A shadow function model based on perspective projection and atmospheric effect for satellites in eclipse

Abstract

Accurate Solar Radiation Pressure (SRP) modelling is critical for correctly describing the dynamics of satellites. A shadow function is a unitless quantity varying between 0 and 1 to scale the solar radiation flux at a satellite's location during eclipses. Errors in modelling shadow function lead to inaccuracy in SRP that degrades the orbit quality. Shadow function modelling requires solutions to a geometrical problem (Earth's oblateness) and a physical problem (atmospheric effects). This study presents a new shadow function model (PPM atm) which uses a perspective projection based approach to solve the geometrical problem rigorously and a linear function to describe the reduction of solar radiation flux due to atmospheric effects. GRACE (Gravity Recovery And Climate Experiment) satellites carry accelerometers that record variations of non-conservative forces, which reveal the variations of shadow function during eclipses. In this study, the PPM atm is validated using accelerometer observations of the GRACE-A satellite. Test results show that the PPM atm is closer to the variations in accelerometer observations than the widely used SECM (Spherical Earth Conical Model). Taking the accelerometer observations derived shadow function as the "truth", the relative error in PPM atm is-0.79 % while the SECM 11.07%. The influence of the PPM atm is also shown in orbit prediction for Galileo satellites. Compared with the SECM, the PPM atm can reduce the radial orbit error RMS by 5.6 cm over a 7-day prediction. The impacts of the errors in shadow function modelling on the orbit remain to be systematic and should be mitigated in long-term orbit prediction.

Comparison of shadow models and their impact on precise orbit determination of BeiDou satellites during eclipsing phases

“…This figure introduces the situation in which the solid Earth and atmosphere partially occult the Sun. Other cases have been described in detail by Li (Li et al 2019). The shadow factor γ 0 in Fig.…”

“…3. The shape of the conical curve includes an ellipse and hyperbola determined by the condition if the Sun's center is inside the Earth's image or not (Li et al 2019). The intersection of Earth's projection and Sun's projection can be computed by combining their projection equations, and the shadow factor is calculated by the ratio of the remaining bright area to the total bright area.…”

“…The SOLAARS-CF model significantly reduced the data and computation cost. Inspired by the perspective projection algorithm proposed by Oswald et al (1982), Li et al (2019) built PPM and PPMatm shadow models. The difference of PPM and PPMatm is that the latter adds modelling of atmospheric effects.…”

asteRisk - Integration and Analysis of Satellite Positional Data in R

“…This is the force generated by the impact of photons from solar radiation on the satellite. A double conical shadow model to account for the reduction in the apparent solar disk seen by a satellite due to the Earth and the Moon (both of which are assumed to be spherical) eclipses is implemented (Li et al 2019). • Atmospheric drag.…”

Applying a Situational Analysis Solver to Problems Involving Umbra/Sunlit Model

“…Another important practical problem is related to the temperature changes of satellite solar arrays. Li et al[ 13 ] developed a model and conducted a thermal analysis of the solar arrays of GEO and LEO satellites based on the conic umbra model.…”