Mission Index

p_c represents the probability of collision with objects large enough to trigger a catastrophic collision, i.e. a collision where enough energy is released that the parent object is destroyed, using the standard criterion of 40J/g. The availability of collision avoidance capabilities is captured by removing from the computation of the collision probability those objects that are large enough to be tracked with current surveillance systems and can be avoided with collision avoidance manoeuvres.

It is computed using an analog method to the kinetic theory of gas, by extracting the debris density p and fluxes from ESA MASTER, and by using the cross-sectional area of the considered objects and the selected time period as inputs.

P_c = 1 - e ^{- p . Δv . A . Δt [ref.]}

The term e_c quantifies the severity of the potential fragmentations in terms of the increase in the collision probability for operational satellites.

It is focusing on the evolution of the consequences of a fragmentation and uses the NASA break-up model to simulate the fragmentation. A set of representative objects of the population of operational satellites is then defined and the collision probability for these objects due to the simulated fragmentations is computed. The severity term is then derived from the increased probability of fragmentation on the rest of the space environment caused by the fragmentation event.

More details on the approach used to model the probability and the severity terms can be found in HERE.

The index value is computed by integrating the index value over the entire orbital lifetime of the object, from launch to re-entry (or upper time limit of the simulation i.e. 100 years). A simplified version of the index can be found below:d bellow:

The formulation of such an index allows to sum the indices of different space objects in order to characterise the associated risk of a given missions that can be composed of one or several spacecrafts. The figure below shows the associated index values of objects depending on their orbital elements, without considering any collision avoidance or post mission disposal strategy.

Variation of I_c with the orbital parameters, without considering collision avoidance and post mission disposal strategies (Source)

The risk metric so-defined (I) is not computed only at a single epoch, but rather evaluated along the mission profile of an object to the implementation of disposal strategies at the end of mission. In particular, this is done by considering the possible paths of evolution of the trajectory depending on the success rate of the disposal strategy (a), so that the index computation becomes:

Where t_EOL represents the epoch of end of operations, t_fD, t_fND, the minimum between 100 years (simulation upper limit) and the epoch of re-entry in the case, respectively, where the object is disposed and in the case where it is not disposed (i.e. abandoned in its operational orbit).

The previous expression highlights the importance of a post mission disposal strategy implementation, with a high success rate. A post mission disposal will both significantly reduce the index value I since in most cases, the disposal orbits will:

1. result in a lower collision probability risk and hence a lower index
2. Reduce the lifetime in orbit (time interval from to t_EOL to t_fD), resulting in a smaller integration interval and a reduced index value.

The importance of a disposal strategy is well reflected and can be observed in the figure below.

It has been shown how the proposed metric, while relying on few high-level parameters, allows capturing the differences among alternative mission architectures, for example considering the adoption of different operational concepts, the deployment of a constellation, and different implementation of disposal strategies.

The mission index also captures the reduction of the collision probability from trackable objects thanks to the implementation of collision avoidance strategies by operators. The adoption of collision avoidance strategies is not treated as binary option (yes/no), but rather with a score  that measures its efficacy. The following formulation shows the index computation formula for trackable objects, during the operational lifetime of the satellite.

I_operational = (1 - y)p_ce_c

The term y designates the mitigated collision risk. It quantifies the risk reduction achieved by the implemented collision avoidance strategy with respect to the case where no manoeuvre is performed. This parameter is computed using ESA DRAMA ARES tool and uses as inputs:

• The orbital parameters of the missions
• The cross-section area of the spacecraft
• The Accepted Collision Probability Level, or probability threshold triggering a maneuver from the operator
• The Lead time, or time required to implement and execute a collision avoidance manoeuvre.

A mitigated collision risk of 75% would mean that the implemented collision avoidance strategy will decrease the index value by 4. More details regarding the detailed computation methodology will be communicated to the SSR applicant by the issuer during the rating process.

The approach defined above provides an absolute evaluation of the impact of a mission on the environment. However, one of the aspects that the SSR wants to highlight is when operators implement better than required behaviours for what concerns mitigation efforts. In order to capture this aspect, besides the evaluation of the absolute debris risk, the computed footprint is compared to the one that the same mission would score in a reference scenario. The reference scenario corresponds to a minimum required level of mitigation actions, defined in the following ways for the different orbit classes (based on commonly applied and internationally recognised space debris mitigation standards):

• LEO: 25 year with 90% PMD,
• GEO: Graveyard with 90% PMD,
• Other: no action.

The relative mission index is the ratio of the absolute index described above over the reference case scenario. The introduction of the relative mission index rewards operators going beyond currently best-advised practises. The final SSR index considers the pondered sum of the absolute (80%) and relative (20%) indices. Here below is a figure presenting the different index values for a mission considering different scenarios.

Computation of the space debris index for the same object using different mission scenarios including no PMD, 25 years PMD, and 10 years PMD (resulting in a better relative mission index score).

The Mission Index in itself can be used to compare different missions, but a normalisation approach is needed to include its contribution in a composite indicator such the SSR and make it compatible with the other modules. The normalisation approach adopted for the SSR is based on the concept of environmental capacity, i.e. the number and type of missions that are compatible with the long-term stability of the environment. As detailed HERE, long-term simulations of the environment can be used to build a reference scenario with a good level of compliance to space debris mitigation guidelines. This scenario is then compared with the actual use of orbital resources, intended as the sum of the index for all objects in orbit, considering their expected mitigation strategies. Currently post-mission disposal (PMD) plans and their expected success rate are not systematically shared by operators, but thanks to space surveillance data, the activity of a spacecraft can be derived and the evolution of its orbit can be predicted, so the status of the environment can be assessed. In terms of environmental capacity, a share of it is consumed by inactive satellites and rocket bodies, whereas the remaining part can be used for active and new missions. It is this value (the available capacity) that can be used to normalise the Mission Index within the SSR to reflect that the criticality of the index of a mission is also related to the global evolution of the environment.