The Arizona STEM Acceleration Project

Orbit Challenge 2

Orbit Challenge 2

A 9th grade STEM lesson

Demian Quiroz

1/31/24

Notes for teachers

• This is a follow up lesson to Orbit Challenge, where students tossed planets to determine the shape of the orbital path. Here they will develop an understanding on what does and does not affect the behavior of an orbit (period).
• Using Algodoo, a free 2-D physics sandbox software program, students will explore planetary orbits and develop Kepler’s Laws conceptually as well as provide foundation for Newton’s laws and data collection techniques.
• Play with the simulation yourself to familiarize yourself with possible pitfalls your students will encounter.
• While touch screens are nifty, it can be frustrating. Try with a mouse.
• Context: This lesson can be a part of an introduction to science or STEM Night activity.
• Let the students play with the simulation and find out a bunch of things and wonders. Be their guide!
• Small groups 2-4 are good.
• See the next slide for some examples of what students may find in addition to getting the planet to orbit the star.
• Silly but true note: Most students would depict our sun as yellow, but it is actually giving off white light, so it is depicted in this simulation as a white circle.

List of Materials

• PC or MAC running Algodoo software�https://www.algodoo.com/ for each group
• Resource Folder: Kepler 3
• Optional Orbit Challenge Student Guide
• SM-Orbital Challenge 2 Student Worksheet
• kepler3.phz Algodoo file
• Touchscreen interface preferred (interactive whiteboard)
• Mouse and keyboard
• Example data on Desmos: https://www.desmos.com/calculator/xoolkejale
• Teacher Guide: Orbital Challenge 2
• Teacher resource: Orbits and Kepler's Laws - NASA Science
• Contact Demian quirozd@sanmiguelhigh.org if you have questions on how to work with the files.

What the Fiziks?

Major Physics Points:

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• Newton’s Law of Gravitation: The force of gravity between two objects is proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between the centers of the objects. Student language: The G arrow gets bigger the closer the objects are, and gets smaller the farther away the objects are, which means the star pulls more on the planet when it is closer, and less when it is farther away. If the orbit is a circle, then the star pulls on the planet the same amount all the time. The G arrow always points to the star.
• Representation: Forces are represented by vectors.

Student Language: “The arrow represents the direction of the pull and how big the pull is”

• Kepler’s 3rd Law: The square of the orbital period is proportional to the cube of the semi-major axis of a planet’s orbit. Boundary: the star mass needs to be very large compared to the planet mass. Student Language: “The bigger the orbit, the longer it takes to go around the star. The mass of the planet does not have an effect on the shape or timing of the orbit. The bigger the mass of the star, the quicker the planet goes around the star.”

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There’s a lot going on in the simulation. Here are a few things that might be noticed along with student examples of how they would describe it.

Other Physics Points:

• Curvature and scale: A round object’s edge can appear flat if you are really close to it. (Zoom in on the star).
• An orbit is actually any trajectory a celestial body makes under the influence of a gravitational field. The kind most students think about are repeating or periodic orbits. Student Language: “The path a planet makes as it goes around a star is called an orbit. A repeating orbit makes an elliptical or circular path.”
• Newton’s 2nd Law: The effect of the same magnitude of force on an object with a larger mass will result in a proportionally smaller acceleration. Student language: “The star is massive so the same pull doesn’t make the star orbit the planet. The star barely changes its motion (but it does move a little!).”
• Newton’s 1st Law: In the absence of a net force, an object will have constant velocity. Student Language: “If you delete the star, the planet starts moving off in a straight line in the direction it was moving when you deleted the star.”
• Kepler's First Law: Student Language: “A repeating orbit makes an ellipse shape. A circle is a type of ellipse.”
• Kepler’s 2nd Law Student Language: “The farther the planet, the slower it goes. The closer the planet the faster it goes.”

NGSS Standards

Earth and Space Sciences: ESS1.B

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“Kepler’s laws describe common features of the motions of orbiting objects, including their elliptical paths around the sun.”

National Academies of Sciences, Engineering, and Medicine. 2012. A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas. Washington, DC: The National Academies Press. https://doi.org/10.17226/13165.

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• Standard: Understand the mathematical relationships governing planetary motion in the solar system.
• Performance Expectation: Derive and apply Kepler's Third Law to calculate the orbital periods or distances of planets in the solar system.
• Science and Engineering Practices: Use mathematical models to represent and analyze the relationship between the orbital period and the average distance from the Sun for different planets.
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AZ Standards

Earth and Space-E2 �Essential HS.E2U1.16

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Standards

Patterns; Cause and Effect; Scale, Proportion and Quantity; Systems and System Models; Energy and Matter; Structure and Function; Stability and Change

Crosscutting Concepts

Objectives:

Today we be able to determine the factors that affect the period of the circular orbit of a planet around a simulated star (Kepler’s Third Law).

Today we will learn about how to measure the period of an orbiting planet.

Today we will learn how to find a relationship between variables using Desmos.

Today we will collaborate and communicate effectively with our peers to complete the orbit challenge.

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Agenda

This lesson can take up as much time as you want. The more time you give for students to play and wonder, the deeper the connections will be to later understanding. BUT, you must be a guide and get students to help and talk to each other. Watch for good behaviors that promote discourse, and adjust as necessary.

Probably <90 minutes, depending on how well you can foster discussions and constructive play.

The faster you get the simulator in the hands of the student the better.

Have them help each other with ideas to foster a scientific community.

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This lesson has been used as an introduction to scientific thinking in the modeling curriculum and follows Orbit Challenge.

1. Play the Simulator
2. Prediction: what things can we change that might affect the period of an orbiting planet? Discussion.
3. Play and Wonder
4. Show and Tell
5. Consensus
6. (Metacognition - How did we participate in science discussion?)

Intro/Driving Question/Opening

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Watch the simulation.

What things can we change that might affect the period of an orbiting planet?

You will be playing with a simulation of a single star and planet. Your goal is to change something about the planet or star that might affect the time for that planet to complete an orbit around the star.

Collaborate with your other groups so you can share data to be more efficient in data collection and act like a scientific community.

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Orbit Challenge 2

• Best done with 2-3 students per machine.
• The video on the top right details some items that will be useful for the teacher to know ahead of time.
• The simulation starts with a star and a planet already in orbit (you may want to double check that!)
• If you run the simulation, what happens?
• Use UNDO to take it back to the beginning.
• When directing students to make measurements, have them explore “Show Plots” (Right Click on the planet) OR use timers (their phones, Google stopwatch etc).
• An interesting way to change the mass of the planet is to change the density. Double the (areal*) density, doubles the mass in this simulation (*because it is 2D). Typing in a mass also works well.
• Worth exploring: change the mass WHILE the simulation is running.
• Changing the star’s mass might be done by the 10s by changing the exponent on the mass.
• To change the properties of an object, right click and explore the materials menu. You can tear off menus so they stay floating!
• Desmos video shows the procedure to attempt to generate a relationship from 3 points of data, and a method to interpolate or extrapolate on that data.

Example Findings

mass of planet: (Mass of planet very small compared to the star). The planet’s mass has no to little effect on the period.

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mass of star: The bigger the mass, the quicker the period. (Inverse-square root proportion – students not expected to know that, but the graph isn’t straight and is an opposite effect).

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radius of orbital path: The bigger the radius, the longer the period. (1.5 power proportion - again, students not expected to know that, but the graph isn’t straight and is a positive effect).

Assessment

Students participate in discussion: After students watch and understand how to play with the simulation, students should discuss what they can change within the confines of the simulation. During discussion, have students address the challenge “What factors affect the period of the orbit?” and agree on terms to make sure everyone knows what to do.

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Guide students in planning data collection and comparison: You can guide students or have them choose their changes. If you guide them, seed groups to have different solar masses, but start with the same orbital distance, for example.

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Assess students on their ability to communicate ideas and provide rapid feedback on how they work together in partner, group and classroom discussions.

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Differentiation

There is an iPad version of Algodoo and the file will work there too for students needing a more one-to-one device.

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Turn on “Snap to Grid” by right clicking on the “Show Grid” button on the Simulation Control Bar” This will keep the planet on a grid, especially if students have difficulty with motor skills.

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Let students play with the simulation and list what they notice and wonder.

Remediation

Extension/Enrichment

Have students create their own planets of different shapes, sizes, and masses.

Have students determine the mathematical function for the orbital period using Desmos.

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Use Desmos to predict what a new planet’s orbit would be and test it.