## 4 Starlink as Case Study
### Stage 3: Parametric Estimation of Propellant Mass  
Based on Table 4, it is evident that estimating the dry mass of the satellite requires the prediction of the propellant mass. The total mass of the Starlink V1 satellite is 260 kg, and the dry mass (Mdry) can only be determined by subtracting the propellant mass from the total mass. Therefore, in this section, parametric estimation techniques are employed to predict the propellant mass for the V1 satellite, as discussed before in the Section 2.2.2. SpaceX uses a Hall-effect electric propulsion subsystem for their satellites [63]. The specific impulse is around 1500 s for the engine and is used to move the Starlink to the operational orbit and then for station keeping as well as eventually to deorbit them after their operational lifetime [64]. Based on the specific impulse value, the BHT600 Hall-effect thruster is taken as a reference. To find the propellant mass and dry mass, the rocket equation is used [25]:  
\[\mathrm{m}_{\mathrm{f}}=\mathrm{m}_{\mathrm{o}}\mathrm{e}^{-(\frac{\mathrm{ \Delta x}}{\mathrm{v}_{0}})}, \tag{1}\]  
where \(\mathrm{m}_{\mathrm{f}}\) (final mass) can be expressed with initial mass \(\mathrm{m}_{\mathrm{o}}\), with the propellant and the mass of propellant \(\mathrm{m}_{\mathrm{p}}\). \[\mathrm{m}_{\mathrm{f}} =\mathrm{m}_{\mathrm{o}}-\mathrm{m}_{\mathrm{p}} \tag{2}\]  
From Table 1, \(\mathrm{m}_{\mathrm{f}}\) value (final mass) of the Starlink version 1 is taken as 260 kg. \begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Subsystem** & **Average Dry Mass Distribution (\%)** & **ESA LCI Database** & **Final Mass Budget Distribution** & **Comment** & **Reference** \\ \hline Payload & 31\%Mdry & Payload type & 31\%Mdry & & [24] \\ \hline Structure and mechanisms & 27\%Mdry & Structure & 27\%Mdry & & [24] \\ \hline Thermal control & 2\%Mdry & Thermal control & 22\%Mdry & & [24] \\ \hline Power (including harness) & 21\%Mdry & Power & 21\%Mdry & 0.02 \(\times\) Mdry & & \\  & & Harness & 0.02 \(\times\) Mdry & average from (0.01-0.04 \(\times\) Mdry) & & \\ \hline TT\&C & 2\%Mdry & TT\&C & 2\%Mdry & & [24] \\ \hline On-board processing & 5\%Mdry & Data handling & 5\%Mdry & & & \\ \hline AOCS & 6\%Mdry & AOCS & 6\%Mdry & & [24] \\ \hline Propulsion & 3\%Mdry & Thruster & 3\%Mdry mass (-) 10\% of propellant calculation & Propellant value/pipeline mass are considered negligible 10\% of propellant & [24] \\ \hline Other (Balance+Launch) & 3\%Mdry & Other (structure) & 3\%Mdry & & [24] \\ \hline Propellant & Propellant calculation & & 4.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Estimating mass budget based on European Space Agency Life Cycle Inventory database. In order to find the propellant mass, the orbital data of Starlink are necessary. These data are acquired from SpaceX filings to the FCC. The insertion altitude of Starlink is from 300 km to 350 km based on the solar activity [63]. For the worst case scenario, 300 km is taken for calculating the DeltaV, with the operational altitude of 550 km. The operational orbit seems to be circular, and different inclinations are planned for the constellation according to the report submitted by SpaceX to FCC [63]. The calculation assumes a fuel-efficient coplanar Hohmann transfer between two circular orbits [24]. \[a_{\rm{tx}}=(r_{\rm{A}}+r_{\rm{B}})/2 \tag{3}\]  
Equating the values of \(r_{\rm{A}}\) = 300 km and \(r_{\rm{B}}\) = 550 km, we can obtain \(a_{\rm{tx}}\) value as \(a_{\rm{tx}}\) = 6796 km. \[V_{\rm{iA}}=(\mu/r_{\rm{A}})^{(1/2)} \tag{4}\]  
where inserting values of \(\mu\) = 631.348 (gravitational constant \(\times\) Earth's mass) and \(rA\) = 300 km yields the following:  
\[V_{\rm{iA}}=7.72\ \rm{km/s} \tag{5}\]  
\[V_{\rm{fB}}=(\mu/r_{\rm{B}})^{(1/2)} \tag{6}\]  
where inserting values of \(\mu\) = 631.348 (gravitational constant \(\times\) Earth's mass) and \(r_{\rm{B}}\) = 300 km, \(V_{\rm{fB}}\) = 7.58 km/s.