Geocenter sensitivity from satellite tracking

Abstract. In this study, we revisit Kaula’s orbit perturbation theory to establish how satellite orbital geometry controls the sensitivity to degree-1 gravitational signals associated with geocenter motion along the z-axis and the (x, y )-plane, respectively. We explicitly derive the Kaula-based expressions for the degree-1 potential terms and provide complete tables of the corresponding inclination and eccentricity functions for all relevant degree-1 terms.

As a case study, we apply this framework to the upcoming ESA Genesis mission, which will be the first in-orbit geodetic observatory carrying all four geodetic techniques (GNSS, SLR, DORIS and VLBI) onboard.

We examine the dependence of the spacecraft orbital parameters through contributions at the spacecraft location of the degree-1 gravitational potential (V₁₀ and V₁₁). Our analysis shows that the V₁₀ term associated with the geocenter’s z-component scales with sin i, implying that polar orbits maximize sensitivity to vertical geocenter variations, whereas equatorial orbits remain largely insensitive to them. Conversely, the two-term structure of the V₁₁ expression enhances the detectability of the geocenter’s x- and y-components for equatorial or near-equatorial orbits, while retaining reduced but non-negligible sensitivity in polar configurations. For the Genesis orbital characteristics, we also assess the orbit inclinations providing the best trade-off to obtain the three components of the geocenter motion.

This work demonstrates how Kaula’s theory can guide the design and orbital configuration of future geodetic missions by identifying orbital parameters that optimize sensitivity to degree-1 signals. Such optimization can enhance the sensitivity to degree-1 signals and thereby contribute to improved geocenter motion recovery and strengthen the link between satellite-based gravimetry and terrestrial reference frame realization.