# Advances in Remote Sensing and Propulsion Systems for Earth Observation Nanosatellites
## 4 Propulsion Systems in Nanosatellites
### Propulsion Fundamentals in Nanosatellites  
The essential fundamental equations for understanding and comparing various propulsion systems' performance in nanosatellites are the specific impulse, total impulse, Tsiolkovsky Rocket Equation, Propellant Mass Requirement, and Power Considerations [49]. The specific impulse and total impulse are fundamental metrics used to assess a propulsion system's performance. The specific impulse (\(I_{sp}\)) measures how effectively a propulsion system converts propellant mass into thrust. It is determined by calculating the ratio of the thrust magnitude (\(F\)) to the product of the propellant mass flow rate (\(\dot{m}\)) and the Earth's gravitational constant (\(g_{0}0\)), as shown in Equation (1). \[I_{sp}=\frac{F}{\dot{m}g_{0}} \tag{1}\]  
For example, cold gas thrusters, such as those used in the MarCO mission, achieved a specific impulse of approximately 50-70 s using nitrogen as the propellant. The low specific impulse is compensated by the simplicity and reliability of these systems, making them ideal for short-duration nanosatellite maneuvers. The total impulse (\(I_{l}\)) is also described as the integral of thrust over the total thruster firing time, as represented in Equation (2). \[I_{t}=\int_{0}^{t}Fdt \tag{2}\]  
In the SNAP-1 mission, the total impulse was a critical factor in determining the satellite's ability to perform orbital maneuvers over its extended lifetime. Cold gas systems provided sufficient total impulse for periodic station-keeping operations. The Tsiolkovsky rocket equation is a fundamental principle governing space maneuvers, as shown in Equation (3). The equation relates the change in velocity \(\Delta V\) (delta-v) \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Evaluation Metric** & **Reference** \\ \hline Improvement of satellite image analysis using deep learning, achieving efficient and accurate cloud, shadow, and land cover classification. & Efficient image analysis, High accuracy in classification tasks. & [46] \\ \hline Development of the INSPIRE project, introducing inflatable antennas for interplanetary CubeSat missions to enable high-gain communication. & Advancement in nanosatellite communication, Feasibility of deep-space operations with low mass and compact storage. & [47,48] \\ \hline \hline \end{tabular}
\end{table} 
Table 7: _Cont._of a spacecraft to the initial total spacecraft mass, including propellant (\(m_{0}\)), the mass of propellant consumed in the maneuver (\(m_{p}\)), and the effective exhaust velocity (\(v_{e}\)) of the propulsion system. \[\Delta V=v_{e}ln\frac{m_{0}}{m_{0}-m_{p}} \tag{3}\]  
This equation is particularly important for electric propulsion systems like FEEP thrusters, which operate with high exhaust velocities. For instance, a nanosatellite with an initial mass of 10 kg using a FEEP system with a specific impulse of 1000 s can achieve a velocity change of approximately 200 m/s. This is sufficient for orbital station-keeping or small adjustments in LEO. Equation (4) shows the calculation for determining the required propellant mass (\(m_{p}\)) to achieve a desired change in velocity (\(\Delta\)V), considering specific impulse (\(l_{sp}\)) and effective exhaust velocity (\(v_{e}\)). \[m_{p}=m_{0}\bigg{(}1-e^{\frac{-\Delta V}{v_{sp}\delta_{0}}}\bigg{)} \tag{4}\]  
For example, in the Busek micro-resistojet system, specific impulses of up to 150 s allow nanosatellites to minimize propellant mass while achieving small orbital maneuvers. With an initial mass of 5 kg and a desired \(\Delta\)V of 50 m/s, the required propellant mass is approximately 150 g.  
In the realm of electric propulsion systems, power consumption emerges as a critical and intriguing factor. Equation (5) offers a comprehensive method to calculate the power input (\(P\)) to the thruster (\(W\)), considering thrust magnitude (\(F\)), specific impulse (\(l_{sp}\)), gravitational constant (\(g_{0}\)), and thruster efficiency (\(\eta\)).