Propulsion

Theory

Propulsion methods rely on the expulsion of mass away from the satellite. The mass is expelled through a nozzle in order to direct it and this will cause an acceleration in the opposite direction, as per the conservation of momentum. Increasing the velocity at which the mass is expelled also increases the acceleration (or thrust), which is why propulsion motors often apply energy to the propellant (the mass that will be expelled).

Chemical propulsion methods make use of a chemical reaction to increase the propellant energy while electric propulsion applies electrical energy to the propellant in some way. A resistojet heats up the propellant before releasing it out the nozzle, and ion drives make use of electrical energy to accelerate ionized gas out of the nozzle.

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Regardless of propulsion implementation, the same theory applies.

The propellant exhaust velocity, 𝑣_𝑒, is related to the thrust generated by the motor through the equation

𝑣𝑒 =

𝐹𝑡ℎ𝑟𝑢𝑠𝑡

𝑚̇

10-1

Where 𝑚̇ is the propellant mass flow rate. The efficiency of the motor in terms of the amount of propellant that it uses is often given in terms of the specific impulse, 𝐼𝑠𝑝

𝐼𝑠𝑝 = 𝑣𝑒𝑔0 10-2

Where 𝑔₀ is the standard earth gravity acceleration (9.80665 m/s2_).

The effect that the propulsion thrust has on the motion of the satellite is governed by the rocket equation ∆𝑣 = 𝑣𝑒ln

𝑚0 𝑚1

10-3

Where 𝑚0 is the initial mass of the satellite and 𝑚1 the mass after the propulsive manoeuvre. ∆𝑣 (delta- v) is the change in velocity of the satellite as a result.

Mass requirement

The required delta-v is usually known for a specific orbital manoeuvre and the propellant mass that is required to execute the manoeuvre can then found from

𝑚𝑝𝑟𝑜𝑝𝑒𝑙𝑙𝑎𝑛𝑡 = 𝑚1(𝑒

∆𝑣

𝑣_{𝑒− 1)} 10-4

In addition to the mass of the propellant itself, the thruster and propellant tanks should also be considered when comparing alternative strategies. If a satellite already possesses a propulsion system in order to fulfil its normal mission, it is only the added mass of the propellant that has to be considered. Propulsion systems vary significantly in terms of thrust capability and specific impulse, as can be seen in Figure 2-2 and Figure 2-3. The mass of available propulsion systems will also vary as a result. Liquid fuel rocket engines are available with mass as little as 4 kg, but as much as 140 kg (Wertz & Larson, 1999). Arcjets – a type of electric propulsion system – are available with relatively low mass, around 5 kg. Commercially available Hall-effect thrusters have a mass range between 10 to 30 kg, and ion engines are available with mass ranging from 10 to 25 kg (Wertz & Larson, 1999). These masses are only for the thruster and control electronics. The propellant tanks and pipework should also be included and is usually accounted for in the mass budget as a percentage of dry system mass.

Propulsive deorbiting strategy

From an initial circular orbit in LEO the deorbit manoeuvre that will require the lowest delta-v (and hence the least propellant) is to transition to an elliptical Hohmann-transfer orbit, from where the effect of aerodynamic drag will limit the orbital lifetime to 25 years (Janovsky, et al., 2004).

This is true even for low-thrust propulsion such as electric propulsion systems. A lower delta-v is achieved by performing multiple thrusts each time at apogee to result in a Hohmann-type orbit, as opposed to a continuous thrusting. This will also have the advantage of reducing the total thruster

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operating time. By choosing the direction of perigee appropriately it might be possible to limit thruster firings to sunlit parts of the orbit where power is available to the EP system from solar cell generation. Controlled re-entry is possible with suitable high-thrust propulsion. In the event of a controlled re-entry, the angle that the velocity vector makes with the local horizon as it enters the atmosphere at 120 km (the flight path angle) should be between -1.5 to -2.5 degrees (Janovsky, et al., 2004). This is so that there can be sufficient control over the area where the satellite and its fragments impact the Earth. If the flight path angle is too shallow, the fragmentation of the re-entering satellite will happen over a wider trajectory and the fragment impact locations will be spread out over a long strip.

Controlled re-entry is performed by applying a single thruster firing with sufficient delta-V to result in the required flight path angle. The time at which the thruster firing is performed is determined by the desired impact location. With typical controlled re-entry delta-v requirements of 150 to 400 m/s, it should be obvious that only very high thrust propulsion systems can fulfil the requirement. A 1000 kg satellite has to fire a 1 kN liquid propellant thruster for 2.5 minutes in order to achieve a delta-v of 150 m/s. This will consume 52 kg of propellant. The thrust levels from typical electric propulsion systems will not allow for such an “impulsive” thrust.

Collision energy and fragmentation risk

The collision cross sectional area for a satellite that deorbits using propulsion remains unaltered from the non-mitigation scenario. Since most (or all) of the satellite areas will have high density any collision will be a debris generating event. The propulsive deorbiting manoeuvre(s) will limit the time during which the satellite is exposed to the debris flux and thus there will be a reduction in collision risk as a result.

Operation, Integration and sub-system requirements

The cost of including a propulsion system on a satellite for the sole purpose of deorbiting at end-of-life may be prohibitively expensive. This expense will be in terms of mass, complexity and as a result of these, financial cost as well. Even if the propellant requirement is low the base mass of a propulsion system is not. This is especially true for smaller satellites where the ratio of propulsion system mass to the satellite mass will be higher. Propulsion systems also require propellant storage tanks, feeding systems, valves and so on, and are often not contained in a single place on the satellite, hence the increased system complexity.

It is thus unlikely that conventional propulsion will be selected for deorbiting unless the satellite already possesses the sub-system for normal mission functions, and it may be used for deorbiting. In this case deorbiting can easily be performed simply by factoring in the required propellant when compiling the mass budget.

For the same reasons as above, electric propulsion also seems like an unlikely contender for deorbiting, unless the system is already present for normal operations. Electric propulsion also places more demand on other sub-systems because the low relative thrust means the thruster will have to remain operational for longer, with high electric power requirement.

High thrust chemical propulsion is the only alternative considered in this study that is capable of a controlled re-entry. But it is likely that satellite operators will only use a controlled re-entry strategy if they have to (as mandated by mitigation guidelines and casualty risk). If a satellite will demise during re-

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entry then it does not make sense to reserve the large amount of propellant in order to perform a controlled re-entry, since it may be better spent prolonging the normal operations.