This is a continuation of https://www.physicsforums.com/showthread.php?t=526249", now that my confusion on Thomas precession has been clarified and my root question has been shown to not stem from this effect.(adsbygoogle = window.adsbygoogle || []).push({});

In classical mechanics for any inverse square force, [itex]\vec{F}=-\frac{C}{r^2}\hat{r}[/itex], one has the Laplace-Runge-Lenz eccentricity vector. This is a constant of motion and has the magnitude of the eccentricity and points from the center of attraction towards the periapsis.

[tex]\vec{e}=\frac{\vec{L}\times \vec{p}}{mC} + \vec{r}[/tex]

For the argument's sake, let's consider a charged mass in orbit about a much more massive oppositely charged mass under Coulomb's law ([itex]C=kQq[/itex]), with a speed high enough that the SR effects are significantly larger than the effects of the curvature of space-time from the mass-energies involved.

Q1) How much precession would such an orbit have in SR? Is this twice the excess in the angle [itex]\theta[/itex] given on http://en.wikipedia.org/wiki/Laplac...lizations_to_other_potentials_and_relativity" evaluated between two consecutive apsis?

Q2) Is this the "Newtonian Model" that I have heard predicts half of the observed precession of Mercury (without clarification and attributed to Einstein), or does that model include a change to the inverse square law force due to the relativistic energy of the orbiting body? Half of the first order estimate of the DeSitter precession in GR would be [itex]\delta=\frac{3\pi C}{c^2rm_0}[/itex], [itex]C=GMm_0[/itex] and r being the semi-latus rectum of the precessing ellipse.

Thoughts) My guess is that the first order SR precession defined above is [itex]\delta_{SR}=\frac{\pi C}{c^2rm_0}[/itex], with an additional [itex]\delta_{E=mc^2}=\frac{2\pi C}{c^2rm_0}[/itex] when the classical effects of Newton's theorem of rotating orbits is considered with the inverse square law adjusted by replacing the rest mass with the relativistic energy. I believe I have worked out the second half of this previously (http://farside.ph.utexas.edu/teaching/336k/Newton/node45.html" [Broken]), but need to relocate those notes. I may have the factor of two in the wrong component, or my guess might be completely off base.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Precession of the LRL Vector in SR

Loading...

Similar Threads for Precession Vector |
---|

I Calculating Killing vectors of Schwarzschild metric |

I Geometric meaning of complex null vector in Newman-Penrose |

I Locality of a vector space |

I Basis vectors and inner product |

I The relativistic de Broglie equation |

**Physics Forums | Science Articles, Homework Help, Discussion**