# Drag and Attitude Control for the Next Generation Gravity Mission
## 2 NGGM Objectives, Measurement Technique, and Fundamental Observables
### The Satellite-To-Satellite Tracking Technique and the NGGM Scenario  
The NGGM will measure Earth's gravity field and its variation in time by means of the low-low satellite-to-satellite tracking (ll-SST) technique already successfully applied on GRACE and GFO. The ll-SST concept is illustrated in Figure 1. When two satellites fly along the same orbital path with a certain separation, the leading satellite (S1 in Figure 1) is subject to the gravitational force exerted by an overflow geographical area in advance of the trailing satellite (S2 in Figure 1) or, equivalently, at any given time the two satellites are subject to slightly different gravitational forces: \(\mathbf{F}_{\rm G1}\), \(\mathbf{F}_{\rm G2}\). The resulting effect is a continuous variation (\(\Delta d_{\rm G}\)) of the distance \(d\) between the centers of mass (CoM) of the two satellites. To increase the amplitude of Earth's gravity field components experienced by the satellite pair, the altitude of their orbit must be as low as possible, in a range where the non-gravitational force on the spacecraft produced by the atmospheric drag is non-negligible. As the satellites are separated along the orbital path, at any given time they fly across atmospheric regions of a different density with different velocity direction; moreover, the coupling of each spacecraft with the drag (function of the attitude and the surface temperature and scattering coefficient) is not identical. Consequently, the two satellites are subject to slightly different drag forces: \(\mathbf{F}_{\rm D1}\), \(\mathbf{F}_{\rm D2}\). The resulting effect is a continuous variation of the inter-satellite distance produced by the non-gravitational force (\(\Delta d_{\rm D}\)) that, together with \(\Delta d_{G}\), contributes to the overall CoM-to-CoM distance variation: \(\Delta d=\Delta d_{\rm G}+\Delta d_{\rm D}\). Ground coverage is another key factor in monitoring Earth's gravity field with a high spatial and temporal resolution. The optimal solution identified to achieve this objective is constituted by two pairs of satellites (S1, S2 and S3, S4) arranged to form a \"Bender constellation\" [21]: one pair flying in a near-polar circular orbit and one pair in a medium inclination circular orbit, as illustrated in Figure 2. By properly selecting the mean altitudes (and so the periods) and the inclinations of the two orbits, it is possible to obtain a dense, homogenous coverage of Earth's surface even in a short period (one week or less), during which sufficient measurements can be collected for obtaining accurate solutions of the gravity field with spatial resolutions \(<\)500 km. Figure 1: Principle of the low-low satellite-to-satellite tracking technique. The orbit optimization of the Bender constellation is a complex problem: concerning a survey on the algorithms developed and used for such a scope, we invite the reader to refer to the publication [23]. In a nutshell, all these approaches have the drawback that they optimize the orbits for a single temporal resolution, whereas multiple temporal resolutions are required to serve the needs of all users. For this reason, a new orbit selection approach that aims at optimizing the spatial sampling of the Bender constellation for multiple temporal resolutions [24] was developed. The approach was successfully used for generating the orbits in a number of ESA-funded simulation studies: recently, in ref. [23], a method to select a definite number of orbits to achieve the NGGM/MAGIC user requirements has been defined and used. The outcome coincides with a set of seven orbits, which has been further investigated and expanded in the current feasibility phase of the mission. Priority has been given to sub-cycles of 3, 5, and 7 days to achieve a high temporal resolution and its relevance for emergency and near-real-time (i.e., daily to sub-weekly) products. For selecting the candidate orbits, the \"ground track homogeneity\" has been defined and chosen as one of the two weighting parameters, together with the regular and common longitude shift.