## 2 Methodology
### Simulation Model
#### 2.3.1. Astrodynamics Module  
The astrodynamics module initializes basic orbit parameters first and calculates satellite trajectories over time. The trajectory of an Earth-orbiting satellite is described using six parameters or orbital elements: _a, e, i_, \(\Omega\), \(\omega\), and \(\
u\)[1]. The first two elements define the geometry of an orbit, semi-major axis (_a_) for size and eccentricity (_e_) for shape. The next two elements define the three-dimensional orientation of an orbit. Inclination (_i_) defines the tilting angle of a satellite's orbit plane with respect to Earth's equator, and the longitude of the ascending node (\(\Omega\)) defines the direction of tilting (location of ascending nodes) relative to the vernal equinox position. For an Earth-centered orbit, the longitude of the ascending node is also referred to as the right ascension of the ascending node (RAAN). From the ascending node, the argument of perigee (\(\omega\)) is measured, from which the satellite's position is determined with the true anomaly (\(\
u\)).  
One of the popular ways to design circular orbit constellations is the Walker Delta constellation (termed Walker constellation hereafter), which provides the most symmetry by having similar orbits amongst satellites. This maximal symmetry not only greatly reduces design space, but also provides advantages in constellation management because any satellite in a constellation undergoes similar effects from orbit decaying or other perturbations. The Walker constellation uses a notation of _i:T/P/F_ where a total of \(T\) satellites are evenly distributed in \(P\) orbit planes inclined at \(i\) degrees and separated from one another by \(360/T\times F\) degrees. Figure 3 shows a Globalstar constellation which uses a 48/8/1 Walker pattern. The phasing parameter \(F\) can take integer values from 0 to \(P-1\)[46].  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Module** & **Input Variables** & **Output Variables** \\ \hline Astrodynamics & _nk, delta\_alt, n\_planes, n\_sats, regard,_ & _rqt\_alt, rom\_revisit, gom\_revisit_ \\ Optics & _regard, delta\_alt, fov, gsd, rgt\_alt_ & _optics\_mass, aperture_ \\ Maneuvers & _prop, delta\_alt, life, n\_recons, rgt\_alt, area_ & _delta\_v, reconfig\_time_ \\ Propulsion & _prop, sat\_dry\_mass, delta\_v_ & _prop\_dry\_mass, propellant\_mass_ \\ Constellation & _n\_planes, n\_sats, optics\_mass, aperture,_ & _sat\_dry\_mass, const\_mass, area_ \\  & _prop\_dry\_mass, propellant\_mass_ & _sat\_dry\_mass, const\_mass, area_ \\ \hline \hline \end{tabular}
\end{table}
Table 7: Inputs and output variables of simulation modules.  
Figure 2: Data flow in ReCon simulation.  
A three-dimensional Earth-centered view is shown in Figure 4a where ROM orbits and COM orbits are represented by thin red lines and thick lines, respectively. Figure 4b depicts ground tracks instead, clearly showing deviation between ROM groundtracks and GOM groundtracks, due to altitude difference. Because there is no specific target of interest in GOM, the coverage statistics were gathered over the entire latitude band in the northern hemisphere which can be reached by the satellites, between the equator and 60\({}^{\circ}\) N, which is marked by light blue grids in the figure. A target of interest during ROM has the latitude of 55\({}^{\circ}\) N as mentioned earlier.  
The RGT orbits considered here repeats after two days at most, so the STK simulations were run for two days in simulation time. The trajectory calculation considers up to J4 effects in this study.