Binary Orbits: Dynamical Reasoning Lab

draft readiness: experimental Orbits Both 16 min

Active development: draft / experimental

Core dynamics and RV-observable workflows are now implemented; parity and launch-gate signoff are still pending.

Launch demo Open fullscreen Station card Instructor notes

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Predict

When $M_2/M_1$ decreases at fixed separation, predict how $P$, $v_1$, and $a_1$ change before revealing readouts.

Play

Change $M_2/M_1$, complete the prediction checkpoint, then compare your prediction to revealed trends in $P$, $v_1$, and $a_1$.
Prediction gating is enforced for snapshots and Copy Results while a reveal is pending.
Use the linear momentum check to verify $M_1v_1 = M_2v_2$ in the barycentric frame.
Use the invariant panel as a discrimination task: select all must-hold statements and avoid distractors.
Toggle angular frequency view and verify $v_1 = \omega a_1$ and $v_2 = \omega a_2$.
Switch to RV view, vary inclination $i$, and compare amplitudes $K_1$ and $K_2$.
Switch to Energy view and track how $K$, $U$, and $E$ scale when changing separation and mass ratio.
Start the RV inversion challenge, click both RV curves to measure amplitudes, infer $q$, then reveal and compare error.

Explain

Explain, using one invariant, one observable, and one energy statement, how this model links conservation laws to stellar mass inference.

Learning goals

Use momentum conservation to explain why the lighter body moves faster around the barycenter.
Explain shared period through shared angular frequency $\omega = 2\pi/P$.
Connect barycentric motion to spectroscopic observables through RV amplitudes $K_1$ and $K_2$.
Relate circular-orbit energies ($K$, $U$, $E$) to separation scaling and virial balance.
Infer mass ratio from measured RV amplitudes using $q = K_1/K_2$ and compare to model truth.

Misconceptions targeted

The larger object stays fixed while the smaller one orbits it.
If one object moves faster, it must have a shorter period.

Model notes

This model enforces Newton's laws for two point masses in circular orbit about a shared barycenter.
It conserves total linear momentum in the barycentric frame: $M_1v_1 = M_2v_2$.
Units: distance in $\\mathrm{AU}$, time in $\\mathrm{yr}$, and masses in $M_{\\odot}$ with $G = 4\\pi^2\\,\\mathrm{AU}^3/(\\mathrm{yr}^2 M_{\\odot})$.
Excluded physics: eccentricity, tides, relativity, and mass transfer.
RV inversion challenge in this pass assumes a circular, double-lined case where $q = K_1/K_2$.

About this demo

This instrument turns binary motion into a reasoning workflow: predict first, test conservation constraints, connect orbital dynamics to radial-velocity observables, then use energy decomposition and RV inversion to close the inference loop.