Every object here — satellite and debris alike — orbits Earth on its own circular shell at the altitude-only angular rate given by Kepler's third law, ω(r) = √(μ/r³), with μ = 398,600.44 km³/s² and Earth's radius folded into r. Lower shells sweep past higher ones faster, so debris in a different shell than the satellite is always lapping it — and every lap is a possible conjunction.
Moving the satellite between shells is a real two-impulse Hohmann transfer, computed exactly from the vis-viva equation rather than approximated:
a = (r1+r2)/2
Δv1 = |√(μ(2/r1 − 1/a)) − √(μ/r1)|
Δv2 = |√(μ/r2) − √(μ(2/r2 − 1/a))|
Δv_total = Δv1 + Δv2
Every evasive burn — automatic or manual — is billed against your Δv budget at this rate. Run it out and the satellite can no longer dodge.
- Debris density — how many tracked fragments seed the field, clustered near the real ~800–900 km congestion band before you regenerate the belt.
- Altitude — the satellite's home shell; changing it fires a priced Hohmann transfer.
- Evasion burn size — how many km the satellite jumps to a safer shell per dodge; bigger jumps are safer but cost more Δv.
- Auto-Shield — when a debris object enters the same shell and closes to inside the conjunction-screening distance, the satellite burns automatically if it can afford to.
A dodge that fails — no fuel, no time, or Auto-Shield off — is a hit: integrity drops and the debris fragments into two or three smaller pieces on nearby shells, exactly the runaway feedback loop known as Kessler syndrome.