there is a huge body of information we accept to be truth soley based on the authority that provides it.

We accept science hearsay because it is based on interacting with reality. It's not really a matter of authority so much as causality. One of the causal nodes just happens to look like authority, and you seem to think this has some significance. It doesn't.

But it is impossible for me, or any other person, to know just from my sensory experience that the earth revolves around the sun (given the practical constraints of my life).

Then it's mighty odd that anyone knows that the earth goes round the sun, seeing as someone had to know it with sensory experience in the first place. And if I don't know it based on sensory experience, then how do I know? Is it a random anomaly that I happen to believe it? No. I believe it because my sensory experiences provide lots of evidence, and yes some of this evidence is expert opinion.

given pre-legitimized mathematical formula.

What is pre-legitimized?

There is a large body of knowledge that we accept without any sensory information on the subject.

So?