Modeling and analysis of solar Doppler difference bias with arbitrary rotation axis

The solar rotation causes the solar Doppler difference bias, which leads to the decline of the velocity measurement accuracy. Modeling and compensation are an effective solution. The limited model with specific geometric direction, where the solar rotation axis is perpendicular to the plane through the Sun, the Earth and Mars, was established. However, in fact, the geometric relationship among the Sun, Mars and the spacecraft is not fully in line with the hypothesis of the model due to the spacecraft orbital angle and the solar rotation axis drift. Thus, this model is not consistent with the fact. In order to solve this problem, a universal solar Doppler difference bias model, which provides the expression with arbitrary rotation axis, is established in this paper. In this method, for any point at the solar surface, four variables including the direction of the solar rotation linear velocity at this point, the distance from this point to the rotation axis, the vector from this point to Mars, and the vector from this point to the spacecraft are calculated. Based on these four variables, the solar Doppler difference bias corresponding to this point is obtained. The theoretical analysis and simulation results demonstrate that the solar Doppler difference bias model with the actual rotation axis is different from that with one of the specific rotation axes. Therefore, it is indispensable to build the proposed model for compensation. Besides, the direction of the solar rotation axis, the spacecraft-Mars-Sun angle and the spacecraft-to-Mars distance are important impact factors for the proposed model.