Teacher Notes

Targeted NGSS Performance Expectation: HS-ESS1-4 Addressed Evidence Statements:

• 1a: Students identify and describe the following relevant components in the given mathematical or computational representations of orbital motion: the trajectories of orbiting bodies, including planets, moons, or human-made spacecraft; each of which depicts a revolving body’s eccentricity $e = \frac{f}{d}$, where $f$ is the distance between foci of an ellipse, and $d$ is the ellipse’s major axis length (Kepler’s first law of planetary motion).

Targeted Dimensions:

• SEP: Using Mathematics and Computational Thinking: Students use the simulation to represent how kinetic impact alters velocity vectors and directly modifies the ellipse parameters (semi-major axis, eccentricity).
• DCI: ESS1.B: Earth and the Solar System: Students observe that Kepler’s laws describe common features of the motions of orbiting objects, including their elliptical paths around the sun, and that orbits may change due to collisions.
• CCC: Scale, Proportion, and Quantity: Students examine simulation data to predict the effect of a change in velocity magnitude or impact angle on the resulting semi-major axis and orbital period.

Part 1: Engage (Anchoring Phenomenon)

The Problem: Scientists have identified a large asteroid on a direct collision course with Earth. Time to Impact (TTI) is currently estimated at 3.50 years. We cannot destroy it, but we can attempt to alter its trajectory by launching a kinetic impactor (like the DART mission) to push it off course. Question: How does changing the velocity of an orbiting body (like an asteroid) through a collision change its elliptical path around the sun, and how much force is required to prevent an impact?

Brainstorm two ways you might alter the asteroid’s orbit to prevent a collision with Earth. What variables do you think we can control? _____

Part 2: Explore (Simulation Investigation)

Estimated Time: 45 minutes Materials: Computer or tablet with internet access, calculator.

1. Open the Planetary Defense: Asteroid Deflection simulation.
2. Note the initial “Asteroid Status” and “Orbital Elements” before taking any action.
   • Initial Trajectory Status: _____
   • Initial Time to Impact (TTI): _____
   • Initial Velocity: _____
   • Initial Semi-major (a): _____
   • Initial Eccentricity (e): _____
3. We have two controls in “Mission Control”:
   • Impactor Δv Magnitude: The change in velocity we impart on the asteroid (0 to 2.0 AU/yr).
   • Impact Direction (Angle): The direction we hit the asteroid. $0^\circ$ is prograde (pushing it forward in its current direction), $-180^\circ$ is retrograde (pushing it backward).
4. Test 1 (Prograde Impact): Set Δv Magnitude to 0.5 AU/yr and Direction to $0^\circ$ (Prograde).
   • Click “EXECUTE IMPACT”. Wait and observe the new trajectory.
   • Does it still collide with Earth? _____
   • New Semi-major axis ($a$): _____
   • New Eccentricity ($e$): _____
5. Test 2 (Retrograde Impact): Click “Reset Scenario”. Set Δv Magnitude to 0.5 AU/yr and Direction to $-180^\circ$ (Retrograde).
   • Click “EXECUTE IMPACT”.
   • Does it still collide with Earth? _____
   • New Semi-major axis ($a$): _____
   • New Eccentricity ($e$): _____

Part 3: Explain (Sensemaking)

Using the data you collected in Part 2, answer the following questions:

1. Kepler’s First Law: Kepler’s first law states that orbits are ellipses. The eccentricity $e$ describes how “stretched” the ellipse is ($e = 0$ is a perfect circle). When you applied a prograde impact ($0^\circ$), did the orbit become more circular or more elliptical? Support your answer with your eccentricity data. _____
2. Semi-major Axis: The semi-major axis $a$ represents the size of the orbit. How did the prograde impact ($0^\circ$) affect the size of the orbit compared to the retrograde impact ($-180^\circ$)? _____
3. Collision Avoidance: Based on your observations, which strategy (prograde or retrograde) was more effective at pushing the asteroid’s path away from Earth’s orbital path at the predicted time of impact? Why? _____

Part 4: Elaborate / Evaluate (Argumentation & Modeling)

Your Mission: You are tasked with determining the minimum required kinetic impact (lowest Δv Magnitude) to safely deflect the asteroid and prevent an Earth collision. We want to save fuel and use the smallest impactor possible.

Task:

1. Use the simulation to find the lowest possible Δv Magnitude that successfully changes the “Trajectory” status from “COLLISION COURSE” to a safe passing orbit.
2. You must decide the best Impact Direction (Angle) to achieve this minimum Δv.
3. Record your final successful parameters:
   • Minimum Δv Magnitude: _____
   • Impact Direction: _____
   • Final Eccentricity ($e$): _____

Final Deliverable: Write a short scientific argument recommending your impact parameters to the planetary defense agency. In your argument:

• State your claim (the exact Δv Magnitude and Direction required).
• Provide evidence from your simulation testing (including how the semi-major axis and eccentricity changed).
• Explain your reasoning using Kepler’s First Law and the relationship between velocity, orbit size (semi-major axis), and the resulting elliptical trajectory.