Fig. 9

Variation in equivalent rotational speed (lower panel) and the corresponding atmospheric density gradient (upper panel). The abscissa is the date, and the ordinate is given in logarithmic coordinates. In the upper panel, the atmospheric density gradient (unit: \({{\rm kg\,m}}^{-4}\)) is the gradient of the atmospheric density at the altitude of Tiangong-1’s position. The atmospheric density model is MSIS 90, and the orbital and space environment parameters are all actual values. In the lower panel, the black point is the equivalent rotation speed \(H/I_z\) (unit: \(^\circ \,{{\rm s}}^{-1}\)), which is estimated from the observational data. The error bar marks the range of one standard error. The four curves present the numerically calculated evolutions of the equivalent rotational speed. Each curve has a short-term oscillation with an amplitude of no more than \(0.01^\circ /{{\rm s}}\). The blue represents the result for classic aerodynamic torque, and the remaining three lines consider the effect of ADGT, where the cyan and brown lines present the results when the angles \(\theta _{{\rm p}}\) between the normal of the solar panel and the z-axis take values of \(0^\circ\) (flat) and \(90^\circ\) (upright), respectively, and the red shows the results when the atmospheric force \({{\rm d}}{\varvec{f}}\) acting on the model element is increased threefold when the solar panels are upright. No significant changes in \(\theta _H\) or L are found in the results, which are comparable to the observational results