# Impact of Mega Constellations on Geospace Safety
## 2 Models and Assumptions
### ACPL Assessment Model  
The probability of collision is an important factor to consider when deciding whether to perform an avoidance maneuver. In this regard, determining the threshold probability to be applied to trigger maneuvers is critical. If this threshold is set too high, a large number of approach points will be ignored, exposing the operator to significant risk throughout the mission's duration. If the threshold is set too low, however, the number of operation tasks may be excessive, with the majority avoiding only a minor overall risk. In this paper, the ACPL (accepted collision probability level) value is selected as the index of this threshold. ACPL is the relationship between the number of avoidance times and collision risk, and represents the average number of avoidance maneuvers with acceptable collision probability [15].  
ESA developed DRAMA to assist with threshold selection (Debris Risk Assessment and Mitigation Analysis) [26]. We primarily employ its ARES (Assessment of Risk Event Statistics) module for the assessment in this paper, and we use DRAMA to calculate the ACPL using collision probability obtained through the above equation, adding the Starlink constellation to the race group of DRAMA to obtain the degree to which the target satellite is affected by Starlink. According to current research for RapidEye constellation, the more acceptable ACPL value is \(10^{-4}\)[15].  
If the ACPL-\(10^{-6}\) is chosen, the residual risk can be reduced to zero when only known objects are considered, but it also implies a large number of avoidance maneuvers, which is unacceptable for in-orbit satellite mission lifetimes, so the ACPL value of \(10^{-4}\) is generally chosen. The computational model is shown below.  
If the spacecraft is maneuvered when the collision risk from the catalog object exceeds the acceptable level, the associated collision avoidance maneuver rate can be determined based on the passage rate (i.e., flux) of the catalog object in the elliptical region as we determine, as shown in Equation (4), and the velocity increments given later \(\Delta V\) and the propellant mass fractions based on different ACPL worthy avoidance maneuvers are calculated.  
The concept of collision risk is shown in Figure 4. As shown below, the collision cross section is defined as an elliptical surface divided into an infinite number of microelements, and \(dA\) denotes a microelement in this surface [27].  
\[\dot{N}_{c}=\sum_{j=1}^{J}\int\limits_{0}^{A_{j}(P_{c,acc})}FdA\;\;j=1,2,3\ldots J \tag{4}\]  
Figure 4: Illustration of the concept of collision risk estimation based on the integration of statistical object fluxes over a collision probability density function in the b-plane centered on the target object.  
\(P_{c,acc}\) represents the acceptable collision level, i.e., ACPL, \(\dot{N}_{c}\) denotes the number of collision avoidance control, and the number of avoidance control operations is calculated according to \(P_{i=m}>P_{c,acc}\). In order to ensure that the satellite safety level is acceptable, the ACPL is generally selected as \(10^{-4}\), which corresponds to the red warning threshold [28].  
\(A_{j}\) denotes the sum of the collision area of different objects with orbiting satellites, i.e., the cross-sectional area of the \(J\)th target object \(A_{c}\), \(A_{c}=\left(\sqrt{A_{t}}+\sqrt{A_{r}}\right)^{2}\), \(A_{r}\) denotes the cross-sectional area of orbiting satellites, \(A_{t}\) indicates the cross-sectional area of different objects, and \(F\) denotes the sum of the fluxes of all target objects (in this paper, i.e., the different fluxes of the orbit with and without Starlink).