# Does the sun have a notable frame-dragging effect on the planets?

Frame-dragging is a general relativistic effect that can be imagined as the effect that the momentum of mass-energy has (the stress elements in the stress-energy tensor) on mass-energy in the surroundings of the moving mass-energy.
For example, a large moving sheet of mass will cause particles to be dragged along in the direction of motion of the sheet (on top of gravitating towards the sheet).

So I was wondering. Does the sun have a noticeable frame-dragging effect on the planets?

Wikipedia gives a formula for the frame-dragging in a a Kerr metric: $$\Omega = \frac{r_{s} \alpha c}{r^{3} + \alpha^{2} r + r_{s} \alpha^{2}}$$
where $$\Omega$$ is the angular speed that the frame of reference rotates at, $$r$$ is the orbital radius (70 billion metres for Mercury), $$r_s$$ is the Schwartzchild radius of the sun (3000 m), $$c$$ is the speed of light and $$\alpha = \frac{J}{Mc}$$ is the angular momentum of the sun divided its mass and the speed of light. For the sun $$\alpha\approx 320$$ metres.
Plugging these values in gives $$\Omega \approx 10^{-18}$$ radians per second.
• I'm not sure I get the meaning of $\Omega$. Jun 5 at 15:28
• It’s “the angular speed that the frame of reference rotates at,” in other words, the effect imprinted on the planet. The quoted value of $10^{-18}$ radians per second is about $\frac {6}{10000}$ arcsecond per century; indeed, not noticeable. Jun 5 at 18:00