## 2 Orbit Selection Approach  
The satellites' altitude is a key parameter for spatial and temporal sampling. A drag compensation system can also maintain the altitude and offers the opportunity to select it such that the spatial and temporal sampling is optimal for the gravity field retrieval. This is an important difference with respect to the GRACE and GRACE-FO missions, where the orbits were allowed to drift naturally and, consequently, the satellites slowly decayed over time due to atmospheric drag. Here, we describe an approach for the selection of orbits of two satellite pairs flying in a Bender constellation [24], where one pair is placed in a polar orbit and the other one in an inclined orbit with an approximate inclination of 70\({}^{\circ}\). This approach was used to define constellations that were investigated in the recent mission simulation studies [31; 32] funded by ESA and also analyzed together with JPL in [37]. To serve the needs of the broad range of users of time-variable gravity field models [29], our objective is to optimize the constellation's spatial sampling for the recovery of mass change signals in a range of temporal scales. The orbit selection is therefore closely related to the characteristics of the mass change signals in space and time, which are realistically represented in the Earth system model (ESM) [38; 39]. These characteristics are illustrated in Figure 1, which shows the amplitude spectral density (ASD) of the combined nontidal mass change signals in the atmosphere, oceans, land hydrology, land cryosphere and solid Earth. The ASD was calculated for each spherical harmonic coefficient of the time-variable gravitational potential using [PERSON]'s method [40] and then averaged per degree. Figure 1 shows large day-to-day mass change signals, which originate to a large extent from the atmosphere and oceans [39]. Since the daily spatial sampling is a consequence of the period of the orbiting satellite and of the fact that Earth makes one full rotation per day, densifying the daily spatial sampling can only be achieved with more satellite pairs. In the gravity field model retrieval, one may use the Wiese approach [41] or the daily Kalman filter method [42] for the (co)estimation of daily gravity field models. Mass change signals with a period of a few days are significantly smaller than the day-to-day ones. In a sense, it takes a few days before the accumulated mass change signal is large enough to become appreciable and, thus, worthwhile to account for in a gravity field model. In contrast to the one-day period, it is, however, possible to optimize a constellation for the retrieval of gravity field models spanning a few days. Simulations by [32] demonstrated that the Bender constellation in combination with a certain accuracy level of the instruments allows the estimation of 3-day gravity field models, even though the spatial sampling is sparse due to the limited number of orbital revolutions within that period. For periods longer than three days, the amplitude of the mass change signals and the number of orbital revolutions increase further. Hence, it is expected that it will be much less challenging to find a constellation that offers a sufficiently dense spatial sampling for the retrieval of, e.g., monthly gravity field models, and capturing the time-variable signal within the month at shorter intervals will also improve monthly models. Since we aim for optimizing the spatial sampling at multiple temporal resolutions (daily to weekly, monthly to seasonal and long-term trends), we need a tool to assess the spatial sampling as a function of time and altitude, where the latter is the parameter that we select in the optimization process. In the following, we introduce two graphs for that purpose: the first graph will guide the selection of the altitudes of the individual satellite pairs, and the second is used for fine-tuning of the selected altitudes, such that the interleaving of the ground tracks of the two satellite pairs remains fixed for one of the temporal resolutions.