Planetary Conjunctions: Alignments in the Sky

Earth Mars
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: $P_{\rm syn} = \dfrac{P_1 \cdot P_2}{|P_1 - P_2|}$.
  • An alignment is detected when the heliocentric angular separation drops below 5 degrees, meaning both planets lie on the same ray out from the Sun.
  • What that alignment is from Earth depends on the target: for a planet inside Earth's orbit (Venus) it is an inferior conjunction; for a planet outside Earth's orbit (Mars, Jupiter, Saturn) Earth lies between the Sun and the target, which is an opposition. The readout label tracks the selected target.
  • Only the same-longitude alignment is detected. The complementary alignment 180 degrees away (superior conjunction for Venus, conjunction for the outer planets) is not flagged.