Ranking Active Debris In LEO.pdf

The main reason behind the adoption of the "25-year rule" by the Inter-Agency Space Debris Coordination Committee (IADC) was to prevent the build-up of intact spacecraft and rocket bodies in Earth orbit, which currently account for approximately 95% of the mass in Earth orbit, to avoid long-term instability triggered by mutual collisions and catastrophic breakups. A ranking scheme based on plausible inferences is a popular way to gauge the latent long-term environmental impact of an orbiting object, refraining from running thousands of complex simulations based on uncertain scenario assumptions and forecasts.

A new normalized and dimensionless ranking index was presented, using as a benchmark a nearly 1-ton object placed into an 800 km sun-synchronous orbit. The index was applied to 58 objects with a mean altitude between 600 and 1000 km and a dry mass greater than 3000 kg, accounting for about 11% of the mass present in low Earth orbit, operational spacecraft included.

The ranking index R of an abandoned object in LEO can be expressed as the product of two functions: f, which depends on the probability of catastrophic breakup Pc due to a collision with a piece of orbital debris, and the number of new "projectiles" Np resulting from the breakup, and g, which characterizes the long-term impact on the environment as a function of the lifetime of the cloud of fragments generated, the volume of space involved, and the interaction with the pre-existing debris distribution.

The probability of catastrophic fragmentation in a given time interval can be written as the product of the flux of debris F(t) able to induce the catastrophic breakup of the target object, the average collisional cross-section A of the latter, and the time t. However, the time evolution of F(t) is affected by significant uncertainties, and the computation of the integral for each specific target object would be cumbersome.

Therefore, a first strong simplifying assumption was chosen to include in the ranking scheme just the current flux F(h, i, M) provided by a state-of-the-art debris model or a sufficiently complete debris catalog, at the mean altitude h and inclination i of the target, supposed to be in a reasonably low eccentricity orbit. This led to the expression:

cP
F h i M
A L
≈
⋅
⋅
where LT is the object residual lifetime.

Considering a distribution of drag coefficients not too far from a standard average value, which is reasonably true for intact objects in LEO, LT can be approximated as the product between the object mass-to-area ratio M/A and a "normalized" lifetime function l(h):

T
M
L
l h
A
≅
⋅

The "normalized" lifetime function l(h) can be computed as follows:

0
0
0
( )
( )
T
A
l h
L
h
M
=
⋅

where LT0(h) can be well approximated, for computational purposes, by the polynomial interpolation shown in Fig. 1, very good above 600 km.