# Impact of Groundtrack Pattern of a Single Pair Mission on the Gravity Recovery Quality
## 1 Introduction
An important benefit of having those solutions is that they can also be employed as de-aliasing products when time-variable gravity solutions of longer time intervals are targeted [22]. Besides the two aforementioned rules, the spatio-temporal groundtrack pattern distribution of a satellite mission scenario can significantly affect the quality of the gravity recovery. Therefore, studying the gap evolution of the satellite mission groundtrack is of a great interest as well. Some studies like [8; 12; 13; 14] investigate the impact of sampling evolution on the gravity recovery quality. For example, [8; 14] look into different categories of orbits where drifting, slow skipping and fast skipping orbits, and their impacts on the quality of gravity solutions for single-pair satellite missions are discussed. Moreover, the work by [12] studies the refinement of Colombo-Nyquist and modified Colombo-Nyquist rules for different latitudes rather than at the equator, where the former studies have focused. The paper by [13], on the other hand, looks into the groundtrack pattern evolution of double pair missions where the influence of relative difference of the right ascension of ascending nodes between the two pairs (\(\Delta\Omega\)) is investigated. In fact, the paper discusses three reasons for the quality variations of the gravity solutions: (i) the sampling pattern of each satellite pair of a double pair mission with different repeat periods evolves differently in the time domain. (Hence, one should expect that within a specific time-interval gravity solution, e.g., 10-day solution, the groundtrack pattern also changes). (ii) the time-variation of \(\Delta\Omega\) can be responsible for the pattern change which, in turn, influences the quality of the gravity recovery. (That is because the two orbits with different inclination angles have different drifting rates of \(\Delta\Omega\)), and (iii) the gravity signals on the Earth are themselves time-variable and cause quality variations of the solutions within the time. Besides studying the aforementioned concepts which were briefly discussed, several research works examine the sub-cycle concept. For example, the works by [8; 14; 15] discuss the meaning of sub-cycle in terms of homogeneity of gap evolution for single pair mission scenarios. The works investigate the impact of the groundtrack pattern and sub-cycle concept on the global gravity recovery up to a fixed spherical harmonic coefficient degree where a big difference between the quality of gravity solutions of drifting and skipping orbits are observed. However, the study by [8] shows that the sub-cycle has no significant meaning in terms of global recovery for a fixed spherical harmonic degree to be solved. Obviously, it makes more sense if the impact of groundtrack pattern and its time evolution, as well as the sub-cycle concept, are investigated for maximum spherical harmonic degrees by Colombo-Nyquist rule (CNR) and modified Colombo-Nyquist rule (MCNR). In this way, for Low Earth Orbit (LEO) missions, adding a day to the time span of the recovery means adding approximately 8 and 16 degrees and orders to the maximum spherical harmonic coefficient to be solved, respectively, for CNR and MCNR, but as long as the number of nodal days is still smaller than or equal to the full repeat period. Moreover, it might be of interest to observe the impact of even and odd orbit parities (\(\beta-\alpha=\textit{even or odd}\)) on gravity solutions which are shorter than the full repeat cycle of the mission orbit scenario. The impact of groundtrack pattern on the regional gravity field (i.e., gravity retrieval for a specific region out of the global recovery) where the pattern is denser or when the sub-cycle happens is also worthy of further study. This paper, therefore, addresses the aforementioned research issues. We try to provide a few examples for different scenarios, and discuss potential future work in this research field.