## 5 Long-Term Evolution
### Simulation Tools  
After designing the BAU scenario, long-term simulations are conducted with the calculated parameters and in most cases also with its variations. At the Institute, there are currently two tools for long-time simulations under development: ESA's DELTA4 [29] and the in-house tool LUCA2 [30]. The general approach for long-term simulations is shown in Figure 8.  
The starting point of all simulations is represented with the creation of an initial background population, usually including objects larger than \(d=10\,\mathrm{cm}\). During the proceedings of the simulation, the different modules seen in Figure 8 are executed at every time step until the desired time frame (e.g., 200 years) is reached. The first step is launching new objects, such as payloads and upper stages, based on the predefined launch rates. In some special cases, it is also possible to launch mega-constellations (cf. Section 5.2). Objects of mega-constellations have the ability to execute maneuvers for spiraling up to their desired orbits with electrical propulsion engines. The next steps are the generation and calculation of explosion as well as collision events. For both, there are several approaches to calculate the number of events. In the case of explosions, the first option includes a fixed number of explosion events per year and the second is described through a time dependent explosion rate. For the calculation of collision events, the first approach (called \"CUBE\") discretizes the space around Earth into small cubes, usually with an edge length of ten kilometers. With a time step of five days, a collision probability is calculated for each pairing of objects that are in the same cube. The second approach is called Orbit Trace and compares all orbits to find crossings within a defined maximum collision distance. Additional filtering within the algorithm avoids collisions between synchronized objects, e.g., constellation satellites. The third algorithm to calculate the collision rate uses the object-flux. Taking into account the time dependent object-flux on a target object, the algorithm extracts the number of collision events using a Poisson distribution. In addition to collision events, active objects have the possibility to perform collision avoidance maneuvers. For the propagation of the population, a various number of different propagators are available. Regarding the amount of simulation time, semi-analytical propagators are used. Nevertheless, numerical propagators like  
Figure 8: Exemplary program flow for long-term simulations.  
NEPTUNE [31] can also be included. At the end of each simulation time step, different mitigation measures are performed, such as PMD and Active Debris Removal. For PMD, there are different kinds of maneuvers possible--for example, an eccentric orbit with less than a 25-year lifetime or a graveyard orbit for objects in Geostationary Earth Orbit (GEO), which conforms with the IADC Mitigation Guidelines. In the past, simulations only took chemical propulsion systems into account when modeling PMD maneuvers. To investigate the impact of different systems, there are also possibilities to include electrical propulsion systems as well as the use of solar/drag sails. Because of randomized parameters within the algorithm, especially for collisions, the simulations are conducted within Monte Carlo Runs to get a statistic variation of these parameters.