Globe Earth question: Percent of the Earth receiving sunlight at a given time

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Discussion Overview

The discussion revolves around the alignment of the daylight region on a 3D model of the Earth with the theoretical 50% of the Earth's surface that receives sunlight at any given time. Participants explore the implications of different viewpoints and the effects of perspective on visibility, as well as the definitions of twilight and daylight in relation to population statistics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants express confusion about why the 50% daylight region does not align with the visible parts of a 3D Earth model, despite attempts to match them.
  • Others note that the viewpoint in the 3D model is likely too close to the Earth, which would limit the visible area to less than 50% of the surface.
  • One participant suggests that achieving a 50% view would require a viewpoint effectively at infinity, where rays from the Sun would be parallel.
  • Another participant questions the necessity of an infinite viewpoint, arguing that the Sun is not at infinity and still illuminates 50% of the Earth.
  • Some participants discuss the mathematical implications of the viewpoint distance needed to achieve a 50% view, suggesting that a compromise distance would yield a view slightly less than 50%.
  • There are mentions of the angular diameter of the Sun affecting the perceived illumination of the Earth.
  • One participant suggests that an orthographic projection of the Earth might be more suitable than a 3D model for this purpose.

Areas of Agreement / Disagreement

Participants generally do not reach a consensus on the necessity of an infinite viewpoint or the exact percentage of the Earth's surface visible in the 3D model. Multiple competing views remain regarding the alignment of daylight regions and the implications of perspective.

Contextual Notes

Limitations include the dependence on the definitions of daylight and twilight, the effects of perspective on visibility, and unresolved mathematical calculations regarding the distance required for a 50% view.

  • #31
This is my analysis and summary of the situation.

It is impossible to see on a 3D model of the Earth, where the 99% of the population, simultaneously illuminated by sunlight or twilight, will be.

That is because the Sun illuminates an extra 0.25° over the horizon due to its angular diameter. The 18° definition of astronomical twilight adds to that, giving 18.25° over the horizon. The part of the sphere that is then deemed to be illuminated is not 180°, but is 18.25° + 180° + 18.25° = 216.5°.

That leaves a dark circle with a diameter of only 360° - 216.5° = 143.5°. That circle, with radius = 71.75°, is centred over the Pacific Ocean above the tropic of Capricorn. The dark circle does not include the populous islands of Japan, Indonesia, or the Philippines, they will probably be in twilight.

What point is on the tropic of Capricorn, at an arc distance of 71.75° from the Japanese coast near Tokyo? Google Earth, Measure, intersects at latitude 23.5°S, longitude 175.464°W, as the approximate centre of the dark circle.

That view of the dark circle looks about right, with Indonesia, Philippines, Japan and California being over the horizon. Only Australia, New Zealand, Papua - New Guinea, Hawaii, many small Pacific islands, and Antarctica are then in the dark. The rest of the world, with 99% of the population, is enlightened.
 
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  • #32
More than one way to skin a cat.

It is possible to see a 3D model of the Earth where a mere 1% of the population are in full darkness. And that's kind of the same thing.
 
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