Gravitational Slingshot (Assist) Simulation

Estimated Time: 45-60 minutes

Materials: Computer with internet access, Simulation link, Calculator

Teacher Notes & Alignment

This task is aligned to HS-ESS1-4: Use mathematical or computational representations to predict the motion of orbiting objects in the solar system.

• Science and Engineering Practice (SEP): Using Mathematics and Computational Thinking (Students will use the computational simulation to describe and predict orbital mechanics and gravitational assists).
• Disciplinary Core Idea (DCI): ESS1.B: Earth and the Solar System (Orbits may change due to gravitational effects from other objects).
• Crosscutting Concept (CCC): Scale, Proportion, and Quantity (Students will predict the effect of changing variables like mass and initial velocity on the final velocity of the probe).
• Evidence Statements:
  • 1.a: Students identify and describe relevant components in representations of orbital motion: trajectories of orbiting bodies.
  • 3.c: Students use Newton’s law of gravitation plus his third law of motion to predict how acceleration varies and argue qualitatively about how this relates to observed orbits.

Part 1: Engage (Anchoring Phenomenon)

In 1977, NASA launched the Voyager 1 and Voyager 2 probes. To reach the outer planets of our solar system, they didn’t just use rockets—they used a “gravity assist” or “gravitational slingshot” from Jupiter and Saturn. By flying close to these massive planets, the probes gained enough speed to eventually escape the solar system entirely!

1. How do you think flying towards a planet can make a spacecraft speed up away from the sun?
2. What happens if the spacecraft flies too close? What if it flies too far away?

Part 2: Explore (Simulation Investigation)

Open the Gravitational Slingshot (Assist) Simulation. You will test how the initial parameters of the probe and planet affect the probe’s trajectory and final speed.

• The simulation controls allow you to change:
  • Planet Mass: Multiplier of Earth’s mass (M⊕)
  • Initial Velocity: Measured in Astronomical Units per year (AU/yr)
  • Approach Angle: The angle at which the probe approaches the planet

Instructions:

1. Keep the Planet Mass at 300 M⊕ (roughly Jupiter’s mass) and Initial Velocity at 3.0 AU/yr.
2. Adjust the Approach Angle to find a trajectory where the probe successfully slingshots around the planet and escapes. If it crashes, reset and try a new angle.
3. Record your data in the table below. Repeat for different combinations of Planet Mass and Initial Velocity.

Data Table

| Planet Mass (M⊕) | Initial Velocity (AU/yr) | Approach Angle (deg) | Max Speed (AU/yr) | Final Speed (AU/yr) | Escape Status | | :—: | :—: | :—: | :—: | :—: | :—: | | 300 | 3.0 | | | | | | 300 | 2.0 | | | | | | 100 | 3.0 | | | | | | 500 | 3.0 | | | | |

Part 3: Explain (Sensemaking)

Using the data you collected, answer the following questions:

1. Analyzing Mass: Compare the results when you changed the planet’s mass from 100 to 300 to 500 M⊕ while keeping the initial velocity constant. How did the mass of the planet affect the maximum speed and final speed of the probe? Explain why this happens using Newton’s Law of Universal Gravitation.
2. Analyzing Velocity: How does the probe’s speed change as it approaches the planet versus as it moves away? Why does the Final Speed sometimes end up higher than the Initial Velocity?
3. Escape Velocity: What was the condition for the “Escape Status” to say “Escaped”? If the probe did not escape, what happened to it?

Part 4: Elaborate/Evaluate (Argumentation & Modeling)

Imagine you are a flight trajectory engineer for a new mission to the Oort Cloud. Using your findings from the simulation, write a brief proposal explaining the optimal conditions for a gravitational slingshot. Your proposal must include:

• A claim about which combination of planet mass and approach angle provides the greatest increase in velocity.
• Evidence from your data table to support your claim.
• Reasoning that connects your data to the concepts of gravity, acceleration, and orbital motion.

Hint: Consider why we use Jupiter for gravity assists instead of Mars.