Retrograde Motion: Apparent Longitude from Relative Motion

Name: ________________________________ Section: __________ Model day window: __________

Station: __________ Group members: ________________________________________________

Goal: Use the demo to make a claim about retrograde motion supported by (1) at least one number/readout and (2) at least one sanity check.

Station card: Retrograde Motion (8-10 minutes) Demo setup: Select Earth $\to$ Mars as the observer/target pair. Set speed in the sidebar, then press Play in the sidebar transport controls. Timeline tip: Use the timeline row near the visualization stage for scrub and stationary navigation. Tip: Click Station Mode to record stationary-point and opposition data into a table you can export.

Your station artifact (fill in):

1. Control(s): observer planet, target planet, elapsed time
2. Observable(s): apparent longitude $\lambda_\text{app}$ (deg), motion state (prograde / stationary / retrograde), retrograde arc size (deg), retrograde duration (days)
3. Governing relationship: Retrograde motion is an apparent backward drift in a target’s ecliptic longitude caused by the changing line-of-sight direction as the two planets follow their orbits at different speeds.
4. Sanity check: Mars retrograde occurs near opposition; Venus retrograde occurs near inferior conjunction. Neither planet physically reverses its orbit.
5. Connection sentence: “Retrograde motion matters for understanding orbital mechanics because…”

Data Collection Tasks (Station Mode)

1. Select Earth $\to$ Mars. Press Play and let the animation run until you see the apparent longitude reverse direction (the longitude plot curves backward). Pause at the first stationary point (where the curve flattens before reversing).

2. Click Add Row in Station Mode. Record model day $t$, $\lambda_\text{app}$, and motion state. Label this row “Mars: start retrograde.”

3. Continue playing until the longitude resumes prograde motion (the second stationary point). Add another row: “Mars: end retrograde.” The difference in model days is the retrograde duration.

4. Find the midpoint of the retrograde arc; this is close to opposition (Sun-Earth-Mars alignment). Add a row: “Mars: opposition.”

5. Now switch to Earth $\to$ Venus. Repeat steps 1-4, recording the start, end, and inferior conjunction midpoint. Venus retrogrades near inferior conjunction (Sun-Venus-Earth alignment).

6. Optional advanced case: set observer = Venus and target = Earth to inspect the same geometry from Venus’s frame.

7. Compare your two tables: Which planet has a longer retrograde duration? Which has a larger retrograde arc?

Data table: Mars

Data table: Venus

Word bank

• Apparent longitude $\lambda_\text{app}$: the target’s position projected onto the ecliptic as seen from the observer planet ($0^\circ$-$360^\circ$).
• Prograde: normal eastward motion along the ecliptic (increasing $\lambda_\text{app}$).
• Retrograde: apparent westward drift (decreasing $\lambda_\text{app}$); caused by the changing line-of-sight, not a reversal of the planet’s orbit.
• Stationary point: the instant when $\lambda_\text{app}$ momentarily stops changing (transition between prograde and retrograde, or vice versa).
• Opposition: Sun-Earth-target aligned with Earth in the middle; occurs for superior planets (Mars, Jupiter, …).
• Inferior conjunction: Sun-target-Earth aligned with the target between Sun and Earth; occurs for inferior planets (Venus, Mercury).
• Synodic period: the time between successive oppositions (or successive inferior conjunctions); determines how often retrograde recurs.

Sanity checks:

• Mars retrograde should last roughly 70-80 days with an arc of about $15^\circ$-$20^\circ$.
• Venus retrograde should last roughly 40-45 days with an arc of about $15^\circ$-$17^\circ$.
• Retrograde always brackets opposition (superior planets) or inferior conjunction (inferior planets).
• No planet ever physically reverses its orbit; retrograde is purely an apparent, line-of-sight effect.