Moon Phases: Light, Not Shadow

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: Moon Phases (6–8 minutes) Demo setup: start at New → First Quarter → Full → Third Quarter. Tip: Click Station Mode to add key-phase rows and print/copy your table. Advanced (optional): Enable Advanced: latitude/season to estimate rise/set using latitude (deg) and day of year (1–365). Polar day/night returns N/A.

Your station artifact (fill in):

1. Control(s): Moon angle $\alpha$

2. Observable(s): phase name, illumination fraction $f$, illuminated (%), days since new ($d$), waxing/waning

3. Governing relationship: write this equation in words:

   $$f=\frac{1+\cos\alpha}{2}$$

4. Sanity check: what is $f$ at $\alpha=90^\circ$?

5. Connection sentence: “This matters for eclipses/totality because…”

Data Collection Tasks (Station Mode)

1. Click Station Mode at the top of the demo. Add the four key phases using the preset buttons: New, First Quarter, Full, Third Quarter. Four rows appear in the table.

2. For each preset row, verify that the phase name, $\alpha$, $f$, and illuminated (%) match your expectations.

3. Now add four custom angle rows by dragging the Moon to approximately $\alpha = 45^\circ$, $135^\circ$, $225^\circ$, and $315^\circ$. Click Add Row for each. You should now have 8 rows.

4. Look at your 8-row table. Describe in one sentence how $f$ changes as $\alpha$ increases from $0^\circ$ to $360^\circ$.

5. Click Export to copy the table, then paste it into your lab document.

Data table template

Phase name	$\alpha$ (deg)	$f$	Illuminated (%)	Waxing / Waning
Full	0	1.00	100	—
First Quarter	90	0.50	50	Waning
New	180	0.00	0	—
Third Quarter	270	0.50	50	Waxing
(custom)	45
(custom)	135
(custom)	225
(custom)	315

Word bank + sanity checks Word bank:

• Phase: the shape we see from Earth; it’s the overlap of the Moon’s lit half and the half facing Earth.
• Illumination fraction $f$ (0–1): fraction of the visible disk that is lit (0 = New, 1 = Full).
• Illuminated (%): the same information as $f$, but scaled to 0–100.
• Days since new ($d$): where we are in the 29.53-day cycle (0 at New, ~14.8 at Full).
• Moon angle $\alpha$ (degrees, this demo): $0^\circ$ = Full, $180^\circ$ = New; quarter phases are at $90^\circ$ and $270^\circ$.
• Waxing: the illuminated fraction is increasing (after New → toward Full).
• Waning: the illuminated fraction is decreasing (after Full → toward New).
• Quarter phase: about 50% illuminated; “quarter” refers to the orbit position, not the lit fraction.

Sanity checks:

• First/Third Quarter should be about 50% illuminated.
• New Moon is not “unlit” — the Sun still lights half the Moon; we’re mostly seeing the dark half.
• Full Moon should be about halfway through the cycle ($d \approx 14.8$ days since new).
• Earth’s shadow is not what causes phases (it matters only during eclipses, which are rare).