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Mission Deorbiting Analysis
Mission Deorbiting Analysis
The United Nations Committee on the Peaceful Uses of Outer Space (UNCOPUOS) mandates that spacecraft in low Earth orbit (LEO) must deorbit within 25 years following mission completion. Additionally, the U.S. Federal Communications Commission (FCC) has established a more stringent requirement, stipulating deorbit within 5 years after the end of operations. These requirements are critical considerations in the design and planning of CubeSat missions.
For the LISSA mission, the planned operational life is 18 months, followed by passive orbital decay. To evaluate LISSA’s deorbit timeline, the Debris Risk Assessment and Mitigation Analysis (DRAMA) tool [1] and MATLAB was used. The analysis assumed an initial orbital altitude of 510 km, corresponding to a semi-major axis of 6881 km. The simulation was initialized with a launch date of January 1, 2027, and assumed a wet mass of 7.5 kg. Atmospheric drag was calculated based on the cross-sectional area exposed in the ram direction, which directly affects orbital decay.
The figure presents three orbital decay scenarios. The solid black line shows LISSA’s deorbit trajectory when modeled with the smallest wetted area of 0.0226 m². In this case, re-entry occurs around the year 2044, approximately 18 years after launch, which ensures full compliance with the 25-year rule, even in the worst-case orientation.
The black dashed line represents a scenario in which LISSA enters a tumbling mode after completing an 18-month mission. This increases the average exposed area to drag, resulting in re-entry after 5.8 years. While this improves deorbit time, it slightly exceeds the 5-year FCC limit.
In the final scenario, represented by the black dotted line, the mission duration is extended to 3 years, and LISSA is placed into tumbling mode after mission end. Under these conditions, the satellite deorbits within 4.4 years, thereby fully satisfying the 5-year FCC requirement.
Vertical lines on the plot denote compliance deadlines. The blue dash-dot line indicates the 5-year deadline following the 18-month mission. The magenta dash-dot line shows the 5-year deadline for a 3-year mission. The red dash-dot line marks the 25-year maximum allowable orbital lifetime.
A 5% lifetime margin was included in the analysis to account for uncertainties in atmospheric density models and simulation assumptions. Overall, this analysis confirms that LISSA will meet the 25-year deorbit requirement, and it can comply with the 5-year rule if post-mission tumbling and mission extension is implemented.
Figure 1- deorbit lifetime analysis
Propellant Mass Onboard
Propellant Mass Onboard
After setting the system operating pressure to 2.67 atm, the thruster module design was finalized and the available propellant storage volume was defined. The tank system consists of 10 individual cartridges, each with a volume of 10 cm³ (10 cc), connected via a block manifold to form an integrated storage assembly. This results in a total tank volume of 100 cm³.
Assuming the propellant behaves as an ideal gas, and considering the tank will be filled at room temperature, the total mass of CO₂ onboard can be calculated using the ideal gas law. This value represents the initial propellant mass available for all thrust events and forms the foundation for subsequent analysis of impulse capacity and burn duration
Nozzle Geometry Optimization
Nozzle Geometry Optimization
To evaluate the influence of nozzle geometry on thruster performance and identify the optimal exit diameter, a MATLAB-based simulation was developed. The model simulates a time-varying cold gas thruster using CO₂ as the working fluid and applies standard isentropic flow relations for compressible gas dynamics [2] .
In the simulation, the specific heat ratio was set to 1.28, and the gas constant was taken as 188.92 J/kg·K, corresponding to the properties of CO₂. The tank conditions were defined with an initial pressure of 2.67 atm, a temperature of 21 °C, and a total volume of 100 cm³. The nozzle was modeled with a fixed throat diameter of 0.5 mm, and the area ratio was varied from 1, representing a non-divergent pipe, up to 10⁶, representing a highly expanded divergent nozzle.
For each configuration, the simulation computed key performance parameters including the exit Mach number, exit velocity, mass flow rate, thrust, specific impulse, and total ΔV over time. The results show a consistent increase in exit velocity with increasing area ratio. The maximum exit velocity was achieved at the highest tested area ratio, confirming that the flow benefits from continuous expansion through the divergent section. The trend supports the design of a nozzle with a large, smoothly expanding divergent section to capitalize on the performance improvements associated with high area ratios.
Figure 2 shows the relationship between exit velocity and area ratio, Figure 3 presents the peak thrust as a function of area ratio. while figure 4 illustrates the peak specific impulse s a function of area ratio. Collectively, these results reinforce the rationale for the chosen nozzle design and its performance benefits in the context of CubeSat propulsion.
Figure 2- Exit velocity vs area ratios
Figure 3-Thrust vs area ratios
Figure 4-specific impulse vs area ratios
Thruster Performance
Thruster Performance
Thrust
Thrust
The generated thrust is a function of the mass flow rate, exit velocity, and the pressure differential across the nozzle. These parameters are influenced by the nozzle geometry and the thermodynamic state of the propellant. In this design, the system does not include a pressure regulator, meaning that tank pressure and hence thrust decrease over time as the propellant is depleted.
To improve controllability and ensure consistent performance for maneuvers, a constant 10 mN thrust level was enforced using PWM (Pulse Width Modulation) control. This approach scales the valve open time proportionally to reduce the average thrust from its peak. The applied PWM duty cycle ensures the thruster delivers a near-constant thrust, mitigating the variability caused by tank pressure decay.
Change in Velocity (ΔV)
Change in Velocity (ΔV)
The satellite has a total wet mass of 7.5 kg. The total change in velocity (ΔV) generated by the propulsion system is determined using the Tsiolkovsky rocket equation and also verified through time-based numerical integration. A full-burn simulation yields a maximum ΔV of 4.2 cm/s.
Figure 5 shows the ΔV accumulated over time under the 10 mN constant thrust scenario.
Figure 5- Thrust vs Delta-V
References
References
[1] European Space Agency, "DRAMA - Debris Risk Assessment and Mitigation Analysis," ESA Space Debris User Portal. [Online]. Available: https://sdup.esoc.esa.int/. [Accessed: 04-Nov-2024].
[2] National Aeronautics and Space Adminstration, ''Thrust Equation Summary", Nasa Glenn Research Center. Available: www1.grc.nasa.gov/beginners-guide-to-aeronautics/thrust-equations-summary/. [Accessed: 04-Nov-2024].
[3] National Aeronautics and Space Adminstration, ''Ideal rocket equation". Available: Ideal Rocket Equation | Glenn Research Center | NASA [Accessed: 12-Dec-2024].
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