Orbital mechanics is notoriously hard to grasp from textbook diagrams alone. This guide maps out a four-lesson sequence that builds intuition before introducing equations.
The conceptual barrier is not the mathematics. Students who can compute orbital velocity from F = mv²/r often have no mental model of what an orbit actually is. They cannot explain why a satellite does not "fall down" — they just know the formula says it goes sideways fast enough. This is a gap between procedure and understanding.
The solution is to let students discover orbital mechanics empirically before they encounter the equations. PHYSIX makes this tractable in a standard classroom period.
Start with Newton's cannon thought experiment. Students drag a cannon ball to increasing horizontal velocities and observe it hitting the ground progressively further away, then curving around the Earth, then escaping into space. No equations yet — just observation and questioning.
By the end of Lesson 1, students should be able to answer: "At what speed does the cannonball never hit the ground?" They will have discovered orbital velocity empirically.
Students build a planet-star system and set it in an elliptical orbit. They then use the PHYSIX timer and ruler to verify Kepler's Second Law (equal areas in equal times) by measuring the area swept during three equal time intervals at different points in the orbit.
Lesson 2 ends with students deriving Kepler's Third Law empirically: plot T² vs a³ for five orbits of different sizes. The straight line is the discovery moment.
Students calculate escape velocity from the empirical formula they derived in Lesson 2, then verify it by gradually increasing velocity until the orbit opens into a parabola. The Hohmann transfer orbit — a two-burn manoeuvre connecting two circular orbits — is then demonstrated as a worked example in PHYSIX.
The gravitational slingshot (or gravity assist) is one of the most counter-intuitive results in classical mechanics: a spacecraft can gain kinetic energy by flying past a planet, with no propellant required. Students set up a Jupiter flyby and measure the spacecraft's speed before and after the encounter in both the planet's and the Sun's reference frames.
Energy is conserved. What changes is the distribution: the planet loses an immeasurably small amount of orbital energy, and the spacecraft gains a large amount.
A suitable end-of-sequence assessment is a design task: "Plan a mission to Mars that uses a gravity assist from Venus to reduce fuel cost. Specify the departure window, transfer orbit, and flyby parameters." Students submit a PHYSIX scenario file and a one-page write-up. This assesses both procedural skill and conceptual understanding simultaneously.