## 4 Effect of Perturbations  
Perturbations usually have major impacts on satellites but they affect the functioning of the constellations as well. Recently, as per the Starlink constellation operations team, more than 40 satellites were declared to be lost due to the effect of solar winds/storms and other perturbations as presented in Refs. [8; 9]. This is a typical scenario for any satellite in LEO/MEO, but the impact on a constellation with small satellites would be much larger than expected and sometimes fatal to all the satellites aligning each other in a plane or in offset to other planes, respectively. Hence, an analysis was separately planned to address this issue and make sure that the impact is studied well and analyzed for building robust constellations using small satellites for the near future. Solar radiation pressure and the atmospheric drag are defined by the formulas as mentioned below:  
After an extensive study of the Ref. [10], the following equations for Solar Radiation Pressure (SRP) and Atmospheric Drag were obtained with due consideration of the proposed configuration of constellation specially with small satellites as given below:  
Solar Radiation Pressure (SRP):  
\[\overset{\rightarrow}{a}_{SRP}=\frac{S*AU^{2}*C_{R}*A_{SRP}}{m*R^{2}*c} \overset{\rightarrow}{Uv} \tag{14}\]  
where, \(\overset{\rightarrow}{a}_{SRP}\) is acceleration due to SRP. \(S\) = Mean flux at one astronomical unit (AU) given as 1400 W/m  
Figure 6: Constellation simulation (48 satellites)—3D and 2D. \(C_{R}=\) Coefficient of Reflectivity of the satellite  
\(A_{SRP}=\) SRP area  
\(m=\) mass of the satellite  
\(c=\) Speed of light  
\(AU=\) Astronomical Unit (generally defined to be distance from Earth to Sun) and numerically is calculated as 149,597,871 Kms. \(\overset{\rightarrow}{U}=\) Essential unit vector from Satellite to Sun  
\(v=\) Eclipse factor (0, if the satellite is in shadow; 1 if in sun light)  
Atmospheric Drag:  
\[\overset{\rightarrow}{D}=-0.5*C_{D}*A_{D}*\rho*v_{rel}^{2}*\overset{ \rightarrow}{U}_{D} \tag{15}\]  
where, \(C_{D}\) is the coefficient of drag, \(A_{D}\) is the drag area, \(\rho\) is the density at the spacecraft's current location, and \(v_{rel}\) is the magnitude of satellite velocity relative to the rotating atmosphere. \[ \begin{split}\overset{\rightarrow}{v}_{rel}&= \overset{\rightarrow}{v}-\overset{\rightarrow}{\omega}_{E}\times \overset{\rightarrow}{R}\\ V_{rel}&=\left|\overset{\rightarrow}{V}_{rel} \right|\end{split}  \tag{16}\]  
\(\overset{\rightarrow}{v}\) is the spacecraft's velocity vector in the reference frame;  
\(\overset{\rightarrow}{\omega}_{E}\) is the Earth's spin axis vector in the reference frame;  
\(\overset{\rightarrow}{R}\) is the spacecraft's position vector in the reference frame;  
\(\overset{\rightarrow}{U}_{D}\) is the unit vector in the \(V_{rel}\) direction. A distinct simulation was carried out to find the possible scenario and changes to the satellite position/altitude with the altering environment surrounding it. Under the influence of atmospheric drag and solar radiation pressure, the variation of height over 90 days is shown in Figure 7 below:  
Now, instead of height, apogee and perigee heights along with solar flux were calculated to observe the environmental variations and subjected to propagation for 90 days as shown in Figures 8 and 9. Figure 7: Changing heights of a satellite from Earth’s surface for 90 days due to SRP-Drag. Hence, it is of the utmost importance to consider the environmental effects on the trajectory that the satellites in a constellation take and perform their functions. The following questions have always been imperative to small satellite constellation research:  
* How does the harsh space environment with growing space debris impact operating small satellite constellations? * How can a certain pattern for a constellation which is effective for a long period for disaster management application be operated?