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What would day and night look like on Earth (or any habitable planet), if the sun was torus shaped, with the same circumference?

And moreover, how much the Earth will be affected, if the sun was rotating on y-axis, vertically?

Additional info if it helps:

  • The sun is seen from the earth, as a torus.
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  • $\begingroup$ And what would be the axis of rotation of this sun? $\endgroup$
    – Alexander
    Dec 4, 2021 at 1:40
  • $\begingroup$ Sorry my bad... for not specifying the axis. Hope it's a little bit clear now. $\endgroup$
    – user91795
    Dec 4, 2021 at 1:45
  • $\begingroup$ a little bit more clarity is needed - how the sun is seen from the Earth - as a torus, or as an oblong rectangle (a torus laying on its side)? Also, how would the visible size of this torus correspond to visible size of the Sun today? $\endgroup$
    – Alexander
    Dec 4, 2021 at 1:48
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    $\begingroup$ On Earth, brightness of the day and warmness of the summer depend on how luminous is the Sun, and that depends on its visible size. If Sun turns into a torus which is exactly the same circumference as the old Sun, then its luminosity would decrease, and Earth would become colder. How much decrease - depends on how thick is this torus. $\endgroup$
    – Alexander
    Dec 4, 2021 at 2:13
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    $\begingroup$ The temperature of the Earth depends on how much the Sun's surface is radiating toward Earth and the amount of energy/surface the Sun is producing. If you make your Sun like a torus, (a) the surface of the Sun will increase, so (assuming the Sun produces the same amount of energy) its temperature will decrease and (b) less of the Sun's surface will face straight towards Earth (e.g. the surface of torus central hole won't radiate straight towards Earth). $\endgroup$ Dec 4, 2021 at 7:17

2 Answers 2

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Q: "how much the Earth will be affected, if the sun was rotating on y-axis, vertically?"

Solar seasons

Depends on the thickness of the torus, but assuming the sun looks flatter or rounder, it would cause variation in the amount of solar energy that reaches the planet. A periodic variation in effective sunlight will cause solar seasons on all planets. These solar seasons will be superimposed on the seasons your planet already experiences from its tilted axis. Some winters become extremely cold, some summers could be extremely warm, because of the additional effect of sun phase.

Danger, depending on the sun's internals

Certain harmful types of radiation/ionization could occur in the plane of the torus. An asymmetric sun, rotating extremely fast, can emit dangerous, high speed flares that reach the planet atmosphere. When the torus is visible as a rectangle (the planet being in the plane of the torus) more of these events will occur.

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Colder

The light we receive from the Sun depends on its temperature and its apparent size in the sky, but not much else. For example, the edges of the Sun don't seem bright, because even though we are looking at a much larger surface area, we're seeing it at an angle. If we were nearer to the Sun it would take up more size in the sky, but any individual part would seem the same brightness, just as a light bulb doesn't seem like it gets brighter if you closer to it.

Your torus model is a Sun with a hole, or a Sun that has the same radius in one direction but much less (unspecified) in another. So we get much less light. For reference, Mars is at 1.52 AU; the inverse square is 43%, and a little outside of the habitable zone. If your torus occupies less than half the apparent area of the Sun, your Earth will be in deep trouble. Something much less dramatic will still cause an Ice Age, at least - even esoteric variations in Earth's real orbit and axial tilt have been blamed for as much.

If your Sun is rotating very rapidly so that Doppler effect is relevant, this answer could change, but I'm not sure in what direction. I don't seriously have a model for a toroidal star. I'm also assuming the surface temperature (color) is the same as ours; if you make it a hotter star you can compensate, at the cost of a bluer sunset.

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