# Combination Analysis of Future Polar-Type Gravity Mission and GRACE Follow-On
## 2 Numerical Simulation Scheme
### Orbit Configuration Selection for FPG  
In gravity field recovery, the orbit altitude and inclination play the key role [52] (pp. 41-43). Since the gravity signals attenuate rapidly with the increase of orbit altitude [47], the ideal gravimetric satellite should fly as low as possible in order to be sufficiently sensitive to the signals. However, the lower altitude of the satellite, the stronger atmospheric drag acting on it, which requires more fuels to maintain the mission operation and thus shortens its lifetime [37]. As regard to the orbit inclination, it could not be better to select the 90-degree inclination for a global coverage of the Earth. However,due to the launch limit, it is a challenge to put satellites in an exact polar orbit. For example, GRACE was flying in a near-polar orbit with 89-degree inclination, which left two 1-degree-radius circles in the south and north poles (namely the polar gaps). In general, a large polar gap will significantly impact the estimation of zonal SHC and eventually corrupt the estimated gravity field. The maximum recoverable degree and order (d/o) of SHC in the case of a given \(g\)-degree polar gap can be roughly calculated via dividing 180 (degree) by \(g\)[51] (p. 205).  
Considering the twin satellites of GFO separated by 220 km both in the near-circular orbit of 490-km altitude and 89-degree inclination [18], its initial orbit configuration in the following simulations will be kept fixed as listed in Table 1. In consideration of a nominal five-year mission lifetime, the FPG initial orbit altitude is currently supposed to be the same as GRACE (namely 500 km) [2]. With regard to the inclination choice of FPG, the relationship between the polar gap and the maximum recoverable SHC d/o, as mentioned above, should be taken into consideration. For typical monthly temporal gravity field model up to 60 d/o, it requires the polar gap smaller than 3 degrees, while for static gravity field models up to 180 d/o, the polar gap should be within 1 degree in theory. Once the polar gap size is determined, there exist two kinds of orbits, namely the prograde orbit (inclination smaller than 90 degrees) and the retrograde orbit (inclination larger than 90 degrees) [53] (p. 99). For example, the previously dedicated gravity missions CHAllenging Mini-satellite Payload (CHAMP) (87-degree inclination) [54] and GRACE (89-degree inclination) are in prograde orbits, while Gravity field and steady-state Ocean Circulation Explorer (GOCE) (96.5-degree inclination) [55] is in a retrograde orbit. In general, the retrograde-orbit satellites require more fuel than the prograde ones during launch in order to overcome the Earth's rotation speed, but it is not a technical problem to launch either prograde or retrograde satellites.  
In the following simulation study, we preliminarily select four sets of FPG configurations, which differ only in orbit inclinations. Their initial orbit elements are listed in Table 1 and denoted as FPG-87, FPG-89, FPG-91, and FPG-93 (corresponding to the inclinations of 87, 89, 91, and 93 degrees, respectively). Note that the initial Right Ascension of Ascending Nodes (RAAN) are selected as 0 degree for GFO, FPG-87, FPG-91, and FPG-93 while 180 degrees for FPG-89, which is designed to avoid the nearly full overlay of ground tracks of GFO and FPG-89 when combining the two [32]. The initial inter-satellite distances for all GFO and FPG configurations are fixed as 220 km.