Point-Ahead Aiming for Deep-Space Laser Links (2D)

Orbital Geometry

Range to orbit center D 1.00 AU

Receiver's orbit radius r 300,000 km

Orbital period T 24 h

Transmit aperture D_tx 22 cm

Laser Wavelength

Live Readouts (this pulse)

Range at launch d

—

One-way light time τ

—

Transverse speed v⊥

—

Point-ahead angle α=v⊥/c

—

Beam footprint radius @d

—

Predicted lead v·τ

—

Naive-aim miss (beamwidths)

—

Point-ahead-aim miss (beamwidths)

—

Launching pulse…

How it works

This is an independent 2D orbital-mechanics model, not a flattened 3D view. The receiver moves on an exact circular orbit of radius r around a center a real distance D from the transmitter, with angular speed ω = 2π/T set by the period slider. At every pulse the sim computes its exact position and velocity vector, then does real geometry:

line of sight  u = (receiver − transmitter) / d,   d = |receiver − transmitter|
one-way light time  τ = d / c
transverse speed  v⊥ = |v − (v·u)u|   (component of velocity ⟂ to the line of sight)
point-ahead angle  α = v⊥ / c   (small-angle form)
predicted position  = receiver(t) + v(t)·τ   (real vector extrapolation, not a canned offset)

The beam is then aimed either at the receiver's current apparent position (point-ahead OFF) or its predicted future position (point-ahead ON), and travels for τ seconds. Meanwhile the receiver keeps moving on its real orbit to its exact position at t+τ — computed from the same circular-orbit equation, not simulated frame-by-frame, so there's no accumulated integration error. The sim then checks, honestly, whether the beam's aim point falls within the diffraction-limited footprint of where the receiver actually ends up:

θ = 1.22 λ / D_tx           (Rayleigh half-divergence)
footprint radius r_spot = d · θ
HIT  if  |receiver(t+τ) − aim point|  ≤  r_spot

Range D — sets the light-time delay τ, and (with aperture/wavelength) the absolute footprint size.
Orbit radius / period — set the receiver's real orbital speed v = rω, which — combined with where it sits on its orbit relative to the line of sight — determines v⊥.
Aperture / wavelength — narrow the beam (smaller footprint), making the same point-ahead offset relatively worse in beamwidths if left uncorrected.
Point-ahead toggle — OFF aims at the receiver's current apparent position (usually a big miss at deep-space ranges); ON leads by the real extrapolated position and lands inside the footprint.

Transmitter Receiver (true orbit) Photon pulse Naive aim point Point-ahead aim point