# Gravity Field Recovery Using High-Precision, High-Low Inter-Satellite Links
## 2 Mission Concept  
### Observation Geometry  
In contrast to the past GRACE and the current GRACE Follow-On missions, which are mainly based on LEO satellites (several hundred km), the MOBILE minimum configuration consists of a constellation of two high and one low orbiting satellites. As done for GRACE and GRACE Follow-On, the main observable is the gravity-induced inter-satellite distance change, which is in case of MOBILE measured between medium orbiting satellites (MEO; several thousand km) and LEO satellites though. As a second gravity observation type, high-precision orbit positions based on Global Navigation Satellite System (GNSS) orbit determination are used. This idea of high-precision high-low tracking was first investigated by [PERSON] et al. 2017 [PERSON] et al. (2017) using the inter-satellite link technique as part of the payload on-board Galileo satellites of future generation in connection with LEO satellites, where the main error sources and the corresponding achievable performance were analyzed. Due to the fact that the MOBILE constellation presents a stand-alone concept without the need to place an additional payload on another space infrastructure, and the very large distance between the high- and the low orbiting satellites, which plays a crucial role in the framework of high-precision high-low tracking, dedicated MEO satellites were included in the concept. It should be emphasized that alternatively, a constellation of one MEO and two LEO satellites could be envisaged, which turns out to provide nearly the same performance as the proposed one, but might be more expensive due to the need to build and maintain at least two LEO satellites in orbit. Figure 1 shows a schematic overview of the MOBILE satellite formation. The orbit parameters, which are used in the simulation environment to build up different satellite constellations, are listed in Table 1. The MEO satellites orbit at an altitude of about 10,150 km in the same orbital plane, separated by an 180-degree mean anomaly as alternating targets of the LEO satellites, in order to maximize the visibility and thus observation time. The LEO satellite is orbiting in an altitude of about 360 km. Both LEO and MEO satellites are flying in polar orbits in order to maintain a long-term stable formation (no relative drifts of the orbit planes). Additionally, two LEO satellites with near-polar orbits flying in an altitude of about 470 km with an inter-satellite distance of 200 km are set up in order  
Figure 1: MOBILE mission constellation: high-precision inter-satellite links between LEO and MEOs (red), micro-wave links from GNSS satellites to MEOs and LEO (black). to perform comparability studies between the MOBILE constellation and a GRACE Follow-On-like mission. All orbits have certain repeat cycles, after which the satellites reach the same position on Earth again in order to maintain a stable ground track pattern and related stable gravity model quality. The choice of the orbit height of the MEO satellites underlies three major constraints: (1) A high altitude of several thousand kilometers is necessary in order to ensure long observation periods and preferably measurements of multi-directional distance variations, with a strong dominance of the radial component, resulting in a close to isotropic error behavior of the retrieved gravity field solution (see Section 4). (2) The distance between a MEO-LEO pair must not be too large, because the larger the distance, the more difficult it is to fulfill the 1-\(\upmu\)m accuracy requirement for the inter-satellite link established by a laser range interferometer (see Section 2.2). (3) The third constraint is driven by solar radiation belts encircling the Earth in which energetic charged particles are trapped inside the Earth's magnetic field [27], which are of different intensities dependent on the solar cycle, altitude, and inclination of the satellite orbit. As a result, altitude ranges of several thousand kilometers below the chosen orbit height drop out.