The Earth goes around the sun.
In 1543, when Copernicus published his argument that the planets went around the sun, just as moons go around planets, he built on a hypotheses offered by Greek, Muslim and Indian thinkers. At the time, most people believed the Earth was fixed in the universe and everything went around it (and around us). This idea works well for the casual observer, but people looked at the location of planets in the night sky and wondered about the things they observed.
Galileo used a telescope to observe the heavens, and by today's standards it was little better than binoculars. There is a reason why we can speak of him by first name afer the passage of nearly four centuries. He shared with the world, at what turned out to be great personal peril to himself, the wondrous things he observed. Times were tough back then, one could be burned alive at the stake for simply speaking or writing about what one saw. It is much better today, at least here in the United States, because we mostly subscribe to something called "Freedom of Speech."
What did Galileo see? Well, he observed that Jupiter had four large moons, and by making careful observations and writing them down, he was able to get to know each one better and give them unique names. His observations clearly indicated that they went round and round the planet in a regular, predictable way. You can use a pair of binoculars and see that for yourself, and if you are really motivated, or curious, or bored ... you can write down what you see every night and see if you believe Galileo or not.
He saw the rings of Saturn. They are quite beautiful and unlike the appearance of Earth, so this made those who heard about it edgy. The Earth was supposed to be unique, and special, and if other planets had rings, and ours didn't, well, why were we left out? We were supposed to be very special. I think that if they had the photos we have today, of the Earth from space, this would not have been such an issue. Our beautiful blue and white marble with its thin, fragile atmosphere and snowy white polar caps, dusty deserts, and vast green forests truly rivals the beauty of anything in our universe.
Or I can just point to that humorous adage, "You are unique and special. Just like everyone else."
Galileo studied the moon. He watched carefully as the moon waxed and waned. A bit after the new moon, about a week to ten days after, he noticed that it seemed as if there were mountain ranges, lit on one side, and in shadow on the other. He saw shadows change, and the depths of craters went from shadow to light over time. It really looked as if something were illuminating a varied terrain of craters, plains and mountains. And, it seemed to Galileo that the illumination was coming from some hidden source. This was heresy. And I mean that in a "burn you at the stake" kind of way.
Popular wisdom held that the moon was a smooth globe that glowed softly in the night sky. I can put myself in that frame of mind. It certainly does seem to be a glowing orb.
Now Galileo got a letter from another observer with a telescope, and it shared a new observation. There were those who said Venus displayed phases, just like the moon. Light on one side, dark on another, slowly varying the appearance, sometimes more light, sometimes more dark. Again, as if it was lit from one direction by a single source of light.
To explain the single source of light, and calculate its position, observations could be made. One could write them down on paper and speculate about what would explain the observations. This was a daunting task, and many people worked on it. I'll leave it to your curiosity to find out more about math, geometry, and physics.
As for me, I have to see things for myself sometimes. I got a little telescope, mostly for looking at birds, but at night the heavens beckon. There's Saturn with rings, Jupiter with four large moons, Mercury close to the horizon, and sure enough, Venus with phases.
I'm convinced. The Earth goes around the sun.
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