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The sun, being a ball, projects its EM radiation and light in all directions. We earthlings only receive a light from a portion of the sun, not all of it. What size is this patch of the sun's surface that sends light across 93m miles of space?

EDIT - There was a faulty premise in my question. We receive heat from all portions of the sun which are visible to us since EM propagation happens in all directions, not just most earth facing portion of the suns surface. Thanks for the thorough comments!

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  • $\begingroup$ You want the area of the sun thats visible, or want to know how much total radiant energy the Earth receives? Patch of the sun's surface is a little strange... The patch is what you can see looking at the sun in the sky (don't do it! ;) $\endgroup$ – anon01 Dec 1 '15 at 5:21
  • $\begingroup$ The "patch" is equal to the central cross section of the sun. The visible equal brightness over the whole cross section shows that the cosine law holds. $\endgroup$ – Dr. Wolfgang Hintze Dec 1 '15 at 6:43
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We receive energy from the entire hemisphere of the sun which faces us (offset by a very small angle corresponding to the 8 minute travel time of light divided by the rotation rate of the sun). For proof, go outside on a sunny day and look at the sun. You see the entire disk, not just some tiny portion.

What you may be thinking of is the fraction of the sun's total output which reaches us, projected onto the sun's surface, and that can be calculated. The earth has a diameter of 12,756 km, and an orbital radius of about 150 million km. The radius of the sun is about 0.7 million km. So the apparent diameter of the earth projected on the surface of the sun is $$D = 12,756 \times{\frac{0.7 \text{ million}}{150 \text{ million}}} = 59.5 \text{ km}$$ The problem with this approach is that light from the sun is not exclusively emitted perpendicular to the surface of the sun, but is emitted in all directions.

EDIT - And I see from comments that my throwaway about proving that we see the entire sun rather than a patch has been criticized as circular. However, when I stated that "You see the entire disk", I assumed that it is well-known that stars and planets can be seen outside the visible disk. If we were only seeing part of the sun, the invisible portion would also block the light from those objects on the far side of the sun. This invisible portion (assuming a spherical sun) would form a dark ring around the sun. Since no such ring is observed, what we see comprises the entire sun, and the fact that we can see it as a disk of approximately uniform brightness demonstrates that light from the entire hemisphere reaches us. There is no circularity of reasoning involved. END EDIT

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    $\begingroup$ +1, but your proof is, if you'll excuse the pun, circular. You tell the OP to go out and look at the sun. You assert that what he sees is the entire hemisphere (and not just "the circular patch of the hemisphere that reaches us"), and then use that to prove that light from the entire hemisphere reaches us. $\endgroup$ – yshavit Dec 1 '15 at 7:47
  • $\begingroup$ @JohnForkosh - Curse those pesky orders of magnitude! I've edited. Thanks. $\endgroup$ – WhatRoughBeast Dec 1 '15 at 16:19
  • $\begingroup$ @yshavit and everybody who supports his comment - see edit. $\endgroup$ – WhatRoughBeast Dec 1 '15 at 16:34
  • $\begingroup$ @WhatRoughBeast I'm still not sure I buy it. When's the last time you looked at/near the sun and saw any star that was nearishly behind it? In the daylight, the only light you see (in any meaningful sense) near the sun is from the sun, either directly or as it bounces through Earth's atmosphere. I think things would look about the same as they do now if we only saw a small patch of it, except of course that it would mean the sun is actually much bigger. And that it's made of lasers. :) Disclaimer: I'm not a real physicist. $\endgroup$ – yshavit Dec 1 '15 at 17:26
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    $\begingroup$ @yshavit - While it's true the sun very bright, which makes it hard to see things close to it, there are some objects which can be seen. Specifically, comets which pass close behind the sun can be observed very close indeed - since they are near the sun and reflecting the sun's light, they are almost as bright as the sun itself. See this video nasa.gov/mission_pages/sunearth/news/comet-lovejoy.html for instance, and if you step through you'll see the comet emerge with almost no separation as it becomes visible. $\endgroup$ – WhatRoughBeast Dec 1 '15 at 17:59

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