The 'authority' in question is/are not some evil subspecies of mankind.
I don't care. If your argument is "this is true because Big Space Man said so", then your argument is useless.
Well. Not useless.
During the Brexit debate there was an infamous quote from Gove about people having "had enough of experts",
I think it was in the context of economists who failed to predict various financial crashes so what do they know about the economic impact of Brexit?
Fairly reasonable, I guess. The economy is notoriously complicated difficult to predict. But the general point is not reasonable.
If I go to the doctor with certain symptoms and he says I need an MRI, after he's looked at the results and told me what he thinks is wrong I don't say "Let me look at that..."
I might ask for a second opinion but I'd want that second opinion to come from another medical expert. I don't have the medical knowledge or experience to interpret the results myself.
They do. That's what makes them the experts, or authorities. Doesn't
automatically mean they're right, but their training and experience makes their opinion about what is wrong more valid than mine.
When every single serious scientist says that we're living on a planet which shares a lot of common features with the other planets and, like the other planets, is revolving around the sun then it's not irrelevant to the debate.
Could they all be wrong? I suppose it's possible.
But that would also mean that every single space agency is lying to us.
Every rocket launch is faked - in the sense that they don't really go into orbit.
Every photo and piece of film from space is faked.
A load of people are involved in the production of those photos and video and are keeping quiet about it.
Every astronaut is lying.
The space tourists are too.
Sky are lying about my TV signals coming from a satellite, or they are being tricked into thinking they are and the signals are coming from some other source.
GPS also works in a way differently to the way we are led to believe.
The airline and shipping industries are lying or mistaken about the way they plot their routes taking into account the curve of the earth.
And so on.
If there was some serious debate about this in science then fine, appealing to an authority who happens to back up a heliocentric model would be fallacious.
But there isn't. This debate was settled hundreds of years ago and nothing has come to light since which casts any doubt on that.
Pointing that out is not invalid or useless as part of the debate.