Frame Dragging Calculator
Estimate the Lense-Thirring frame-dragging precession rate of a gyroscope in orbit: Omega_LT = 2GJ / (c^2 * r^3), where J is the angular momentum of the central body.
Precession Rate
0.00000000000003061105 rad/s
Precession Rate vs Central Body Angular Momentum (J)
Formula
## Lense-Thirring Frame Dragging A rotating massive body drags the surrounding spacetime, causing gyroscopes to precess. ### Formula **Omega_LT = 2GJ / (c^2 r^3)** - *G* = gravitational constant - *J* = angular momentum of the central body - *c* = speed of light - *r* = orbital radius This effect was confirmed by Gravity Probe B to within about 19% of the predicted value for Earth.
Esempio Risolto
Satellite at 630 km altitude around Earth (r = 7e6 m, J_Earth = 7.07e33 kg m2/s).
- 01Omega = 2 * 6.674e-11 * 7.07e33 / (8.988e16 * 3.43e20)
- 02= 9.437e23 / 3.083e37
- 03= 3.061e-14 rad/s
- 04In mas/yr: about 39 mas/yr
Domande Frequenti
What is frame dragging?
A rotating mass drags spacetime around with it, similar to how a spinning ball in honey drags the surrounding fluid. This is a prediction of general relativity.
How was frame dragging measured?
Gravity Probe B (2004-2005) used four ultra-precise gyroscopes in orbit to detect the tiny precession. The LAGEOS satellites also provided evidence through laser ranging.
Is frame dragging significant near black holes?
Yes. Near a rotating (Kerr) black hole, frame dragging is enormous and creates the ergosphere, a region where nothing can remain stationary.
Impara