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计算弯曲时空中陀螺仪的测地线进动角。
Geodetic Precession Rate
0.000007169604637788 rad/s
Geodetic Precession Rate vs Central Mass
公式
## 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.
计算示例
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
常见问题
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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