Let m * v^2 = k * T, where m is the electron mass, k is Boltzmann's constant, and T is the cosmic background temperature = 2.73K. Then v = escape velocity (velocity of escape from the sun) at 42.9 AU. One obtains the above formula by modifying the Maxwell distribution formula for the root-mean-square speed, to give the (r.m.s.) velocity component in one direction only, e.g., parallel to the solar system's magnetic field lines (because the two components perpendicular to the field lines would be ineffectual in helping the electron escape). Because the states are so uncrowded, the Maxwell distribution doesn't need to be modified for fermion statistics.
Let the speed parallel to the field line be "vx". Another estimate would use mean(abs(vx)) because a group of electrons, once agitated by the background temperature and moving in the same direction along the field line, might then tend to equalize their speeds with each other. This would correspond to a distance of pi/2 * 42.9 AU = 67.4 AU. Solar radiation pressure and solar wind would tend to reduce the effective escape velocity and thereby reduce the 67.4 AU figure.
Yuri Galaev's recent experiments indicate that the "ether", whatever it is, travels, in a sense, at the same speed as the dominant transparent physical medium such as air. In the above, free electrons are treated as the physical medium.
The solar system would seem to sit in a spherical block of ether of radius 53 AU. Pioneer 10 tracking indicates that special-relativistic time dilation depends on whether the source is inside or outside this block: if outside the block, then the operative relative velocity of source and observer, for the time dilation calculation, is that which pertains when the light enters the block, not when the light reaches Earth. Two star occultations by Saturn's rings, reported in Alexander, showed flickering position (or fused flickering) of the order of 0.1 arcsecond, as if the aberration of light is analogously affected, by whether the light arrives directly from the star (operative relative velocity is that when the light enters the block) or interacts with transparent gas in Saturn's rings (operative relative velocity is that when the light reaches Earth). Both Pioneer 10 and Saturn lie near the ecliptic; also for sources away from the ecliptic, the Kimura (1902) phenomenon confirms, to 30% accuracy, similarly altered aberration due to the 53 AU barrier.
At 53 AU, the equilibrium temperature of solar radiation is much higher than the cosmic background temperature. If the solar radiation temperature isn't involved, then Earth should have a barrier at 67.4 AU / 333,400 = 18,790 mi. from its center. The electron maximum of the outer Van Allen electron belt (Enc. Americana 1998) is, in Earth's equatorial plane, 17,630 miles from Earth's center.
For Mars, the barrier would be at 2010 mi; Mars' radius is 2110 mi. Apparently a solar system body has a strong magnetic field if, and only if, it rotates rapidly and is more massive than Mars.
