Spacecraft attitude estimation during orbit descent is an important part in the field of human spaceflight. With the increase in station measurement accuracy and mission requirements recently, it has been shown that attitude affects the aerodynamic forces on the spacecraft during trajectory descent, which in turn affects the orbit. Therefore, the development of high-precision attitude-orbit coupling prediction is crucial for the real-time measurement and control of spacecraft. In this paper, the forecast of aerodynamic coupling along the ballistic trajectory during the trajectory descent of the Tiangong-1 spacecraft is taken as the background, and the influence of the integral error of the linear multistep method on the forecast accuracy of the spacecraft are studied. The multistep methods include the Adams-Bashforth, Adams-Moulton, and prediction correction method, etc. The results provide references for the attitude-orbit coupling prediction and the fallout prediction missions during the trajectory descent of the large spacecraft.