We were tobogganing early this morning when this picture was taken–in fact it was so early we had the entire hill to ourselves. Because of the perfect cloud cover, not thick enough to obscure the sun but enough to take away its rays, the sun looked like the moon. After struggling to photograph it, the pale disk reminded me that because the moon and the sun are almost of the same apparent diameter in the earth sky, it implies that the sun’s real diameter is equal to that of the moon multiplied by the ratio of the earth-sun distance to that of the earth and the moon. I had the same unoriginal but very exciting thought last spring, and I did the math while sitting in church. I reasoned that if there is a God, I’m sure he likes astronomy, so he would not mind the transgression.
In church, I remembered that the moon was about 225 000 miles from the earth compared to about 93 million miles for the astronomical unit (earth-sun distance). 93 000 000/225 000 without a calculator was close to 400. Our planet is about 4 times bigger than the moon, which puts the sun-diameter at about 100 earth diameters. The diameter of the earth is about 24000/ π miles*1.6 km /mile, so the sun is approximately 100* 24000/π *1.6 km in diameter.
After church, I confessed to my wife and daughter that although I heard most of the sermon, I had also estimated that the sun was 200 *24000/π*1.6 km wide. I mentioned that if God exists he likes astronomy and would not mind my wandering thoughts. On our way home, I pulled the calculator out of the glove compartment and 100 *24000/π*1.6 yields a diameter of 1 220 000 km corresponding to a radius of 611 000 km.
If we use the more accurate earth-sun distance of and the corresponding earth-moon distance of 384 400 km, we get the sun equaling 389 moon diameters. The real earth-moon ratio is 6378.1 km/ 1737.4 km = 3.67 km. So the sun would be 389/3.37 = 106.1 earth diameters wide. This spells out a radius of 106.1* 6378.1 km* 2 = 676 148 closer to the expected value of, an error of 2.8%.
In reality, the sun appears to be 31/60 degrees in the sky. The moon is only 30/60 degrees wide. The assumption that they are equal introduces an error of 1/60 = 1.7%.
predicts a radius of 0.266 degrees which corresponds to an apparent diameter for the sun of 0.532 or 32/60 degrees.
For more simple astronomy calculations see
Sciences in the Mural of Life 