Geodetic Precession Calculator — Formule
## Geodetic (de Sitter) Precession
A gyroscope orbiting a massive body precesses due to the curvature of spacetime, even if the central body is not rotating.
### Formula
**Omega_geo = 3 GM v / (2 c^2 r)**
- *M* = central mass
- *v* = orbital velocity
- *r* = orbital radius
For a satellite at 630 km altitude around Earth, this is about 6.6 arcsec/year. Gravity Probe B confirmed this to 0.28% accuracy.
A gyroscope orbiting a massive body precesses due to the curvature of spacetime, even if the central body is not rotating.
### Formula
**Omega_geo = 3 GM v / (2 c^2 r)**
- *M* = central mass
- *v* = orbital velocity
- *r* = orbital radius
For a satellite at 630 km altitude around Earth, this is about 6.6 arcsec/year. Gravity Probe B confirmed this to 0.28% accuracy.
Exemple Résolu
Satellite at 7000 km from Earth centre, v = 7545 m/s.
- Omega = 3 * 6.674e-11 * 5.972e24 * 7545 / (2 * 8.988e16 * 7e6)
- Numerator = 3 * 3.986e14 * 7545 = 9.019e18
- Denominator = 2 * 8.988e16 * 7e6 = 1.258e24
- Omega = 7.17e-6 rad/s ... wait, let me recompute
- Omega = 9.019e18 / 1.258e24 = 7.17e-6 -- this needs checking