<p>An effect, but not a noticeable effect.</p>
<p>Wikipedia gives a formula for the frame-dragging in a a Kerr metric:
<span class="math-container">$$\Omega = \frac{r_{s} \alpha c}{r^{3} + \alpha^{2} r + r_{s} \alpha^{2}}$$</span></p>
<p>where <span class="math-container">$\Omega$</span> is the angular speed that the frame of reference rotates at,
<span class="math-container">$r$</span> is the orbital radius (70 billion metres for Mercury), <span class="math-container">$r_s$</span> is the Schwartzchild radius of the sun (3000 m), <span class="math-container">$c$</span> is the speed of light and <span class="math-container">$\alpha = \frac{J}{Mc}$</span> is the angular momentum of the sun divided its mass and the speed of light. For the sun <span class="math-container">$\alpha\approx 320$</span> metres.</p>
<p>Plugging these values in gives <span class="math-container">$\Omega \approx 10^{-18}$</span> radians per second.</p>
<p>This isn't noticeable (compared to other relativistic effects and Newtonian perturbations) Frame dragging can be detected in carefully designed experiments on Earth satellites since the effect is greater at smaller orbit radius.</p>

CC BY-SA 4.0
2021-06-05T15:28:53.167Z
I'm not sure I get the meaning of $\Omega$.
Deschele Schilder
CC BY-SA 4.0
2021-06-05T18:00:06.003Z
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.
Pierre Paquette
CC BY-SA 4.0
2021-06-05T14:27:30.427Z
2021-06-05T14:33:45.400Z
2021-06-05T14:33:45.400Z
James K
<p><a href="https://en.wikipedia.org/wiki/Frame-dragging#:%7E:text=Frame%2Ddragging%20is%20an%20effect,%E2%81%A0%E2%80%94%20rotating%2C%20for%20instance." rel="nofollow noreferrer">Frame-dragging</a> 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.<br />
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).</p>
<p>So I was wondering. Does the sun have a noticeable frame-dragging effect on the planets?</p>

CC BY-SA 4.0
2021-06-05T23:16:06.970Z
you can also read about other instances of frame dragging in Space Exploration SE: https://space.stackexchange.com/search?q=%22frame-dragging%22
uhoh
<the-sun><planet><general-relativity>
Does the sun have a notable frame-dragging effect on the planets?
Deschele Schilder
# Does the sun have a notable frame-dragging effect on the planets?

(Asked by: username_0 on 2021-06-05)

[Frame-dragging](https://en.wikipedia.org/wiki/Frame-dragging#:%7E:text=Frame%2Ddragging%20is%20an%20effect,%E2%81%A0%E2%80%94%20rotating%2C%20for%20instance.) 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?

**Tags:** the-sun, planet, general-relativity
> **Comments:**
> **username_1**: you can also read about other instances of frame dragging in Space Exploration SE: https://space.stackexchange.com/search?q=%22frame-dragging%22  

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## 1 answers

### Answer by username_2 on 2021-06-05. Score: 2 | Accepted answer

An effect, but not a noticeable effect.

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.

This isn't noticeable (compared to other relativistic effects and Newtonian perturbations) Frame dragging can be detected in carefully designed experiments on Earth satellites since the effect is greater at smaller orbit radius.

> **Comments:**
> **username_0**: I'm not sure I get the meaning of $\Omega$.  
> **username_3**: 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.  

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