Frame Dragging Calculator Formula

Understand the math behind the frame dragging calculator. Each variable explained with a worked example.

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Formulas Used

Precession Rate

precession_rate = 2 * 6.674e-11 * angular_momentum / (pow(2.998e8, 2) * pow(orbital_radius, 3))

Precession (mas/yr)

precession_masyr = 2 * 6.674e-11 * angular_momentum / (pow(2.998e8, 2) * pow(orbital_radius, 3)) * 180 / pi * 3600000 * 3.156e7

Variables

VariableDescriptionDefault
angular_momentumCentral Body Angular Momentum (J)(kg m2/s)7.07e+33
orbital_radiusOrbital Radius(m)7000000

How It Works

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.

    Worked Example

    Satellite at 630 km altitude around Earth (r = 7e6 m, J_Earth = 7.07e33 kg m2/s).

    angular_momentum = 7.07e+33orbital_radius = 7000000
    1. 01Omega = 2 * 6.674e-11 * 7.07e33 / (8.988e16 * 3.43e20)
    2. 02= 9.437e23 / 3.083e37
    3. 03= 3.061e-14 rad/s
    4. 04In mas/yr: about 39 mas/yr

    Frequently Asked Questions

    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.

    Ready to run the numbers?

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