Refinement of the geomagnetic perturbation index by processing orbit measurements of a test satellite

We describe the refinement of the geomagnetic perturbation index $K_p$ by processing radio tracking data of the orbital motion of a simplest test satellite. A test satellite has the shape of a sphere and a constant ballistic coefficient. Approximation of its orbital data by solutions of quite accurate motion equations allows specifying the index $K_p$ in the atmospheric density model used to calculate the satellite aerodynamic drag. We demonstrate this approach by processing the data of the satellite Sphere launched from the ISS in August 2012. Orbit measurements were performed by the Russian means of passive radar system several times a day. For checking we also used orbital data generated by the two-line elements of the orbit of this satellite. Clarification of the approach is also confirmed by the results of statistical modeling.