A sensitivity study of the effectiveness of active debris removal in LEO

TLDR: In this article, a removal criterion based upon mass and collision probability is developed to rank objects at the beginning of each projection year, with removal rates ranging from 2 to 20 objects per year, starting in the year 2020.

About: This article is published in Acta Astronautica.The article was published on 2009-01-01 and is currently open access. It has received 205 citations till now. The article focuses on the topics: Population & Space debris.

Figures

Figure 1 shows the effective numbers of objects, 10 cm and larger, in LEO from the four scenarios. The effective number is defined as the fractional time, per orbital period, an object spends between 200 and 2000 km altitude. Each curve represented the average of 100 Monte Carlo runs. The business-as-usual scenario predicted a fast non-linear growth of the future LEO debris population in the next 200 years. The three ADR scenarios, on the other hand, predicted a much slower increase in the environment. A simple parameter, Effective Reduction Factor (ERF), can be calculated to quantify the effectiveness of each ADR scenario using the non-mitigation scenario as a benchmark. ERF is defined as:

Figure 1 shows the effective numbers of objects, 10 cm and larger, in LEO from the four scenarios. The effective number is defined as the fractional time, per orbital period, an object spends between 200 and 2000 km altitude. Each curve represented the average of 100 Monte Carlo runs. The business-as-usual scenario predicted a fast non-linear growth of the future LEO debris population in the next 200 years. The three ADR scenarios, on the other hand, predicted a much slower increase in the environment. A simple parameter, Effective Reduction Factor (ERF), can be calculated to quantify the effectiveness of each ADR scenario using the non-mitigation scenario as a benchmark. ERF is defined as:

Figure 7. Top four curves: masses in LEO from the

Table 2: Effectiveness of active debris removal in terms of cumulative collision probability of the environment. The LEO population (objects 10 cm and larger) from the non-mitigation scenario is used as the benchmark for the comparison.

Figure 4. Inclination distributions of objects removed from the three ADR scenarios. Each distribution is the average of 100 Monte Carlo runs.

Figure 5. Altitude distributions of objects removed from the three ADR scenarios. Each distribution is the average of 100 Monte Carlo runs.

Frequently asked questions

Q1. What are the contributions in this paper?

This paper does not intend to address the technical or economical issues for active debris removal. Rather, the objective is to provide a sensitivity study to quantify the effectiveness of various remediation options. A removal criterion based upon mass and collision probability is developed to rank objects at the beginning of each projection year. This study includes simulations with removal rates ranging from 5 to 20 objects per year, starting in the year 2020. The summary of the study serves as a general guideline for future debris removal consideration. 

Q2. What are the future works in this paper?

The scenarios were designed to demonstrate and quantify, in a relative way, how ADR could reduce the growth of the future debris population in LEO. The objects identified to have the greatest potential of contributing to future population growth through 2206 ( Figures 4-6 ) depend on two factors. Spacecraft and upper stages launched in the future will certainly be different from those in the assumed launch cycle. Moving the starting time somewhat further into the future ( while the population growth is still linear ) should only postpone the population reduction accordingly. 

Q3. What are the criteria used for removal of objects?

Objects with perigee altitudes above 2000 km, or with eccentricities greater than 0.5, were not considered for removal in this study. 

Q4. how many objects will be removed by the end of 2206?

It means for every object that is removed (via ADR) from the environment, a total of 36 objects will be reduced by the end of 2206. 

Q5. What is the collision probability of a cube?

For any object i that has a finite collision probability with a second object j, within the same cube at time t, its collision probability can be expressed as: ,)( dtdUVsstdP impjii σ= [1] where si and sj are the spatial densities of objects i and j in the cube, respectively, Vimp is the relative velocity between the two objects, σ is the combined collision cross-sectional area, dU is the volume of the cube, and dt is the time interval. 

Q6. What was the criterion used for removing objects?

For any object i which was eligible for removal consideration, a simple criterion, Ri, was adopted: iii mtPtR ×= )()( , [2] where Pi(t) was defined by Equation (1), and mi was the object’s mass. 

Q7. What was the analysis of historical explosions between 1988 and 1998?

Explosion probabilities of rocket bodies and spacecraft were based on an analysis of historical explosions between 1988 and 1998. 

Q8. How is the mass in LEO calculated?

The total mass in LEO is calculated based on the mass of each LEO-crossing object weighted by the fraction of time the object resides in LEO. 

Q9. What other scenarios can be considered for a benchmark?

Other scenarios, including the “no new launches”2 and “postmission disposal”5, can also be considered for benchmarks to test the effectiveness of various ADR strategies. 

Q10. What was the NASA standard model for generating debris fragments?

After each breakup, fragments were generated with the NASA Standard Breakup Model, which described the size, area-to-mass ratio, and velocity distributions of the debris9. 

Q11. How many objects were removed from the environment by 2006?

The cumulative collision probabilities, by 2006, for the non-mitigation, ADR 2020/5, ADR 2020/10, and ADR 2020/20 scenarios are 172.9, 74.2, 55.4, and 45.8, respectively. 

Q12. What are the three distributions of the objects with the greatest potential of contributing to future collision fragment?

They are (1) massive objects between 1000 and 1500 kg and between 2500 and 3000 kg, (2) objects with inclinations in one of the three bands: 70°-75°, 80°-85°, and 95°-100°, and (3) objects that spenda significant amount of time in one of the three altitude regions: 800 km-850 km, 950 km-1000 km, and 1450 km-1500 km. 

Q13. What is the average mass of an object in LEO?

When ADR is implemented, significant amounts of mass are removed (the bottom three curves), and total mass in LEO is kept more or less constant through 2206. 

Q14. What is the way to reduce the population in the near-term?

ADR scenarios based on the selection criterion of Equation (1) effectively reduce the population in regions which have the greatest potential of growth in 200 years (see Figure 3). 

Q15. What is the cost-to-benefit ratio of ADR?

if ADR is not implemented before the population reaches a much faster or even exponential growth rate, the cost-to-benefit ratio of ADR would be significantly increased.