How Rockets Land Themselves

Neither a missile nor an aeroplane

The clearest account of the problem comes from Lars Blackmore, then principal rocket-landing engineer at SpaceX, in a 2016 article for the US National Academy of Engineering’s journal The Bridge. His starting point is that a rocket coming back to land is an awkward kind of vehicle. A ballistic missile hits its target at high speed, so winds hardly move it. An aeroplane is pushed around, but its wings give it the control to correct for that. A rocket descending vertically has neither advantage.

It also has little room for error. Blackmore notes that for most landings the first attempt has to succeed, and that large rocket engines are hard to throttle down to a hover, which wastes propellant for every second spent hovering. So the Falcon 9 first stage, which he gives as about 35 tonnes, has to reach zero velocity at exactly zero altitude. Reach zero too low and it crashes. Reach it too high and it starts climbing again, and the only option left is to cut the engines and fall.

How the descent is steered

Blackmore describes the return of a first stage as a series of steps, each one a chance to shrink the errors that wind and uncertainty add. The article calls these errors dispersions.

The boostback burn sends the stage back towards the launch site.
Entry through the atmosphere, where the stage is steered with fins and feels a peak deceleration of about six times Earth’s gravity.
The landing burn, the last chance to correct, which needs the ability to divert, meaning to move sideways.

The target he gives is demanding. At least 99% of the possible landing points have to fall inside the landing zone, which means dispersions of 10 metres or better for a landing on the drone ship, and 30 metres or better at Cape Canaveral.

The maths that makes it possible

The divert is the hardest part. The vehicle must compute a path from where it is to the target, ending at rest and upright, without asking more of the engines and legs than they can give. It must do that on board, in a fraction of a second. If it cannot find a workable path in time, it crashes. If it finds a wasteful one, it can run out of propellant, with the same result.

Blackmore says a general solution existed in one dimension from the 1960s, but not in three. The route to one came from research on landing on Mars. Behçet Açıkmeşe and Scott Ploen of NASA’s Jet Propulsion Laboratory showed in 2007 that the minimum-fuel descent problem, which has awkward non-convex limits on engine thrust, can be rewritten as a convex problem of a type called second-order cone programming. The NASA record of their follow-up work states the practical payoff: such problems have efficient solvers with deterministic convergence, so the algorithm can potentially run on board a spacecraft in real time.

In plain terms, a convex problem has no false bottoms: a solver cannot get stuck on an answer that is worse than the best one, and it can be shown to finish. That is the property a landing computer needs. Blackmore adds that Earth is a different problem from Mars, because Earth’s atmosphere is 100 times as dense, so aerodynamic forces become a main concern. He says SpaceX uses CVXGEN, a code generator for embedded convex optimisation, to produce customised flight code that runs very fast on board.

What it achieved, and what is still open

By the time of his article, SpaceX and Blue Origin had both landed rockets within metres of their targets: Blue Origin’s New Shepard at its West Texas site, and the Falcon 9 first stage on land at Cape Canaveral and on a floating drone ship. This article reports that 2016 snapshot, not later flights.

Blackmore is equally clear about what does not transfer. Elsewhere in the solar system there is no GPS, and tracking from Earth gets less accurate with distance. For precise landings, the lander must navigate from the destination itself. One approach is terrain-relative navigation, where the lander images the surface and matches it against an onboard map. Tests had reached accuracy on the order of tens of metres. Planetary landing ellipses, the area where a vehicle is 99% likely to land, were still measured in kilometres.

Our take: reusable rockets are as much a computing achievement as a rocket one. The engines and legs matter, but the new ingredient was an algorithm that is guaranteed to give an answer in time, running on the vehicle, with no one to call.

Questions and answers

How does a rocket land itself?

Using an on-board computer that plans and re-plans a path to the target in a fraction of a second. SpaceX's Lars Blackmore describes boostback burn, steering with fins during entry and a final landing burn with a sideways divert.

Why does the rocket have to hit zero speed exactly at the ground?

Large engines are hard to throttle down to a hover and hovering wastes propellant. Blackmore says that if the stage reaches zero velocity too low it crashes, and if too high it starts going back up.

What is convex optimisation and why does landing use it?

A class of maths problems with no false bottoms, so a solver cannot get stuck on a worse answer and can be shown to finish. NASA JPL researchers showed that a Mars descent problem could be written this way and solved fast enough to run on board.

How accurate are the landings?

Blackmore gives a target of dispersions of 10 metres or better for a drone-ship landing and 30 metres or better at Cape Canaveral, for the Falcon 9 in his 2016 article. Mars landings were still precise only to kilometres.

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Sources

Autonomous Precision Landing of Space Rockets (L. Blackmore), The Bridge vol. 46 no. 4, Winter 2016 · US National Academy of Engineering · Accessed 5 November 2026
Enhancements on the Convex Programming Based Powered Descent Guidance Algorithm for Mars Landing (Açıkmeşe et al.) · NASA Technical Reports Server / JPL · Accessed 5 November 2026

Published 5 November 2026

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