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The Long Secondary Period (LSP), a phenomenon manifesting as a fluctuation in the brightness of aging stars, remains an unsolved enigma. It is observed in about one third of the cool evolved stars, in particular those characterized by masses a few times that of our Sun. These stars, exhibiting significant inflation and lower temperatures, disperse material from their atmospheres into the surrounding space. Oscillations in the luminosity are a common feature in these stars, and when the LSP is present, it represents the longest of these oscillations. Over the past two decades, various hypotheses have been formulated to explain this phenomenon, with the primary contenders being pulsations — movements of the stellar material inducing fluctuations in stellar size, a phenomenon explaining other luminosity variations — and binary interactions. The latter suggests the existence of a much smaller star or a very large planet orbiting the main star at a close distance. Although observations of binary systems are frequent among stars with similar masses, the hypothetical companion in this scenario is not directly detected. The proposed mechanism involves the smaller companion capturing a portion of the material expelled by the larger central star, forming a thick dust cloud. Due to the circular motion of the companion, the cloud assumes an elongated shape, resembling a comet-like configuration. When the secondary object, accompanied by its surrounding dust cloud, passes in front of the primary star, it obstructs a portion of its light, leading to observable periodic reductions in brightness. To test this cosmic dance theory, we employ powerful computer simulations that reproduce the interaction between the stellar outflows and its unseen companion. These simulations replicate a spiral pattern in the stellar wind, marked by a denser region following the companion. Incorporating details about the dust produced within the system and around the companion, we then use sophisticated computations to create images at different wavelengths, similarly to observing in different colours. These images are finally compared to real observations, in order to assess the validity of the original hypothesis. Our study focuses on RT Pav, a star that experiences a 757-day LSP. We gather data from the existing literature and also with telescopes, including the Very Large Telescope Interferometer (VLTI). This instrument is particularly powerful since it allows us to distinguish, to some extent, the structures forming in proximity of the stars. From data relative to the luminosity of the system, we estimate the star's surface temperature and the rate at which it is losing mass. Comparing our simulations with the VLTI observations, we could partially replicate the telescope data. However, our models fall short in simultaneously explaining all the considered observations. Despite a few incongruities, the idea of a stellar duo remains a valid one. In order to improve our understanding, additional values for the parameters defining our models should be tested. Moreover, diving into more details regarding the cosmic dust is required if we want to get closer to solving this celestial riddle.