According to this answer, energy has some (minimal) mass associated with it. Therefore, when lots of energy hits the earth (such as solar radiation in a 24 hour period) shouldn't the earth gain some small additional mass? And if so, how much?
Answer
There's an answer to your question, but it's not all that meaningful.
The sun strikes the Earth with $1.5\cdot10^{22}J$ of energy every day. Using $m=\frac{E}{c^2}$ we find this has a mass equivalent of 166897kg.
However, the Earth does not actually gain mass this way. The Earth is also radiating energy into space, continuously. If we assume the average , so the amount of energy coming into the system equals the amount of energy leaving the system. As a result, the earth is not gaining mass by this at all. (or if any, its a small amount attributable to global warming).
We also gain about 40000kg of space dust every day, and lose about 95000kg of hydrogen from the atmosphere. You win some, you lose some.
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