### How much mass does the Earth gain from sunlight?

The luminosity of radiant energy is 4 x 10^33 ergs/sec. Since 1 gram is worth 9 x 10^20 ergs, sunlight equals 4 x 10^12 grams/second or 4.4 million metric tons of equivalent mass per second .This is radiated over a sphere equal to the radius of the earths orbit 147 million kilometers in radius or 2.7 x 10^27 square centimeters. The Earth's cross section is 1.3 x 10^18 square centimeters, so the ratio of the total mass per second, to that intercepted by the earth is 1.9 kilograms/sec. During the entire life of the sun...4.5 billion years, the earth has gained 2.7 x 10^17 kilograms, which is only 1/21 millionth of its mass. The problem is that the earth is in thermal equilibrium with the sun at this distance, which means that whatever energy or mass-equivalent it gains, it also looses by re-radiating this energy in the infrared spectrum. So, the net gain is only a small fraction of what it receives given that it is not a perfect black body.