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Why a Perfectly Good Avoidance Burn Sometimes Does Nothing

Along-track burns are the cheapest way to move a spacecraft. For a head-on conjunction they are also close to useless — and the geometry explains why.

The standard collision avoidance manoeuvre is a small burn along the direction of travel. It is cheap, it is well understood, and for a large class of conjunctions it barely moves the number you are trying to move.

Why along-track is the default

Firing along or against the velocity vector changes orbital energy, which changes the period, which makes the spacecraft arrive early or late. Over several orbits a tiny impulse accumulates into a large displacement — roughly three times the velocity change multiplied by the time you have. Give a spacecraft a few centimetres per second a day in advance and you have moved it kilometres. Nothing else buys displacement that cheaply.

The part that catches people out

What matters in a conjunction is not how far you moved. It is how far you moved in the plane perpendicular to the relative velocity — the encounter plane. That is the only plane in which the two objects have a meaningful separation at closest approach.

Now consider a head-on conjunction, the classic high-relative-velocity case between objects in opposing orbits. The relative velocity vector points almost exactly along your direction of travel. So does your burn. Moving along the relative velocity direction does not change how close you pass — it changes when you get there. The miss distance is almost unchanged, and the probability can sit still or even rise.

The same trap applies to overtaking encounters, where one object slowly catches another in a similar orbit. It feels like the opposite case, but the relative velocity is again in-track dominated, and a tangential burn is again working in the wrong direction.

The geometry that does respond well is a crossing encounter, where the orbit planes are meaningfully inclined to one another. There the relative velocity has a large component out of your in-track direction, your along-track displacement projects strongly into the encounter plane, and a modest burn produces a real change in miss distance.

What a planner should do about it

It should solve the problem in the encounter plane rather than in the orbit, and it should be willing to say no. OrbitIQ computes how effectively an along-track burn projects into that plane. When the answer is near zero, it does not quote a plausible-looking Δv anyway — it reports that the geometry is unfavourable and recommends a radial or cross-track burn instead.

A number you cannot justify is worse than no number, because someone will spend propellant on it.

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A Collision Probability Is Only as Honest as Its Covariance
Public orbital elements carry no uncertainty data. Every probability computed from them rests on an assumption — and most tools never tell you what it was.