FA-69534 / Orbital propagation / Member archive

Fixed-step RK4 two-body propagation: Acceleration uses |r|^2 in the vector form · case 04

Gravity has the wrong falloff and scales with distance.

Member previewVariant 4 · 3 implementations · 7 checks per implementation

Case contract

Input [r0, v0, mu, T, steps] for a planar two-body orbit. Integrate state [x,y,vx,vy] with acceleration -mu r/|r|^3 using classical RK4 with h=T/steps for exactly steps steps. Return the final state rounded to 6 decimals.

Why this case matters

Orbit determination and mission planning chain many small conversions; one wrong branch or unit silently moves a spacecraft by kilometres.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
fixed-step rk4 two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]	`[-0.989991, 0.141114, -0.141116, -0.989995]`	`[-0.98999, 0.141112, -0.141113, -0.989997]`	Failed

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