Future Mission Design Options for Spatio-Temporal Geopotential Recovery

Sampling the Earth from single-satellite missions or single-orbit formations is necessarily limited by the mandatory balance between spatial and temporal resolution. A short repeat period leads to sparse ground-track spacing. Conversely, dense satellite coverage can only be attained at the cost of time resolution. For future gravity field missions, geoscience communities are pushing for ever higher resolution than GRACE, both in time and space. A logical consequence would be multi-satellite and/or multi-groundtrack configurations. We investigate the basic parameters that determine space-time resolution. Under the assumption of a repeat orbit two basic rules for sampling the Earth from space are provided. The familiar Nyquist rule of thumb links the number of revolutions in a repeat period to the maximum spherical harmonic degree. A second sampling rule, expressing the balance between spatial and temporal resolution, is coined the Heisenberg rule. Simulations demonstrate how future mission concepts might benefit from multi-satellite/multi-groundtrack configurations.