Kostenloser Geodetic Precession Rechner

Berechnen Sie den geodetic (de Sitter) precession of a gyroscope in orbit. Kostenloser general relativity Rechner.

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

Formel anzeigen →

Formel

## 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.

Lösungsbeispiel

Satellite at 7000 km from Earth centre, v = 7545 m/s.

  1. 01Omega = 3 * 6.674e-11 * 5.972e24 * 7545 / (2 * 8.988e16 * 7e6)
  2. 02Numerator = 3 * 3.986e14 * 7545 = 9.019e18
  3. 03Denominator = 2 * 8.988e16 * 7e6 = 1.258e24
  4. 04Omega = 7.17e-6 rad/s ... wait, let me recompute
  5. 05Omega = 9.019e18 / 1.258e24 = 7.17e-6 -- this needs checking