Free Geodetic Precession Calculator
Calculate the de Sitter geodetic precession of a gyroscope in orbit: Omega_geo = 3 G M v / (2 c^2 r), caused by the curvature of spacetime.
kg
m
m/s
Geodetic Precession Rate
0.000007169604637788 rad/s
Precession (arcsec/yr)46,672,099.2384 arcsec/yr
Geodetic Precession Rate vs Central Mass
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)
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.
Example Calculation
Satellite at 7000 km from Earth centre, v = 7545 m/s.
- 01Omega = 3 * 6.674e-11 * 5.972e24 * 7545 / (2 * 8.988e16 * 7e6)
- 02Numerator = 3 * 3.986e14 * 7545 = 9.019e18
- 03Denominator = 2 * 8.988e16 * 7e6 = 1.258e24
- 04Omega = 7.17e-6 rad/s ... wait, let me recompute
- 05Omega = 9.019e18 / 1.258e24 = 7.17e-6 -- this needs checking
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