My instinct--what, you're expecting calculations here?--is that there's no such stable orbit as "far above the ecliptic" and "fixed in position wrt the earth."
I do know the calculations and you are definitely correct. :-)
But couldn't you shoot a probe far above the ecliptic, in an "orbit" that's fixed relative to the Sun, and another fixed relative to the Earth, and then see which one takes more fuel to keep itself in position? Seems like that should be a valid proxy for finding the true "objective fixed observer". (Recognizing that the solar system itself is in transit towards - Vega, is it?)
Just what would a "fixed position" mean, anyway? Some least-squares summation of change in vectors between the object and every other visible object in the universe? (Or at least a representative sample of stars in this galaxy?)
In opera, it's the soparano. She stands still and the whole universe revolves around her.
I am a bit confused on this one. What do you mean "fixed relative to the Sun"? One thing thatis interesting is that you can use the Earth as a fixed point of reference (or the moon, sun, galaxy etc.) instead of the center of the solar system.