Retrograde Motion: Apparent Longitude from Relative Motion
draft readiness: experimental EarthSky Orbits Both 12 min
Core demo behavior is implemented, but parity and launch-gate signoff are still pending.
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This exhibit's copy was imported from the legacy ASTR101 SP26 demos and has not yet been
fully reviewed against the current instrument UI, units, and exports.
Predict
Predict
If Earth is moving faster than Mars, what do you predict happens to Mars’s apparent direction in the sky near opposition?
Play
Play
- Use the Earth (observer) $\to$ Mars (target) preset and find a retrograde interval (shaded).
- Use sidebar transport controls; use the stage-adjacent timeline row to scrub model day $t$.
- Switch to Earth $\to$ Venus and compare how the geometry hint changes for an inferior planet.
Explain
Explain
Use relative motion and the observer-to-target direction to explain why $d\tilde{\lambda}/dt$ can become negative even though neither orbit reverses.
Learning goals
- 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.
Misconceptions targeted
- Retrograde means the planet reverses its real orbit.
Model notes
- The model uses coplanar Keplerian ellipses around the Sun with elements $(a,e,\varpi,L_0)$ defined at an epoch $t_0$; it is not ephemeris-grade.
- Apparent (sky) longitude is defined by $\lambda_{\mathrm{app}}(t)=\operatorname{wrap}_{0..360}(\arctan2(y_t-y_o,\,x_t-x_o))$ and is unwrapped with the 180-deg jump rule to form $\tilde{\lambda}(t)$.
- Retrograde is defined by $d\tilde{\lambda}/dt<0$ using a central-difference derivative on an internal step of $\Delta t_{\mathrm{internal}}=0.25$ day (model day).
- Time is model time only: $1$ model month $=30$ model days; do not interpret the output as calendar dates.
About this demo
Use a simple Keplerian model to visualize how the direction to a planet can briefly reverse in the sky (retrograde) even though the planet never reverses its orbit.
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