So, if a clock is seen from the Sun's perspective as revolving around the Earth (at the right speed and direction), its worldline is longer than the one of a stationary clock (in the same frame), but if the clock is revolving around the Sun, its worldline is shorter than the one of a stationary clock. For me it's quite confusing ... (I'm not saying that it's wrong, just that it is confusing), so I'll try again without worldlines:The rotating worldline referred to above is one that is going around a rotating object at the right speed and direction to minimize time dilation. Due to rotational frame dragging this is not a stationary worldline, but one that slowly revolves around the central object. This scenario was identified in the Wikipedia article on frame dragging.
It is not a clock orbiting the sun at 1 AU. So my comment was correct, that worldline is longer,
From Sun's perspective, I see a clock revolving (at the right speed and direction to match the frame dragging) around the stationary/hovering Earth and another clock stationary (in the same - Sun's - frame), and contrary to everything I know, the stationary one is more time dilated than the moving one, while the gravitational time dilation is the same, both clocks being at the same distance from de Earth/Sun. That makes me think that a clock being in that rotational dragged frame is "more stationary" than the one that appears stationary from Sun's perspective. Now, if the Earth is orbiting the Sun, that frame is co-moving with it (while dragged around the Earth) and the question is if a clock stationary in the dragged frame would be influenced by the orbital speed of the Earth around the Sun, or not, being again "more stationary" that it appears to be.
Ok, but how are these tests/examples related to my scenario? How can we measure/detect, without atomic clocks, the way is time passing on the surface of a distant massive body?GR has already been tested for multi-body systems, using numerical solutions. The solar system and binary pulsar systems are two well known examples.