An analytical study of the theory of ignition and burning of a plastic material immersed in an atmosphere of a space cabin which may be subjected to gravity force changes is considered. The hazardous condition in a space cabin environment where the changes of gravity may effect the combustion process is evaluated. The model considered the analysis of the coupled gas and solid phases and is based on the premise that material heating leads to the formation of pyrolysis gases from the decomposed solid which then react with the ambient oxidizer to further the combustion process. Moreover, free convection plays a dominant role in transporting these hot gases to the virgin material. A time-dependent study of the coupled gas-solid model as required for ignition processes with emphasis on the surface energy interchange of the gas and solid phases has been made. Detailed distribution of species composition and temperature patterns provide a spatial and time map of the evolving gases from the material combustion.