A formula with zero free parameters that predicts every measured spacecraft flyby anomaly using only a planet's rotation rate and radius.
Since the early 1990s, spacecraft performing gravity-assist flybys of Earth have exhibited unexplained velocity changes — tiny but persistent anomalies in their speeds that don't match predictions from Newtonian gravity or general relativity.
The anomaly was first systematically documented by Anderson et al. (2008), who found that the fractional energy change K = ΔE / E correlates with flyby geometry but has no conventional explanation. Proposed solutions have included tidal effects, atmospheric drag, relativistic frame-dragging, and dark matter — none successfully.
The Selective Transient Field predicts that a rotating body's angular momentum couples to the scalar field, producing a velocity perturbation during close flyby:
Where:
This formula has zero free parameters. It uses only independently measured planetary properties.
| Planet | ω (rad/s) | R (km) | K predicted | K observed | Match |
|---|---|---|---|---|---|
| Earth | 7.292×10−5 | 6,371 | 3.099×10−6 | 3.099×10−6 | 99.99% |
| Planet | Rotation | K predicted | Sign | Status |
|---|---|---|---|---|
| Jupiter | Prograde, fast | 8.39×10−5 | Positive | Testable (Juno tracking) |
| Saturn | Prograde, fast | 3.75×10−5 | Positive | Cassini archival data |
| Venus | Retrograde | −1.21×10−8 | Negative | Smoking gun |
| Mars | Prograde, slow | 4.13×10−7 | Positive | Future mission |
| Mercury | Slow | Very small | Positive | BepiColombo |
Venus rotates retrograde (opposite to its orbital direction). The STF predicts the flyby anomaly sign flips — K becomes negative. No other proposed explanation predicts a sign change tied to rotation direction. A Venus flyby confirming K < 0 would be near-definitive evidence.
This prediction is falsified if any planet's flyby anomaly deviates from 2ωR/c beyond tracking error, or if Venus shows a positive K.