Kepler’s Laws: Patterns of Planetary Motion

Name: ________________________________ Section: __________ Date: __________

Station: __________ Group members: ________________________________________________

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

Station card: Kepler’s Laws (6–8 minutes) Controls: $a$, $e$, time (mean anomaly $M$, deg) (and in Newton mode: central mass $M$, $M_{\odot}$)
Overlays: foci, apsides, equal areas, vectors

Your station artifact (fill in):

1. Observation: where is the planet fastest (perihelion or aphelion)?
2. Kepler law: explain using “equal areas in equal times.”
3. Geometry: identify perihelion and aphelion in the orbit.
4. Scaling: if $a$ doubles (same $M$), what happens to $P$ (longer/shorter, and why)?
5. Connection sentence: “This connects to another course idea because…”

Word bank + sanity checks Word bank:

• Semi-major axis $a$ (AU): the orbit’s size scale.
• Eccentricity $e$ (unitless): orbit shape (0 = circle; larger = more stretched).
• Perihelion / aphelion: closest / farthest point from the star.
• Kepler 2: equal areas in equal times (a timing law $\rightarrow$ speed changes).
• Kepler 3: bigger orbits have longer periods (for the same central mass).

Key relationship (period scaling):

$$P \propto a^{3/2}$$

Sanity checks:

• If $e=0$, speed should be constant around the orbit.
• For an ellipse, the planet should move fastest at perihelion.
• Increasing $a$ should increase the period $P$.