In a shell, some of the material is above the planet and some below. In this case all the material is below the planet (which is not on the torus' plane, but an Earth radius away from it, all the material pulls toward the same direction, not in opposite directions). The only difference from...
The center of mass of the slender torus is at the same distance from the planet as Earth is from the sun and the masses are the same, yet the force is not the same, just like the luminosity is not the same.
According to all formulae, density and geometry play no role on gravity, only mass.
Do you think that the force Earth exerts on you is the same as the force you exert on Earth? although the resultant force is the same, the components of the force are clearly different.
No it's not for a science fiction story. Why should anyone care about young Einstein riding on a light beam? Thought experiments allow us to look from a different perspective
Thanks, I chose too small a diameter for the neon tube. However, the point is that density and geometry clearly influence luminosity and gravity. In this case the star would never be seen nor its gravity felt by the astronomer (the planet does not orbit the star) and the star hardly distorts...
Perimeter is the length of the tubing making up the torus, measured along the center of the tube's section. One can think of a doughnut of 1 mm diameter tubing and 10 to 28 km long as a line, instead of a 3d body.
All photons from the sun arrive from a relatively small area and close to Earth, so we see and feel the sun (unless there is an eclipse, once in a long while). In contrast, photons from the torus arrive from myriad directions and from an extremely long distance (any particle of dust, etc...
Imagine a planet similar to Earth, but exposed to a completely different star. The star has the same mass and emits the same amount of photons as the sun, but it is a huge, extremely slender torus made of 1 mm diameter neon tubing. The planet is on the axis of the torus and at the same distance...