We live on the earth, which is like a ball.
We live on the earth which is like a ball.
Only the first one is correct. The second one implies that there are a number of earths, only one of which is like a ball. I prefer to capitalise "the Earth".
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Only the first one is correct.
The second one implies that there are a number of earths, only one of which is like a ball.
I prefer to capitalise "the Earth".