Students in physics and astronomy are often expected to be able to understand, explain, and interpret basic orbital mechanics using Kepler’s law of orbital motion. The work of Isaac Newton to expand and generalize Kepler’s laws is often the focus of student activities. Luckily, we are awash in authentic data, which students can leverage to explore how we came up with these laws and their applications to modern science learning.

One aspect of using orbital mechanics in an introductory physics or astronomy class is determining something unknown about an orbital system. For example, students can use periods and orbital radii of objects in a system to determine the central object’s mass. Linearization is a common way for a student to achieve this goal. When a student linearizes data, the goal is to produce a linear relationship such that the slope of the line can reveal a physical parameter of the system, such as the central object’s mass.

The scenario we are describing is perfect for computational thinking (CT). We can take data and reduce it to create a linear regression where the slope can lead to determining the mass of the central object. The video below shows an example of me using the periods and distances of the planets in our solar system to explore Kepler’s 3rd law through linearization. This example uses Desmos, but several modes of CT work here, including using a spreadsheet or computer programming. Exploring Kepler’s laws through data is also an application of data science pedagogy.

The Kepler spacecraft made some incredible discoveries over the years. The planetary system Kepler-11 is fascinating. It is a very compact solar system with six planets. Of course, the spacecraft is named after Johannes Kepler, who first empirically determined the three famous laws of planetary motion.

This small dataset would make a great computational thinking (CT) activity. CT can mean writing programming code, working with a spreadsheet for data science, or creating or using a model or simulation. The goal is to explore Kepler’s third law of planetary motion.

In the first version of this activity, students linearized the data set using Kepler’s third law of planetary motion to determine the mass of the star Kepler-11. Check out the spreadsheet version here. This is an introductory exercise to working with data in a spreadsheet. Students create a plot and answer questions using some basic skills. Using formulae and linear regression techniques with a spreadsheet can be very cognitively demanding for students, so leave time for scaffolding and differentiation.

Although the spreadsheet version of the lab worked out pretty well, I decided to make a Desmos calculator version. Students can work with the whole list of planetary data all at once, more like creating a numerical model to find the star’s mass. Check out the Desmos version here.

Finally, I decided to create a version of Kepler’s 3rd law lab using some Python code in Google Colab. This version uses some standard data science techniques to determine the central star’s mass in the Kepler-11 system. Check out the Google Colab version on my GitHub repository.

Over the years, I have used these three activities individually and in concert sometimes. In my Astro 101 classes, I treat these activities as guided inquiries and give many hints and help. In my AP Physics C Mechanics classes, I might expect students to figure things out independently or in small groups.

While the only data I have about these activities is anecdotal, my research supports the general claim that students’ attitudes about computing improve when CT and data science are used in a science course. My experience was that using CT and data science to explore Kepler’s 3rd law helped students construct knowledge about building and using mathematical models while also cementing the use of the law in a learning context. For the most part, students have fun and feel a sense of agency about their learning. Using CT and data science, students learn not just an algebraic formula but also data literacy and CT skills.

This work is licensed under a Creative Commons Attribution 4.0 International License.