The Arizona STEM Acceleration Project

Kepler’s 2nd Law of Planetary Motion

Kepler’s 2nd Law of Planetary Motion

A 9th-12th grade STEM lesson

Jeff Steinert

January 2024

Notes for teachers

List of Materials

• Projector for display of PowerPoint and demonstration of how to use the Kepler’s Laws PhET simulation.
• Student access to a device to access the internet and the PhET simulation.
• Paper copy of Kepler’s 2nd Law Activity to record data and observations.
• 24” by 32” dry erase whiteboards and markers for student groups to display their data and observations to class.
• Reading/Listening: Kepler’s First Law of Planetary Orbits. It may also be profitable to have students complete the ASAP Lesson: Kepler’s 1st Law of Planetary Motion prior to this activity.

• Context: This lesson takes place in a classroom for about one hour. It uses a PhET simulation on Kepler’s Laws.
• Students should work in small groups of no more than three (3).
• The goal of the lesson is for students to use the simulation to closely replicate the orbits of Mercury, Venus, Earth, Mars, and Jupiter and use characteristics of those orbits to describe Kepler’s 2nd Law of Planetary Orbits.
• Supervise student use of the simulation to assure reasonable accuracy of the orbits as they work in small groups.
• Engage the whole class in coming to consensus on patterns observed in the orbits via a post-analysis “board meeting”.

Arizona Science Standards

Science Standards:

Plus HS+E.E2U1.14: Use mathematics and computational thinking to explain the movement of planets and objects in the solar system.

Science and Engineering Practices:

​

• Ask questions and define problems
• Develop and use models
• Plan and carry out investigations
• Analyze and interpret data
• Use mathematical and computational thinking
• Construct explanations and design solutions
• Engage in argument from evidence
• Obtain, evaluate, and communicate information

​

• ​
• ​

Arizona Mathematics Standards

Mathematics Standards:

G.G-MG.A: Apply geometric concepts in modeling situations.

​

Number & Operations-Fractions

Geometry

Ratio & Proportion

Expressions & Equations

​

Standards for Mathematical Practice:

​

• Make sense of problems and persevere in solving them.
• Reason abstractly and quantitatively.
• Construct viable arguments and critique the reasoning of others.
• Model with mathematics.
• Use appropriate tools strategically.
• Attend to precision.
• Look for and make use of structure.
• Look for and express regularity in repeated reasoning.

​

Objectives:

Today we will review Kepler’s 1st Law of Planetary Motion.

Today we will collaborate to make observations and collect and analyze data to determine a physical law governing the motion of planets (Kepler’s 2nd Law of Planetary Motion) .

Today we will share our observations of planetary motion with others to identify patterns and reach consensus about what those patterns tell us about planetary orbits.

​

Agenda (60 minutes per period)

This lesson will take one to two class periods to complete.

​

Younger students may need two classes, while older students may get the entire lesson done in one period.

Day 1

Introduction and demonstration of the PhET simulation with tips for using it to complete the Kepler’s 2nd Law Worksheet.

Student groups investigate the orbits they are assigned, replicating them as best they can, and making and recording observations of speed, distance, time intervals, and areas.

Students share their observations and data for their planets on small whiteboards.

Day 2 (if necessary)

Whole class discussion or ‘Board Meeting’ is used to reach consensus on the relationships between speed and orbital distance from the Sun and time intervals and areas swept out.

Teacher facilitates discussion among students to arrive at a statement of Kepler’s 2nd Law of Planetary Motion and summarizes the findings.

​

Investigating Planetary Orbital Motion

​

​

We have already learned that the planets orbit the sun on elliptical paths, but we have not yet explored the motion of the planets along those paths. What are some questions to which we wish to have answers?

Have students come up with questions in a whole-class discussion. Some possibilities include:

How fast do the planets move on their orbits?

How much time does it take for the planets to complete an orbit?

How does the distance from the Sun affect their motion?

KEPLER’S 2^nd LAW

OF

PLANETARY MOTION

Kepler’s First Law of Planetary Motion

Linear Eccentricity (c)

Sun

All planets orbit the Sun on elliptical paths with the Sun at one focus.

Follow along on your paper and computer as I demonstrate how to open and set up the Kepler’s Laws PhET Simulation.

​

​

​

​

​

​

​

​

Please ask questions, if you have them!

Kepler’s Second Law Activity

Hands-on Activity Instructions

• Work in groups of two or three, but complete your own activity sheet.
• Your teacher will demonstrate how to use the Kepler’s Laws PhET Simulation before you get started. The full instructions are also on the activity sheet. Follow along there
• If you have questions, please ask your teacher for help. Once you have made observations and collected data for your planet, prepare a whiteboard to share what you discovered with the rest of the class.

​

Kepler’s 2nd Law Activity

Kepler’s Laws PhET Simulation

Assessment

Observations and Data Collection: Which planet’s orbit did your group study? What did you observe about the speed of your planet and its distance from the Sun? What did you observe about the areas swept out by your planet during equal periods of time? Share your group’s results on your group whiteboard and class data tables. Be prepared to discuss them in our “Board Meeting”.

​

Compare and Contrast: How do your results compare to your classmates? What is the same and what is different? Are there patterns you can see in the class results? If so, what are they?

​

Complete Worksheet: Document what you have learned and share with others.

​

Differentiation

Circulating as groups work will allow the teacher to provide additional assistance to groups that may need it. For issues that perplex multiple groups, a whole- class discussion can help, especially if suggestions come from the other groups in the classroom instead of the teacher.

Students who are absent can complete this activity on their own after a brief demonstration of how to use the Kepler’s Laws PhET Simulation.

Remediation

Extension/Enrichment

Episode 5 of James Burke’s The Day the Universe Changed, titled Infinitely Reasonable: Science Revises the Heavens provides an exceptional look at the historical context of Kepler’s Laws in advancing our understanding of the Universe. It is well worth taking an hour to show in class or it can be assigned to students who are interested as an enrichment activity.

​