Light is fast, but interplanetary distances are huge: a photon needs t = R / c just to reach the receiver. During that transit time the receiver — a ground telescope riding Earth's ~30 km/s orbital motion, or another moving spacecraft — has shifted sideways by:
Δx = v⊥ · t = v⊥ · (R / c)
Point-ahead angle: α = Δx / R = v⊥ / c
A deep-space optical terminal cannot just point at where it currently sees the receiver — it must aim α radians ahead, at the position the receiver will occupy once the light arrives. NASA's Deep Space Optical Communications (DSOC) demo on the Psyche mission does exactly this, computing α onboard from the known relative trajectory.
Whether skipping that correction actually causes a miss depends on how wide the beam is. A diffraction-limited transmitter of aperture D at wavelength λ has a half-divergence angle and a footprint radius at range R of:
θ = 1.22 λ / D (Rayleigh criterion)
footprint radius r = R · θ
Because both the point-ahead offset (R · α) and the footprint radius (R · θ) scale linearly with range, the range cancels out of their ratio:
miss, in beamwidths = (R · α) / (R · θ) = α / θ = v⊥ · D / (1.22 · λ · c)
That ratio — not the distance — decides hit or miss. For DSOC-like numbers (D ≈ 22 cm, λ = 1550 nm, v⊥ ≈ 30 km/s) the point-ahead offset is roughly 100× wider than the beam itself, which is why an uncorrected optical downlink misses by a huge margin however far or near the target sits, while a corrected one is dead-on regardless of range.
- Range — sets the light-time delay and the absolute footprint/offset size in kilometres, but not the hit/miss outcome.
- Aperture / wavelength — a wider dish or a shorter wavelength narrows the beam (smaller θ), making the same point-ahead offset relatively worse in beamwidths.
- Transverse speed — a faster relative sideways motion widens the point-ahead angle α directly.
- Point-ahead toggle — with it off, the beam is aimed at the receiver's apparent position now; with it on, the transmitter leads by exactly α, landing the beam back on target.