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At present, the further missions of China's planetary exploration projects to Venus, Jupiter has also begun, and their key technical researches have been carried out. However, these planets all have dense atmospheres and higher atmospheric pressures, which are significantly different from the atmospheric environments of Earth and Mars. In successful planetary explorations in the past, it has been found that the aerodynamic deceleration process in such complex planetary atmospheric environments requires multi-stage parachutes to complete and parachute opening and operation under transonic/supersonic conditions. It should be noted that the nominal diameter of the first stage guide parachute is significantly smaller than the main parachute and smaller than the forebody diameter. The fluid structure interaction mechanism and aerodynamic characteristics between two-stage parachutes of different sizes and the forebody are still unclear, till now, there are very few related research reports. In this study, based on conical ribbon parachutes and disk-band-gap parachutes suitable for dense atmospheric planetary exploration missions, the fluid structure interaction mechanism of flexible parachutes in different planetary atmospheric environments is numerically studied using the immersion boundary method, and the aerodynamic characteristics under different freestream Mach numbers, canopy types, atmospheric components, and parameter to diameter ratios are investigated in details. As a result, it was found that in the atmospheric environment of Titan, the conical ribbon canopy (its diameter ratio is 0.3) steadily descends at transonic speeds, and the projected area of the canopy gradually increases over time. The drag coefficient reaches its maximum at Mach 1.5, but its fluctuation monotonically increases with the increase of Mach number. In addition, at Mach number 0.95, the canopies exhibit extremely severe oscillation when the diameter ratios are 0 and 1.0. By comparison, in the atmospheric environment of Jupiter, when the freestream Mach number is transonic, the change in projected area of the conical ribbon canopy becomes smaller over time. The drag coefficient and its fluctuation will monotonically increase with the increase of Mach number, and the lateral force coefficient and its fluctuation reach their maximum at Mach 1.5. Finally, a comparison was made between the stable descent process of parachutes in the atmospheric environments of Titan, Venus, and Jupiter, and it was found that the conical ribbon canopy in the Jupiter atmospheric environment has the best performance, larger drag coefficient, and better stability.