# How small would the patch of sun be that delivers heat to the earth?

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!

• 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! ;) – anon01 Dec 1 '15 at 5:21
• 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. – Dr. Wolfgang Hintze Dec 1 '15 at 6:43

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.