# What percentage of the sky could the sun be in?

For every location on earth, there are parts of the sky that the sun can never be in (e.g., directly overhead anywhere outside the tropics).

I think the sun can be in about 40% of the sky (a hemisphere).

I'll withhold my reasoning/calculations for now, because I'd like the opinion(s) of others more-expert (most are) than me in this subject.

Please weigh in. I believe this "simple" geometric question will have been answered centuries ago, but I have not found it as an answer, nor even as a subject.

• You shouldn't withhold your calculations on this. Either your math is correct or it isn't. When asking a question, it is important that you give as much information as you can. – Phiteros Jan 10 '17 at 0:56
• OK - I used sin(23.5) (degrees, the inclination of the axis of the rotation of the earth vis-a-vis the plane of its orbit around the sun). The sun's angle at any given time of day varies by twice that much across the year, but half of that angle is occluded by the earth itself (at night). – N. Joseph Potts Jan 10 '17 at 0:59
• My first thought is "all of it". Consider an observer at the South Pole. Over the course of a six month long summer, the Sun will have painted every bit of the sky at an elevation below 23.5 degrees. That's 40% of the sky right there. Add in strings of observers along the Arctic and Antarctic Circles and the Sun will have painted every bit of the sky at an elevation below 47 degrees. That's 73 percent of the sky. A couple of more strings of observers along the Tropics should get that remaining 27 percent. – David Hammen Jan 10 '17 at 12:24