You can have situations where the entire planet is almost completely rock/ice/water (such as the Earth), or situations where a large amount of gas is subsequently attracted to the rock/ice core (such as Jupiter, Saturn, etc.). [OK]
A text from an authority on planets
Why does NASA study Earth? [OK]
A test from another authority authority on planets:
Both are used. And please note: in either case, if you are saying the rotation of the Earth, even if your text is not using the determiner "the", you would have to use it for the "genitive".
- Both the Earth's and human health are the topics I love. [OK in speech]
- Both Earth's and human health are topics I love. [Ok in speech]
If one is writing a text, perhaps the clearest way might be:
Both human health and (the) Earth's health are topics I love.
Both (the) Earth's health and human health are topics I love.
I put the "the" in parenthesis, because both are grammatical. It is the speaker's choice here.
For me, the sentence given in the question does not lend itself to one noun possessed by Earth and humans. That is because we would not write in a formal text:
- John's and Mary's health.
For clarity's sake, one would write:
- John's health and Mary's health.
Whereas you could say: John and Mary's car, where car belongs to both of them. With health, they each have or don't have health, as separate entities.
Please note: this is a stylistic suggestion based on the fact that the word health belongs to entities in a separate manner. So, I suggest repeating the noun health, rather than using a single possessive. Some languages do not "like" word repetition, but in English, that is not an issue.