Investigation of the Applicability of the Boer Formula for Estimating the Angular Velocity of Rotation of a Small Spacecraft by Measuring the Components of the Induction Vector of the Earth's Magnetic Field in Evaluating Micro-Accelerations and Forming Control Laws

Abstract

The paper presents studies on the correctness of the application of the simplified Boer formula for estimating the components of the angular velocity vector of the spacecraft using the example of the small ISOI spacecraft (SXC3-219). The simplification consists in neglecting the total derivative of the induction vector of the Earth's magnetic field in time compared to the local derivative. This is due to the fact that measurements are carried out quite often. Therefore, the magnetic induction vector in two adjacent dimensions can be considered unchanged. The aim of the work is to estimate the error in determining the angular velocity due to this simplification. The presented results show the admissibility of neglecting the full derivative, provided that the measurement frequency is sufficient. Reference metrological tests were carried out, in which a gyroscopic angular velocity vector meter was selected as the reference measuring instrument. The errors in the estimates of micro-accelerations and the control moment, which are a consequence of the error in determining the angular velocity, are calculated.