exupero's blog

Toroidal interior

In the previous post I discussed some visual phenomena as observers approached 90°N. The sights get more interesting as the trip continues into the interior.

While on Earth latitudes range from 0° at the equator to 90° at the poles, on a torus it's convenient to think of latitude as being from 0° at the outer equator to 90° at the polar rim to to 180° at the inner equator. This means that even though our explorers pass 90°N and start heading south, their latitude continues to increase.

As they go, the far side of the torus becomes increasingly noticeable in the sky. Exactly how it looks depends on the torus's axial tilt and the sun's apparent size. In the absence of axial tilt (which I've assumed so far), the interior always falls within the torus's penumbra and only receives partial light all year long, but how much of the interior is in the umbra and receives no light at all depends on how large and how close the sun is. For an Earth-like orbit around a Sun-like star, most of the interior falls under perpetual solar eclipse from the sunward side of the torus:

sun →

This permanent arctic night means that though our explorers are headed south after they pass 90°N, the temperature continues decreasing as latitude increases.

With an interior completely in the torus's own shadow, all our explorers see of the far side is a tiny limb of sunlight and complete black. They could be excused for thinking they were looking at a distant mountain range. As they continue south, the darkness blocks out more and more of the night sky, until eventually the occlusion lifts from the ground ahead and stars become visible beneath it.

If any resident scientists are still reluctant to adopt a toroidal solution to such phenomena, they might suppose their world has a partial planetary ring that hovers over only one side of the sphere. But why the equator has a day/night cycle and the seeming opposite side of the world doesn't should give them pause. We'll explore that more in the next post.