A method of and apparatus for determining and controlling the inertial attitude of a spinning artificial satellite without using a suite of inertial gyroscopes. The method and apparatus operate by tracking three astronomical objects near the Earth's ecliptic pole and the satellite's and/or star tracker's spin axis and processing the track information. The method and apparatus include steps and means for selecting preferably three astronomical objects using a histogram method and determining a square of a first radius (R12) of a track of a first astronomical object; determining a square of a second radius (R22) of a track of a second astronomical object; determining a square of a third radius (R32) of a track of a third astronomical object; determining the inertial attitude of the spin axis using the squares of the first, second, and third radii (R12, R22, and R32) to calculate pitch, yaw, and roll rate; determining a change in the pitch and yaw of the artificial satellite; and controlling on-board generated current flow to various orthogonally-disposed current-carrying loops to act against the Earth's magnetic field and to apply gyroscopic precession to the spinning satellite to correct and maintain its optimum inertial attitude.