I was recently asked to do a presentation about the upcoming solar eclipse at our library as I am one of a small local group of amateur astronomers. I happily accepted. I always enjoy putting together Keynote presentations for such events. I spent several days last week assembling the 38 slide presentation and did the presentation last night. It seemed to go well. For one part of the presentation I used three volunteers to serve as the sun, moon, and Earth. The idea was to illustrate the phases of the moon as well as the angle of the moon’s orbit with these three people and in truth, after a bit of initial confusion, I think it went pretty well. But it wasn’t to scale as we were crowded into a fairly small room at the library. After the event I got to thinking about how that sort of presentation, in particular the bit involving the volunteers, could be expanded into something really fun but in an outside location so that a sense of scale could be created. It would involve a bit of math so I thought it might be fun to recruit Siri as my helper in preparing this activity.
The idea would be to create a scale model of the Earth in relation to the sun and moon based on a circle of 365 feet in circumference. Each foot represented one day in the Earth’s orbit around the sun. Now, at this scale, I wanted to properly represent the position the sun at the center of our orbit. I needed the radius of my circle. Okay. I asked Siri to calculate the radius of a circle with a circumference of 365 feet. I was given a WolframAlpha calculation screen as a result: 58.1 feet. But I wondered if I could copy/paste the content. It had never occurred to me to tap the WolframAlpha icon, just a bit of text in a square in the corner of that display of results. I’ve done this kind of thing many times but never thought to see what would happen if I tapped. I expected it would do nothing. Instead, it took me to the AppStore for the WolframAlpha app. It never occurred to me that there was such an app but of course there is! I downloaded it and it opened my results into the app. It’s a very nice app that allows further input and new calculations among many other things. But no option to copy/paste the content.
Now, back to working out the activity. I’ll need to get some string but before that, I now know that if my orbit is scaled to 365, feet my radius is 58.1 feet. So, I’ll position my sun with a pole with string tied to it. From there I’ll walk out 58.1 feet and place another pole. I’ll have two strings. One which I’ll keep tied to the center pole (my sun) and which will guide my “orbit”. The second string will be tied to the second pole. Now it’s just a matter of walking the circle around the sun and dropping my string to represent the 365 feet of orbit. The next step is to convert a few other distances. For this I hopped over to this solar system scale model calculator.
Next, I used Siri to do a bit of math. First I asked her for the average circumference of the Earth’s orbit. Then I asked her to convert this from miles into feet. Then I divided that by 365 come up with my model scale of 8,447,618,973. With that number input into the solar system scale calculator I confirmed my Earth orbit radius of 58.1 in the results. Next, I wanted to get the moon’s orbit as well as the size of my three solar system objects at this scale. I made sure to select the Moons option and on the form and I got an orbit radius for the moon of 1.79 inches. TINY!! With that radius the average circumference of the lunar orbit is just 11.25 inches. Whats’ the size of the sun, Earth and moon at this scale? According to this same calculator, at this scale the sun is just 6.49 inches in diameter. Of course, the Earth and moon are very tiny! The Earth is just .06 inches in diameter and the moon is .016. Just a spec.
So, I’ve got the scale though in truth it might be best done at a slightly larger scale given how tiny the Earth and moon are in this model. Regardless of the ultimate scale of the model it is fun to play with and I expect it will be a fun model to explore in the yard. The idea would be to set the scale and then discuss the movement of the moon in it’s orbit of the Earth and the Earth’s orbit around the sun. By positioning volunteers it becomes a bit more obvious why a new moon is invisible to us. By adjusting the position of the volunteer “moon” in orbit around the volunteer “Earth” it become easier to understand how the moon gradually becomes more visible as a crescent then a quarter then a full moon and so on. Further discussion of the 5° elevation of the moon off of the ecliptic helps participants further understand why we do not have solar eclipses with every new moon.