Lense-Thirring Precession Calculator
Lense-Thirring Precession Calculator finds orbital precession rate due to frame-dragging, with a plot.
Formulas Used in Lense-Thirring Precession Calculator
The calculator computes the Lense-Thirring precession rate for an orbit around a rotating body:
Precession Angular Velocity:
\\[ \Omega_{\text{LT}} = \frac{2 G J}{c^2 a^3 (1 – e^2)^{3/2}} \\]Precession Period:
\\[ T_{\text{LT}} = \frac{2\pi}{\Omega_{\text{LT}}} \\]Where:
- \\(\Omega_{\text{LT}}\\): Precession angular velocity (rad/s)
- \\(G\\): Gravitational constant (\\(6.67430 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2}\\))
- \\(J\\): Angular momentum of the primary (kg·m²/s)
- \\(c\\): Speed of light (\\(2.99792458 \times 10^8 \, \text{m/s}\\))
- \\(a\\): Semi-major axis (m)
- \\(e\\): Orbital eccentricity (dimensionless, \\(0 \leq e < 1\\))
- \\(T_{\text{LT}}\\): Precession period (s)
Example Calculation
Example: Earth (\\(M = 5.972 \times 10^{24} \, \text{kg}, J = 7.072 \times 10^{33} \, \text{kg·m}^2/\text{s}, a = 7000 \, \text{km}, e = 0\\))
\\[
\Omega_{\text{LT}} = \frac{2 \times 6.67430 \times 10^{-11} \times 7.072 \times 10^{33}}{(2.99792458 \times 10^8)^2 \times (7000 \times 10^3)^3} \approx 1.03 \times 10^{-14} \, \text{rad/s} \approx 0.019 \, \text{deg/yr}
\\]
\\[
T_{\text{LT}} = \frac{2\pi}{1.03 \times 10^{-14}} \approx 1.92 \times 10^6 \, \text{years}
\\]