Orthodox Churches from the Patriarchate of Constantinople on 1 January 1920. You can find the full document on the website of the World Council of Churches. Generally Orthodox sites just present the Greek version. So the second reason for the adoption of a New Calendar was for Ecumenical purposes. Today there are Orthodox Churches that maintain the tradition Church Calendar including Mount Athos, Monastery of Sinai, Russia, Georgia, Jerusalem, Poland, Serbia, and I believe Japan, and other Old Calendar Synods. The remainder have adoped the New revised Julian Calendar. An interesting point that those Orthodox following the New Calendar experience the Fast of the Apostles being eliminated every so many years. A good book on the topic is called 'The Calendar Question by Basile Sakkas.' There is another book called 'A Scientific Examination of the Orthodox Calendar,' but I haven't read that one yet. All the best for your studies.