Conservation Laws: Energy & Momentum
draft readiness: experimental Orbits Both 10 min
Core demo behavior is implemented, but parity and launch-gate signoff are still pending.
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Predict
Predict
In an ideal closed system with no external forces, what happens to total momentum over time?
Play
Play
- Start at $v/v_{\rm circ}=1$ and direction $0^\circ$ to see a near-circular bound orbit.
- Increase $v/v_{\rm circ}$ toward $\sqrt{2}$ and notice $\varepsilon$ approaches 0 at the escape boundary.
- Change direction (e.g., $60^\circ$) and compare how $|h|$ and periapsis $r_p$ change even at similar speed factor.
Explain
Explain
State what appears conserved in the model, and what assumptions make that conservation reasonable.
Learning goals
- Identify quantities that remain constant under specific assumptions.
- Use conservation ideas to predict qualitative outcomes.
- Connect ‘conserved’ to ‘closed system’ and stated assumptions.
Misconceptions targeted
- Energy is always conserved in the same form without exceptions.
Model notes
- Teaching units: AU / yr / $M_{\odot}$ with $G = 4\pi^2\,\mathrm{AU}^3/(\mathrm{yr}^2\,M_{\odot})$.
- Orbit type is determined by conserved specific energy $\varepsilon$ and angular momentum $h$.
- Escape at $v/v_{\rm circ}=\sqrt{2}$.
About this demo
Start with a circular case ($v/v_{\rm circ}=1$), then move toward escape ($\sqrt{2}$) and beyond to see how $\varepsilon$ changes sign.