Description and User Instructions for the Quaternion_to_Orbit_v3 Software

For a given inertial frame of reference, the software combines the spacecraft orbits with the spacecraft attitude quaternions, and rotates the body-fixed reference frame of a particular spacecraft to the inertial reference frame. The conversion assumes that the two spacecraft are aligned with respect to the mutual line of sight, with a parameterized time tag. The software is implemented in Python and is completely open source. It is very versatile, and may be applied under various circumstances and for other related purposes. Based on the solid linear algebra analysis, it has an extra option for compensating the linear pitch. This software has been designed for simulation of the calibration maneuvers performed by the two spacecraft comprising the GRAIL mission to the Moon, but has potential use for other applications. In simulations of formation flights, one needs to coordinate the spacecraft orbits represented in an appropriate inertial reference frame and the spacecraft attitudes. The latter are usually given as the time series of quaternions rotating the body-fixed reference frame of a particular spacecraft to the inertial reference frame. It is often desirable to simulate the same maneuver for different segments of the orbit. It is also useful to study various maneuvers that could be performed at the same orbit segment. These two lines of study are more timeand labor-efficient if the attitude and orbit data are generated independently, so that the part of the data that has not been changed can be recycled in the course of multiple simulations.