Hi, my name is Joel Rubin and I teach astronomy at Staten High School where on the first day of class students make Uncle Al Starwheel. But I ask you, why don't we see the planets on the Starwheel? And you've all seen drawings like the one I have on the screen representing the solar system. Is this an accurate model? There's another one, of course. You may have heard about Earth as peppercorn. Well, the moon is 2.4 inches away from the peppercorn, a pinhead representing 100,000 miles every inch. We have the sun, an 8 inch basketball, and we walk all the way across the fields to have the distance between the sun and Saturn in scale. Saturn is an 8 corn. Well, here's another model that you may have heard of, Copernicus. The first person to show that there was a relationship between the 30 years it takes Saturn to get back to the same part of the sky. And the 12 years it takes Jupiter, the year it takes Earth, and so forth. It's because of their distance from the sun that they're going around that illuminates them, he says. The first step for my students is to go to Google Classroom and to add or create a dock and a sheet. And then they have to put this template into their dock. Then they could take a look at some resources like the notes that kids and IEPs need to have access to. And then that includes these diagrams. This diagram here in the upper left is the one that Copernicus actually used, involves basically thousands of calculations to figure these things out. The kids can do the same thing with just five calculations, one for each planet. For the interplants, it's pretty much the same as Copernicus did. He weighs still the angle as far as it's going to get between the sun and the planet. And that angle he takes the sign of it. And because there's a tangent line here to the orbit, as you can kind of see in this image here, a model of the same thing. Because that's a tangent, he knows this is a right angle. And so he's able to do his trick. Not so easy though with the inner planets, the outer planets, sorry. The outer planets, he does have some information that he could have used, but he doesn't actually use it. He knew how many degrees per day each of the planets went Mars, Jupiter and Saturn. And he could look at the positions between opposition when the planet is as far away from the sun as it ever gets in the sky. In other words, the planet's rising as the sun is setting, the planets in the sky all night. No parallax. Very useful. There's another position many days later when the planet seems to be at a right angle to the position of the sun. It's seen from Earth. You need another angle to do trick, either this one here or that one there. And those are unknown. How do you figure them out? Well, the method that was used by Thomas Kuhn and other people at Harvard back in the 1950s and 60s was this one. It count the number of degrees per day between the position where they were in a straight line in the position with the right angle. And compare how far the planet moved, how far Earth moved. And the angle of the sun would be subtracting the shorter distance the planet had gone from the further distance Earth on the inside track had gone. And then you could do one over the cosine of that and you'll get the answer. That's not what Copernicus did though. Why would we want to know how far the different planets are from the sun? Well, you know, if you're studying exoplanets today, it makes a great difference to the climate if you're closer to the star or further from the star you're orbiting around. Right? So that's kind of where we're at with this. Copernicus understood some things correctly that the reason why planets appear to go backwards is because planets are passing Earth or vice versa, not because they're on loop deloops, but he still needed the loop deloops because he didn't accept the idea that planets were going faster when they were close to the sun and slower when they were further from the sun. That had to wait until Kepler came along. So we don't do it exactly the same way as Copernicus. He used epic cycles to account for this anomaly that the planets speed it up and slowed down. He believed that they kept going at constant speed on their circles. But these are important things that we relate from Copernicus to astronomers today that the orbital periods are related to the distances from the sun that the planets are whirled seen from far away, not tiny points of light in that Earth is a moving planet just seen up close. And that's some reasons why it would be good to bring our students to an understanding of Copernicus besides which of course spreadsheet functions are really useful for students to know here in the 21st century. So that's my presentation for now. If you want to get a hold of me, I'm J underscore, are you BIN at StotenSchools.org. Nice talking to you.