Accurate thermospheric mass density is crucial for precision orbit determination, trajectory prediction, and collision warning in the increasingly congested Low Earth Orbit (LEO) region. Traditional high-precision instantaneous inversion methods rely on dedicated onboard accelerometers (e.g., CHAMP and GRACE satellites), which are costly, scarce, and unable to meet the expansive monitoring needs of modern mega-constellations. In recent years, orbit data inversion methods based on high-precision orbit determination data have been extensively studied. Among them, the interpolation–differentiation method, although capable of retrieving instantaneous atmospheric density, severely amplifies position errors and measurement noise, significantly limiting retrieval accuracy. To address this gap, this study proposes a novel atmospheric density retrieval scheme for accelerometer-free LEO satellites, introducing an orthogonal polynomial (Legendre and Chebyshev) sliding-window fitting approach. The proposed method is evaluated using high-precision simulated orbit data. Under instantaneous inversion conditions, the Legendre method yields an average relative error (MRE) of 16.55%, a normalized root mean square deviation (NRMSD) of 12.80%, and a correlation coefficient R of 0.9370. To further evaluate its potential in climatological modeling, this paper also proposes a local solar time (LST) bin-averaging method to assess atmospheric inversion accuracy. Under this LST averaging approach, the inversion performance achieves an MRE of 6.83% and a correlation coefficient R exceeding 0.98. This demonstrates the feasibility of the inversion method for analyzing diurnal effects on atmospheric field evolution.

In this paper, a trajectory optimization method without an initial value guess is proposed. The method employs the Lagrange multipliers from the nonlinear programming process to estimate the costate of the optimal control problem. It utilizes a homotopic process to address the minimum-fuel problem. The estimated costate serves as a useful initial guess for the indirect shooting method, mitigating the initial value sensitivity. The sequential quadratic programming process used in the shooting process avoids the non-optimal results of the direct method. The minimum-time and minimum-fuel low-thrust rendezvous problems on cislunar L1-vicinity, L2-vicinity, and L2-south near rectilinear halo orbits are solved in this paper. The numerical results demonstrate that using low-thrust propulsion can reduce fuel consumption by 42.36% to 84.62% compared with traditional two-impulse maneuvers in the circular restricted three-body rendezvous problem.