Parallax Distance: Measuring the Stars

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: Parallax Distance (6–8 minutes) Artifact: a capture log with one inference and one quality claim.

At the station, produce:

• A chosen true distance $d_{\rm true}$ and two capture phases (A and B),
• A measured shift $\Delta\theta$ and effective baseline $B_{\rm eff}$,
• Inferred parallax $\hat p$ and inferred distance $\hat d$,
• One sentence about quality: “This inference is (strong/weak) because $\hat p/\sigma_{\hat p}$ is ____.”

Word bank + sanity checks Word bank:

• Parallax: apparent shift caused by observer motion, not star motion.

• Measured shift $\Delta\theta$: detector-space change between captures A and B.

• Effective baseline $B_{\rm eff}$: projection of the capture baseline onto the parallax axis.

• Inferred parallax $\hat p$: $\hat p=\Delta\theta/B_{\rm eff}$.

• Parsec (pc): defined so that:

  $$d,(\mathrm{pc})=\frac{1}{p,(\mathrm{arcsec})}$$

Sanity checks:

• If $d=1,\mathrm{pc}$, then $p=1,\mathrm{arcsec}=1000,\mathrm{mas}$.
• If distance increases by $10\times$, inferred parallax should decrease by about $10\times$ for the same capture geometry.
• If $B_{\rm eff}$ is too small, inference becomes unstable even when chord baseline looks large.