The second high school class focused on units and distances used in Astronomy. I started class with a lecture on constellations (Chapter 2-1 in Foundations of Astronomy) and how they started out has stories in the sky but are now considered sections of the sky, just like states are sections of the United States. If you tell someone you went to a museum in Ohio, most people will have a general idea of where you went. Likewise if you tell an astronomer you are studying a star in Orion, they will know what part of the sky you are looking at. We talked the difference between linear diameter (the diameter of a circle, like a 16″ pizza which is 16″ across at the widest point) and angular diameter. I used a large ball to demonstrate that when the ball is close to me, the angular diameter of the ball could be quite big but as we moved it further away, the ball appears smaller so its angular diameter gets smaller. So the angular diameter depends on the distance from the object. We used the small angle formula to calculate the angular diameter of the moon and the sun, which both come out to about 1/2 a degree. Even though the sun is much bigger than the moon, it appears to be the same size because its so much further away. The sun and moon are the biggest objects in the sky and they aren’t even a degree across, so we need smaller units for talking about the angular diameter of other planets and stars. 1 degree = 60 arcminutes and 1 arcminute = 60 arcseconds. So in astronomy you will frequently see angular sizes listed in arcseconds.
The lab activity involved using parallax to measure the distance to an object (Ch 9-1 in Foundations of Astronomy) and is one of the activities on BHP. If you close one eye and hold up your thumb so it is covering a distant object, say a lamp, then close the eye you had open and open the other eye, you will see your thumb ‘jump’. This apparent shift in position is because of the distance between your eyes. The bigger the distance between observation points (your eyes in this case), the bigger the parallax. This distance between observation points is called the baseline. When we’re measuring the parallax of stars we use the baseline of the earth’s orbit around the sun – observing stars 6 months apart so that the earth is at opposite ends of its orbit. Crash Course Astronomy has a nice video on distances in astronomy:
I placed some paper stars around the room and students had to measure the angle of the star from two ends of a baseline (1 meterstick). To find the distance to the paper stars, students drew a scaled version of the baseline (1 in = 1 meter, or 4 cm = 1 meter) on a piece of paper, then used a protractor to draw the lines of sight with the angles they measured. Where the two lines intersect is the location of the star. Unfortunately this is incredibly sensitive to the angles so its hard to get accurate results. We have errors in measuring the angle and then in drawing them. Astronomers have the same problem because the parallax is usually a very small angle because the stars are so far away and our atmosphere smears out the stars making it hard to measure. This is why they like to put telescopes in space, above the atmosphere – it makes these types of measurement more accurate.
We ran out of time so did not get to talk about the Origin Stories from the Big History Project, will try to do that next week. I did do the Claim Testing Snap Judgement activity from BHP – hung up the claims (ex: the earth is flat) and asked students to put a green stickie note on the claim if they agreed with it, a pink one if they disagreed. We discussed the different claim testers; intuition, logic, authority and evidence as we went through the different claims. I told my students that I highly recommend the “Calling Bullshit” class from U of Washington if they are interested in learning more about claim testing. They have a series of lectures online and recommended reading. My kids and I did this a few years ago along with the book Thank you for Arguing by Jay Heinrichs for high school English.
For the middle school class, we started with the Claim Testing exercise as well and then spent a lot of time discussing the origin stories and sharing our favorites. I don’t think many of them filled in the chart provided by BHP but I did some of it on the white board as we discussed it as a class. I also showed them my favorite origin story:
I gave them a shorter version of the lecture on angular diameter and units like the Astronomical Unit (AU = distance between Earth and Sun) and light years. I ran out of time and did not do parallax with the middle school class so we’l do that next week.