The Cost of Future Collisions in LEO - Star Technology and Research

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To put estimate (B5) in perspective, let us consider a commonly used formula
N m = k (M/m) γ ,
(B6)
where N m is the number of fragments heavier than m, and M is the total mass involved
in the collision. The original Kessler’s formula has k ≈ 0.8 and γ ≈ 0.8 [21],
an early version of the NASA breakup model uses k ≈ 0.45 and γ ≈ 0.75 [18], the
mass distribution of the tracked fragments of Solwind fits k ≈ 0.3 and γ ≈ 0.8 [16],
while the estimate (B5) corresponds to k ≈ 0.4 and γ ≈ 0.8 for M ∼ 1 ton. Extended
formally toward masses over 10 kg, the estimated distribution converges
with the early NASA model. Debris models are evolving [22], and new breakup
models are introduced [20, 23]. They will become more accurate when more data
on small fragments is gathered.