Antarctica is renowned for its breathtaking natural beauty, rugged terrain, and harsh climatic conditions. Türkiye has made significant contributions to the scientific research conducted on the continent. In this paper, the low Earth orbit-based small-size constellation satellite system design is proposed for communication between Türkiye and Antarctica. The communication strategy is examined by making assumptions regarding the transmission of data from an unmanned aerial vehicle stationed within a designated region in Antarctica, with subsequent transmitting of this data to a ground station in Türkiye via a satellite. To the best of our knowledge, it is the first study for the communication between Türkiye and Antarctica using the low Earth orbit-based small-size constellation satellite system design. The investigations are devoted to the considerations involved in the design of the communication window, as well as optimization and analysis studies by making assumptions.