(EFOMM 2025) Problema perfeito misturando Gravitação com MHS

A system consists of two stars of equal mass that describe a flat, circular orbit of radius R. The motion occurs around the center of mass of the system and is due solely to the mutual gravitational attraction between the stars, which are always at diametrically opposite points. Simultaneously, a cosmonaut, subject only to the gravitational force of the stars, describes an oscillatory motion with amplitude d, much smaller than R, on the line perpendicular to the plane of the orbit that passes through the center of the circle. Since d is much smaller than R, consider that the distance between the cosmonaut and either of the stars is always approximately equal to R during the oscillation. The ratio between the period of oscillation of the cosmonaut and the period of rotation of the stellar system is: #ita #ime #efomm