What to notice 3 bullets

• Venus laps Earth frequently (~584 days) because their orbits differ significantly in period.
• Mars has the longest synodic period (~780 days) among naked-eye planets because its sidereal period is closest to Earth's.
• As you go to outer planets (Jupiter, Saturn), synodic periods approach Earth's year (365 days) from above.

Model notes AU / yr / $M_\odot$

• Teaching units: AU / yr / $M_{\odot}$ with $G=4\pi^2\,\mathrm{AU}^3/(\mathrm{yr}^2\,M_{\odot})$.
• Orbits are shown as circles at the mean semi-major axis (eccentricity ignored for visual clarity).
• Sidereal periods come from JPL J2000 approximate elements via Kepler's third law: $P^2 = a^3$.
• Synodic period: $P_{\rm syn} = \dfrac{P_1 \cdot P_2}{|P_1 - P_2|}$.
• A conjunction is detected when the heliocentric angular separation drops below 5 degrees.