Stellar Aberration¶

Stellar aberration is the apparent displacement of star positions caused by the finite speed of light combined with the observer's velocity — analogous to how rain appears to fall at an angle when you're moving.

Effect Size¶

For Earth-based observers, stellar aberration shifts apparent star positions by up to ~20″ (\(v/c \approx 10^{-4}\) rad). Without correction, the solved attitude is biased by up to ~20″.

Velocity source	Magnitude	Aberration
Earth's orbital velocity	~30 km/s	~20″
LEO orbital velocity	~7.5 km/s	~5″
Earth's rotation (equator)	~0.46 km/s	~0.3″

For ground-based observers, Earth's orbital velocity dominates and the rotation contribution (~0.3″) can usually be neglected. For LEO star trackers, the spacecraft's orbital velocity around Earth adds a further ~5″ direction bias on top of the Earth-barycentric ~20″ — not negligible for arcsec-precision attitude. Pass the observer's total barycentric velocity (Earth-around-Sun + spacecraft-around-Earth, or ground station surface rotation if applicable) rather than just earth_barycentric_velocity() alone.

Correction¶

To correct for aberration, pass the observer's barycentric velocity (ICRS, km/s) via the observer_velocity_km_s parameter:

from datetime import datetime
import tetra3rs

# Get Earth's approximate barycentric velocity
v = tetra3rs.earth_barycentric_velocity(datetime(2025, 7, 10))

# Pass to solver
result = db.solve_from_centroids(
    centroids,
    fov_estimate_deg=10.0,
    image_shape=image.shape,
    observer_velocity_km_s=v,
)

The solver applies the exact classical correction \(\mathbf{s'} = (\mathbf{s} + \boldsymbol{\beta}) / |\mathbf{s} + \boldsymbol{\beta}|\) to all catalog star vectors before matching and refinement, producing an unbiased attitude. The relativistic correction is \(O(\beta^2) \sim 10^{-8}\) rad for Earth (~2 mas) and is not applied.

Rust¶

use tetra3::{earth_barycentric_velocity, SolveConfig};

// days since J2000.0 (2000 Jan 1 12:00 TT)
let v = earth_barycentric_velocity(9321.0);

let config = SolveConfig {
    observer_velocity_km_s: Some(v),
    ..SolveConfig::new((10.0_f32).to_radians(), 1024, 1024)
};

Earth Barycentric Velocity¶

The convenience function earth_barycentric_velocity() provides an approximate Earth velocity using a circular-orbit model:

Accuracy: ~0.5 km/s (~1.7%), sufficient for the ~20″ aberration effect (~0.3″ error)
Input: Python datetime (UTC) or days since J2000.0 (Rust)
Output: [vx, vy, vz] in km/s, ICRS equatorial frame

Note

Enabling aberration correction shifts the entire solved pointing by up to ~20″, not just the within-field residuals. This is the physically correct result. Most plate solvers (e.g., astrometry.net) do not account for aberration, so comparing results may show a systematic offset.