Angular Size: The Sky’s Ruler

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: Angular Size (6–8 minutes) Demo setup: Compare Sun and Moon (Today); then toggle Moon orbit mode.
Tip: Click Station Mode to add rows and print/copy your table.

Your station artifact (fill in):

1. Control(s): diameter $D$, distance $d$

2. Observable(s): angular diameter $\theta$ (deg/arcmin/arcsec)

3. Governing relationship: write this equation in words:

   $$\theta = 2\arctan!\left(\frac{D}{2d}\right)$$

4. Sanity check: what happens to $\theta$ if $d$ doubles?

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

Word bank + sanity checks Word bank:

• Angular size $\theta$ (degrees/arcmin/arcsec): how big an object looks on the sky (an angle).
• Physical diameter $D$ (km in this demo): the object’s actual size.
• Distance $d$ (km in this demo): how far the object is from the observer.
• Small-angle idea: larger $D$ → larger $\theta$; larger $d$ → smaller $\theta$.
• Unit ladder: $1^\circ = 60,\mathrm{arcmin}$ and $1,\mathrm{arcmin} = 60,\mathrm{arcsec}$.

Sanity checks:

• If $d$ doubles, $\theta$ should get about half as big (for small angles).
• The Sun and Moon have similar angular sizes today, which is why total solar eclipses are possible sometimes.
• Perigee vs apogee: the Moon’s angular size is slightly larger at perigee than at apogee.