Simulating the earth magnetic field according to the 10th generation of IGRF coefficients for spacecraft attitude control applications

In recent decades utilizing satellites in low earth orbits have had increasing tendency. These satellites experience the earth magnetic field more than others. The earth magnetic is used to control the attitude of spacecraft by the interaction between the earth magnetic field and magnetic dipoles. First of all, in order to use this phenomenon the intensity and the direction of the earth magnetic field have to be obtained. There are various ways in order to simulate the earth magnetic field and among these ways the most accurate one is the harmonic coefficients and the earth magnetic field mathematical model. In this study, the earth magnetic field is modeled based on the 10^th generation of the IGRF coefficients and the results are verified with a valid reference. To utilize the earth magnetic field in the attitude control of a spacecraft, it is necessary to transform the magnetic filed into the spacecraft body frame. The transformation between orbital and body frame could be linear or nonlinear. In the next step, based on the comparison of the results of the spacecraft attitude dynamics with linear and nonlinear transformation, the validity of linear transformation is studied regarding spacecraft attitude angles.