Yes, we fly anywhere on earth and earth (or the earth) is the third planet from the sun. " Earth at the moment is the only astronomical body ,where life is proven to exist." Notice here that 'earth' is defined as 'the astronomical body", so the definite article 'the' is already used and no need to use it twice ,that is why it is left out to avoid repetition. " The physical properties of the earth allowed life to persist on it so long." Here it is optional to use the definite article or to omit it. Assuming that there is only one earth , the noun is definite and unique by its definition,so the usage of the definite article 'the' could many times be redundant in context. Here 'earth' has the sense of being a planet, like Mars ,Venus etc.. When it means the land we live on, the definite article is more likely to be used. It could be left out sometimes and other times used for the proper syntax of the sentence.

Rule: planet names have no "the" Mars; Saturn; Jupiter; etc When referring to the Earth as a planet, we say "Earth". When referring to the Earth as our home we say "the Earth". Examples: Earth is a planet The Earth is ALSO a planet. (because it is our home first)

You can omit "the" and it still sounds right, since "Earth" can act as the planet's name. So, just how you don't say "the" before a person's name, you can omit it. Now that I think about it, only "Earth" and "Sun" ever have "the" possibly before them. You would never say "the Mars" or "the Jupiter" etc. For Earth and Sun you can put "the" before it or not, both are correct, but don't put "the" before any other planets.