Creating a C++ program to model the movements of a binary star around a black hole is indeed possible. The discussion emphasizes the importance of having the correct equations to simulate the behavior of celestial objects. While the original poster expresses a desire to undertake the programming themselves, they seek confirmation on feasibility. Other participants highlight that C++ and Fortran are widely utilized in scientific computing and modeling, suggesting that with the right mathematical framework, implementing such a simulation in C++ is achievable. The conversation underscores the significance of understanding the underlying physics and equations governing stellar movements for successful modeling.