Sentence Correction

like kevin says.

more detail on the inverted construction (verb before subj):

you can spot the inversion because there is nothing before 'are' that could possibly be a subject. the entire preceding portion of the sentence is a giant prepositional phrase.

the placement of 'on earth' is also much better in e than in a.
- e says what it's supposed to say: we're looking at indications that are on earth. (this answer choice implies that better indicators are available elsewhere - presumably closer to the sun.)
- a says that tree growth is believed to be a good indicator by people on earth (--> martians beg to differ).

and finally, yes, 'the rate that' is simply... wrong. things don't 'happen a rate'; they happen at a rate, so that preposition has to stay. same reason you can say 'the grocery store at which i bought that food', and not 'the grocery store that i bought that food'.

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some things wrong with c:
* the placement of 'on earth' is just as problematic as in choice a (again, the sentence seems to be saying that residents of other planets disagree with us).
* 'as seen in the rings...' is a modifier that must be placed next to the thing that it modifies, which is 'the rate at which trees grow'. the way choice c is currently written, it says that indications of sunspot cycles can be seen directly in the rings - and it also implies that sunspot cycles (instead of trees) have rings!

...so in case it's not clear, the answer to this problem is (e).