Kostenloser Geodetic Precession Rechner
Berechnen Sie den geodetic (de Sitter) precession of a gyroscope in orbit. Kostenloser general relativity Rechner.
Geodetic Precession Rate
0.000007169604637788 rad/s
Geodetic Precession Rate vs Central Mass
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)
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.
- 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
Häufig Gestellte Fragen
What is the difference between geodetic precession and frame dragging?
Geodetic precession comes from the curvature of spacetime around a non-rotating mass. Frame dragging is an additional effect caused by the rotation of the central body. Geodetic precession is about 170 times larger near Earth.
Can geodetic precession be observed on Earth?
The Gravity Probe B mission measured it to high precision. The Moon-Earth system also shows geodetic precession, measurable via lunar laser ranging.
Does this affect GPS?
The effect is tiny for GPS but is important for precision experiments and for understanding orbits around compact objects like neutron stars.
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