Five-day instructional plan with calculations, misconceptions, differentiations, accessible resources and teacher-reviewed evidence.
Purpose, sequence and safety
Essential question: How can the same gravitational interaction explain falling and orbiting? Connect Week 08 centripetal motion to the inverse-square law and orbital free fall. Lessons offer quantitative modeling related to HS-PS2-4 and HS-ESS1-4, without claiming these five sessions alone establish full standards mastery.
Prerequisites: mass and gravity forces, vector directions, Newton's three laws, radial force F=mv²/r, unit conversions between km and m, exponents and square roots. Students who need help receive the worked examples and printed CSV tables; advanced students derive circular speed and orbital period algebraically.
Monday — Why Astronauts Float
8-minute launch: Ask whether low Earth orbit has gravity. Students draw a curved satellite path and an inward arrow at one point.
17-minute explanation: Velocity is tangent, gravitational force and acceleration radial. Astronauts and the spacecraft share free fall and experience little support force: apparent weightlessness is not absent gravity.
15-minute check: At 400 km above Earth, r=6,771 km and g≈8.69 m/s². Compare with g≈9.82 m/s² in our Earth surface model.
5-minute exit: Explain shared free fall and two omitted realistic effects.
Derivation: μm/r²=mv²/r for a circular orbit with gravitational force as its radial resultant. Satellite mass cancels, giving v=√(μ/r). Divide circumference by speed: T=2πr/v=2π√(r³/μ).
Earth model worked answer: h=400 km, r=6,771,000 m, v≈7.67 km/s and T≈92.4 min. Larger orbital radius gives lower circular speed but longer period.
Misconception probe: An ellipse is not a circular orbit; its instantaneous speed need not equal √(μ/r) at every point.
Gravity study: Three altitude trials for Earth with identical test mass; record g, F and center radius; compute one field ratio.
Orbit study: Three altitude trials for Earth; record circular speed and period; explain their opposite altitude trends.
Comparative enrichment: Repeat for the Moon, naming that its radius and μ both differ from Earth's, so this is not a one-variable experiment across planets.
Model quality: Ensure JSON notes include a testable question, named controlled variable, rounded units and one absent physical effect. Both labs provide accessible numeric tables and offline CSV alternatives.
Require a diagram with orbital tangent velocity and inward gravitational force; one correct inverse-square ratio, one orbital calculation, a limitation, a counterclaim corrected and one independent follow-up question.
Example: a satellite at 400 km has substantial gravity, ≈8.69 m/s² in the simplified model, and orbits with T≈92.4 min in the same model. A passenger floating in the spacecraft is in shared free fall, not outside Earth's gravity.
Randomized ten-question Friday exercise is open-book formative practice from a twenty-item bank. Corrective retries aim at 80%; public source-code questions and client-side scores are not proctored midterms, finals or authoritative grades.