Conservation Laws: Energy & Momentum

near-ready Orbits Both 10 min

Active development: beta / candidate

Presets, starting state, energy readouts, orbit timing and screen-reader announcements were checked against independent calculations on 2026-09-11; awaiting classroom use before stable.

Launch demo Open fullscreen Station card Instructor notes

If the embed doesn’t load, open the demo fullscreen.

Predict

A planet on an elliptical orbit moves closer to its star. What happens to its speed, its kinetic energy and its total energy?

Play

Press Play (or Step) on the Elliptical preset and watch $K$ and $U$ trade places while $\varepsilon$ stays fixed.
Drag $v/v_{\rm circ}$ from 1.41 to 1.42: the orbit switches from elliptical to hyperbolic. Press Escape for exactly $\sqrt{2}$, where $\varepsilon = 0$.
Set the direction to $60^\circ$ and compare $|h|$ and periapsis $r_p$ with $0^\circ$ at the same speed factor.

Explain

Which quantities stayed constant while the body moved, which changed, and what assumptions make that true?

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.
A faster-moving orbiting body has more total energy.

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 $v/v_{\rm circ}=\sqrt{2}$; the Escape preset sets it exactly, while the slider steps from 1.41 to 1.42.

About this demo

Start with a circular case ( $v/v_{\rm circ}=1$ ), press Play on the Elliptical preset to watch $K$ and $U$ trade, then press Escape ( $\sqrt{2}$ ) and go beyond to see $\varepsilon$ change sign.