Orbits

Learning goals aggregated from all exhibits in this topic.

• 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.
• Identify quantities that remain constant under specific assumptions.
• Use conservation ideas to predict qualitative outcomes.
• Connect ‘conserved’ to ‘closed system’ and stated assumptions.
• Describe how orbital speed changes along an ellipse.
• Connect orbital period to distance from the central body.
• Use qualitative evidence to support a Kepler-law claim.
• Define conjunction and opposition as seen from Earth.
• Explain why conjunctions repeat using Earth’s motion relative to another planet.
• Use the model to estimate the time between successive conjunctions (synodic period).
• Define retrograde motion as an apparent reversal caused by viewing geometry and relative motion.
• Interpret apparent (sky) longitude $\lambda_{\mathrm{app}}$ as the direction from an observer planet to a target planet in an inertial frame.
• Identify stationary points as times when $d\tilde{\lambda}/dt = 0$ and connect them to the start/end of retrograde.