3 of 15

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 3rd 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 and Kepler’s Second Law of Planetary Motion. It may also be profitable to have students complete the ASAP Lessons: Kepler’s 1st Law of Planetary Motion and Kepler’s 2nd 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 3rd 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”.
Kep l er’s 3rd Law “Board Meeting” Notes

4 of 15

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.

5 of 15

Technology Standards

Computational Thinker

9-12.5.Students collect data or identify relevant data sets, use digital tools to analyze them, and represent data in various ways to facilitate problem-solving and decision-making.

9-12.5.Students break problems into component parts, extract key information, and develop descriptive models to understand complex systems or facilitate problem-solving.

9-12.5.Students understand how automation works and use algorithmic thinking to develop a sequence of steps to create and test automated solutions.

6 of 15

Objectives:

Today we will review Kepler’s 1st and 2nd Laws 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 3rd 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.

7 of 15

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 3rd Law Worksheet.

Student groups investigate the orbits they are assigned, replicating them as best they can, and making and recording observations of period and average orbital radius.

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

Day 2 (if necessary)

Student groups graph period vs average orbital radius and modify graphs to arrive at a mathematical relationship.

Whole class discussion or ‘Board Meeting’ is used to reach consensus on the relationship between period and average orbital radius. Teacher facilitates student discussion and summarizes the findings for the class.

8 of 15

Investigating Planetary Orbital Motion

We have already learned that the planets orbit the sun on elliptical paths, with the Sun at one focal point (Kepler’s 1st Law) and that the orbital speed of each planet is greatest when it is closest to the Sun and smallest when farthest away, but that equal areas are swept out in equal periods of time (Kepler’s 2nd Law). 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 much time does it take for the planets to complete an orbit?

How does the distance from the Sun affect the time to complete an orbit?

Is there a relationship that all planet’s orbits share?

9 of 15

KEPLER’S 3^rd LAW

PLANETARY MOTION

10 of 15

Kepler’s First Law of Planetary Motion

Focus

Center

Minor Axis

Semi-Major Axis (a)

Major Axis

Perihelion

Aphelion

Linear Eccentricity (c)

Sun

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

11 of 15

Planets move fastest when closest to the Sun (perihelion) and slowest when farthest away (aphelion). An imaginary line connecting the planet and the Sun sweeps out equal areas in equal intervals of time.

Kepler’s Second Law of Planetary Motion

12 of 15

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 Third Law Activity

13 of 15

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, share your results with the rest of the class.
Prepare a whiteboard to share your graph and relationship with the rest of the class.

Kepler’s 3rd Law Activity

Kepler’s Laws PhET Simulation

14 of 15

Assessment

Observations and Data Collection: Which planet’s orbit did your group study? What did you observe about the period (T) of your planet’s orbit and its average distance (R_AVG)from the Sun? What mathematical relationship did you find between T and R_AVG when you graphed the class data? Share your group’s results on a whiteboard and in class data tables. Be prepared to discuss them in our “Board Meeting”.

Compare and Contrast: How does your planet’s T and R_AVG compare to those of other planets? Are there patterns you can see? If so, what are they?

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

15 of 15

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.They can use the class data to complete graphing.

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.