How would a metal bar built around the world react to gravity?
If this band is made of ferrous metal, you’ll get interactions with the magnetic field in addition to gravity. Let’s make a couple assumptions: -Get rid of the Earth and replace it with a gravity source of equivalent magnitude that is infinitely small. -The band is a perfect circle with its center exactly coinciding with the point gravity source -The gravity of the band is negligible compared to the gravity source. -The entire universe is comprised of the gravity source, the band, and nothing else. If these conditions are met, I would argue that the band stays perfectly still, centered on the gravity source. In the real world, I think one of several things could happen: -The band will be large enough that its own gravity will cause it to collapse. -It’s really next to impossible to perfectly center the band around the gravitational center of the Earth, so one side will get a stronger pull than the other and it will crash in to the Earth. Any other imperfections will cause the same. Ass
It’s true that the overall force of gravity on said solid ring would be neutral. But there would be compressive force on the ring. What you have is something akin to the arch of an arch bridge, which is held up by the compressive strength of the material from which it is built. (An ideal arch bridge is a subsection of an ellipse which has one focus at the center of gravity of the planet.) If the force on the arch (due to weight and loading) exceeds the compressive strength of the material, it collapses. Equally, if the compressive force on your hypothetical ring exceeds the compressive strength of the steel from which it is made, it buckles and collapses. And it turns out that’s what would happen, because the compressive force of a ring that large would exceed the compressive strength of all known materials — by a very large margin.
ssg, your argument from the thought experiment is very elegant and convincing, but I think it may have a problem, even though it leads to a correct qualitative result in the case of the ring; namely, it seems to work equally well for a spherical shell (imagine a massless spherical shell with two point masses at the antipodes, and etc.), and we know that the spherical shell will not be drawn toward the Earth if we move it off center. The difficulty seems to be one of dimension. Points don’t necessarily add up, even infinitely, to a sphere– or a ring. Vacapinta’s link is careful to frame the argument in terms of adding up (integrating) balanced segments whose length approaches zero in the case of the ring, and little balanced caps whose area approaches zero in the case of spherical shells. If the force of gravity were to vary by the inverse of the distance rather than the inverse square, your argument would predict that the nearer part of the ring would still be pulled toward the Earth
