Pretty much every mention of Earth on this site will be referring to the celestial body, the planet Earth. So in my opinion, just as it is weird to say the Jupiter, it is weird to say the Earth.
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When the Earth is spoken of as a physical body, occupying space-time, it's normally preceded by the article, and often capitalised. As are Sun and Moon, but there's no universality about either convention, nor is capitalisation necessarily governed by whether the article is present or not. I've capitalised every usage after the article (as do most people), but there are exceptions.
When Earth is used more "metaphorically" to mean our whole environment (really, just the thin skin of biosphere on the surface of the planetary body, where nearly all things that concern us take place) it's more normal to omit the article, and I wouldn't normally capitalise either.
Note that despite the last clause, FumbleFingers did indeed capitalise Earth without its definite article, and so would I)