## Classroom Stories: Energy and Kepler’s Laws: A Surprise for Me about Where the Difficulty Lies

##### 02/14/2020

By **Stacy Palen**

Recently, my students worked on the “Working with Kepler’s Laws” activity from the *Learning Astronomy by Doing Astronomy* workbook. In this activity, students learn about ellipses, consider the “simple” version of Kepler’s second law (a planet travels faster when nearer to the Sun and slower when farther away), and run some numbers for Kepler’s third law: P^{2}=a^{3}. To my surprise, Kepler 1 and Kepler 3 brought almost no questions from the students (aside from “Am I doing this right?”). It was Kepler’s Second law that brought the most substantive questions.

Over and over they asked “Yes, but WHY does it go faster when it’s closer?”

I used this question as the basis for a whole new activity.

Approaching this question as an energy problem, I had the students throw a ball straight up in the air and make pie charts representing how much kinetic energy, gravitational potential energy, or thermal energy the ball had at various points in its trajectory. Then they threw the ball to a friend and made similar pie charts (in this case the velocity is never zero, so the kinetic energy is also never zero). Then I had them consider a planet in orbit around the Sun and make a third set of pie charts.

Wow! This was so much harder for them than I expected!

First, it turned out that pie charts are a concept that most (but not all) of my students have in common. Who knew?

Second, we ran into the issue about where to put the “zero” of gravitational potential energy. This information was in the Background section, so it was invisible.

Third, we faced our biggest issue: Convincing students that when they threw the ball straight up into the air, the ball had zero speed at the apex of the trajectory. That alone was a 20-minute conversation!

Finally, even though I told them to describe what happens to the ball between the moment after it left their hand to the moment before they caught it, many students turned all the energy into thermal energy. I’ve edited the activity to try to correct these problems and will use it again in the fall in search of perfection.

Despite these problems, I was very happy about the conversations that I overheard as I moved around the room. Some students were completely unfamiliar with the conservation of energy. They made progress simply by learning how the energy transformations occur for a ball thrown in the air!

Other students rocked that part but were stuck when the questions about orbits showed up; this was often because they drew the Sun at the center of the orbit instead of at a focus. What a great opportunity to correct this problem!

Finally, some students spent a very long time arguing about whether they needed to account for energy lost to thermal energy in our current Solar System.

Overall, I was pleased by what I learned about how they think about energy as well as how well they grappled with this material. And I’ve now set them up to have a spark of recognition when they learn about planet migration later in the semester. This activity is a work in progress, but I will definitely try it again!

You can access the activity by clicking here!

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