Page - 17 - in Contributions to GRACE Gravity Field Recovery - Improvements in Dynamic Orbit Integration, Stochastic Modelling of the Antenna Offset Correction, and Co-Estimation of Satellite Orientations

effect mass flux in the solid Earth. The pole tides are the disturbing potential generated due to this mass flux. Ocean Pole tides Similarly, polar motion indirectly induces mass fluxes in the ocean basins throughcentrifugal accelerations.These massredistributions thengenerate a disturbing potential, the ocean pole tides. A secondary effect of tidally-induced mass fluxes is loading, the displacement of mantle material due to additional weight above the affected area. Where the additional masses first increase the gravitational attraction of the area, the mass loss due to loading reduces the net excess of mass, mitigating the initial effect. Further, self-attraction of the additional and displaced masses contribute to the equilibrium state of the system. Due to the constant change in tides and tidally generated effects, such an equilibrium is never reached. 3.3 Non-Conservative Forces In addition to the various conservative forces due to the effects described above, some non-conservative forces act directly on the GRACE satellites. Solar radiation pressure When solar radiation interacts with satellite surfaces, mo- mentum is imparted on the satellite. This momentum depends on the area and orientation of the exposed satellite surfaces, as well as the absorption rate of the radiation and the reflectivity of the material. Earth albedo Similar to solar radiation pressure, radiation reflected by and emitted from Earth’s surface also imparts momentum on the satellite. Atmospheric drag At the altitude of GRACE, the remnant atmosphere slows the satellites through friction. The density of the remnant atmosphere is strongly influenced by solar activity. Atmospheric drag is the most important contributor to the orbital decay of the satellites (Frommknecht, 2008). 3.4 Representation of the Gravitational Potential Earth’s exterior gravitational potential can be described through a series expansion of spherical harmonics coefficients. These are the Stokes coefficients cnm and snm of degree n and order m. The potential is (see e.g. Hofmann-Wellenhof and Moritz, 2005) V(r,λ,θ)= GM R ∞ ∑ n=0 ( R r )n+1 n ∑ m=0 [cnmCnm(λ,θ)+snmSnm(λ,θ)] (3.4.1) 3.3 Non-Conservative Forces 17