Introduction A LGORITHMS are developed to solve the geometry required to point telescopes mounted on a low Earth-orbiting satellite at features in the aurora (at height of typically 100 km above Earth's surface). It is based on requirements for the proposed AURIO telescopes, which may be flown on a polar platform of the European Space Agency (ESA). The idea of pointing an instrument and tracking a target from space is not new and the geometry has been solved for several cases (see, e.g., Jerkovsky, Burdick et al., and Hablani). The traditional approach is to use vector notation, but at the implementation stage this method usually needs to be supported by a library of subroutines to implement the basic vector operations of addition, cross and scalar products, and rotations of vectors about the coordinate axes, which raises difficulties in a small embedded computer system. In this Note a computational method is presented to find the line-of-sight (LOS) vector in the satellite-body-attached coordinate frame. This method uses homogeneous transformation matrices (normally used in robot kinematics) to provide efficient algorithms that can readily be implemented on-board the satellite. A spherical Earth is assumed in this work as the basic model. However, the spheroidal model of Earth has been used to assess errors due to this assumption. The software coding of the pointing equations can easily be implemented in any high level programming language, and they have been tested in the occam language.