We started class by playing with the SpillNot – a device used to hold a cup of water, which you then swing in a circle over your head. If you swing it fast enough the water stays in the cup, even when its upside down. It works really well and no body got wet. This little demonstration goes along pretty well with circular motion and gravity, which we were covering today. One of the topics in my slideshow today was about how the astronauts in the space shuttle and space station appear to be weightless, but gravity is still pulling on them… just like the water in the cup. But the astronauts and the space shuttle are falling towards earth constantly, and constantly missing. Eek, I just realized I forgot to talk about the vomit comet today, will have to do that next week.
After reviewing some of Chapter 9 (Light and Matter), I gave a slideshow on Copernicus, Galileo, Brahe and Kepler to name a few. This is a presentation I’ve given many times over the years, the first time being in a Story of the World co-op. Along with the history, we went over Kepler’s laws of planetary motion and then Newton’s formula for the gravitational force between any two objects. Then I had the students draw ellipses, label the two foci and pick one to be the sun. The way to draw an ellipse is to put two pushpins through the paper and into cardboard, put a loop of string around the pins and put your pencil inside the string and pull it taunt, forming a triangle. Now you can pull your pencil around the pins, keeping the string tight and you get an ellipse. How elliptical or circular your ellipse looks will depend on how close you put the push pins. Once they had their ellipse, they labeled the perihelion (point on the orbit closest to the sun) and aphelion (point on the orbit farthest from the sun). Then they measured the semi-major axis, a, the distance between the sun and the aphelion and c, the distance from the center of the ellipse to the sun. From these measurements they calculated the eccentricity of the ellipse, e = c/a. If c = a, then e = 1 and you have a straight line, but if c = 0, basically the two pins are on top of each other and you have a circle. They drew one or two more ellipses, either changing the distance between the pins, or the length of string to change the eccentricity. In the slideshow I had shown an image of some of planets orbits and how they really aren’t very elliptical, with the exception of Mercury (and dwarf planet Pluto which isn’t shown). I found this image on the Windows to the Universe webpage which also has some nice interactives, like this one, where you can change the eccentricity and watch the orbit change.
For Kepler’s 2nd Law, which states that planets sweep out equal areas in equal time, I modified a worksheet I found on the web by Professor van der Veen to make it a bit shorter. The original worksheet gives the data for Mercury’s position around the sun for a complete orbit and asks the students to plot it. I knew we wouldn’t have time for that, so I made the graph and gave copies to my students. They had to pick two points on the orbit where Mercury was closest to the sun and two points where it was farthest and find the area of the ‘triangular’ sections swept out between those two points. The time interval was 5 days between each data point. The worksheet gives clear instructions on how to find the area and the students found, that indeed, the areas were almost the same.
Another fun thing to go along with topic, is the FREE Voyager: Grand Tour app. Its a game but you have to launch your rockets at the right angle and speed to put your satellite in orbit and collect data to complete the missions and move on. What’s really nice about this app is that it shows you the path for each trial, so you can figure out what you need to change… and it really hard not to laugh when you keep crashing directly into Jupiter, or time your launch so poorly that it hits the moon on its way to Mars.
Before class, I had asked the kids to watch these videos on youtube.