Do particle accelerators have to adjust for the sun's gravity due to length contraction? I believe particle accelerators move atoms at 99.999% the speed of light.  If the accelerator was oriented perpendicular to the sun, a particle moving at this speed would experience sizable length contraction in the direction of the sun. I calculated the normal gravitational acceleration of the sun at the radius of earth's orbit is 0.005 m/s2.  At 99% the speed of light the length contraction is 1/7 (the effective radius is 1/7 the radius of our frame of reference).  At 99.9% the contraction is contraction is 1/22 and when the earth's orbital radius is adjusted by this factor the gravitational acceleration is 0.27 m/s2.
There would be no such increase in the gravity experienced from the earth since the accelerator is parallel to the earth's surface.
At 99.99% the acceleration is 2.6 m/s2 and at 99.999% we have 26.8 m/s2, which is 2.6 times earth's gravity at the surface.
My question is do the operators of CERN, etc., have to account for these effects?  Have they been able to measure them?  I am thinking that even though the force is stonger than the earth's gravity the particle is moving too fast for the force to have any noticeable effect.  Also, the circular motion of these accelerators would make it difficult to detect and wold tend to cause the effect to cancel out, but it still might be possible to detect slowing/speed up on one axis.
Also, I know there have been linear accelerators.  Did length contraction and the sun's gravity have any measurable impact on these accelerators?
If this is not a concern or measurable effect I would be curious why.
 A: I'm not sure where you are getting the idea that length contraction means a larger acceleration from gravity, but it doesn't really matter anyway. The magnetic force on a single proton in the LHC, which has a field strength of $8.33~\rm T$ is about $4\times 10^{-10}~\rm N$. Comparatively the force of gravity of the earth on the same proton is around $1.6\times 10^{-26}~\rm N$, and the force of the sun's gravity is even less. Either way, gravitational force is utterly negligible to a relativistic particle in a particle accelerator.
Interestingly, the gravitational force of the sun and moon on the accelerator itself is much more important. The changing force of gravity on the accelerator causes its length and shape to shift ever so slightly with the tides, and this forces the LHC operators to re-tune the machine as the tides change. You can read more about that here.
A: I assume you are talking about the effect of Lorentz transformations on forces and acceleration (see this wiki, for example).
If we, the experimenters, are performing measurements from the lab frame on Earth, then the force exerted by the Sun on the particles would not be affected by this large Lorentz $\gamma$ factor. Only if we consider a reference frame, which is boosted at high velocity with respect to the Sun, would we observe such high values of the acceleration due to the Sun's gravitational force.
I assume experimentalists would not need to take into account such a small effect.
