The forgotten second dimension of GRACE-like systems

Intersatellite ranging systems as implemented in the GRACE and GRACE-FO mission are considered one-dimensional observation systems. Range or range-rate are observed in the direction of the line-of-sight and connected in the modelling process to the relative position and velocity projected on the line-of-sight, respectively. However, the observed range is also proportional to the relative velocity vector projected on the change of the line-of-sight vector which is by definition perpendicular to the line-of-sight vector. This vector is nearly in radial direction of a GRACE-like system thus implying that the range observation also contains information about the radial direction of the gravity field. This contribution will show the mathematical derivations and investigates the feasibility of the using the additional direction in the gravity field recovery process.