Answer key: Stellar Parallax Worksheet
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Goal: Use parallax angles to measure distances to nearby stars, and explain why the method gets harder for distant stars.
Completed results table
| Setting | Distance | Light travel |
|---|---|---|
| Proxima Centauri (0.768″) | 1.3 pc | 4.25 years |
| Ten parsecs (0.1″) | 10 pc | 32.62 years |
| One kiloparsec (0.001″) | 1,000 pc | 3,261.56 years |
| Sirius (0.379″) | 2.64 pc | 8.61 years |
| Parallax 0.05″ | 20 pc | 65.23 years |
Answers
How far away is Proxima Centauri in parsecs and in light-years?
1 ÷ 0.768 ≈ 1.30 parsecs, about 4.25 light-years.
Compare the “Ten parsecs” and “One kiloparsec” rows. The angle became 100 times smaller. What happened to the distance? Write the rule.
The distance became 100 times larger, from 10 to 1,000 parsecs. Distance is inversely proportional to parallax: d = 1/p.
Predict: how far away is a star with a parallax of 0.05″? Check with the lab.
1 ÷ 0.05 = 20 parsecs, about 65 light-years.
Sirius has a parallax of 0.379″. How far away is it in light-years?
About 2.64 parsecs, or 8.6 light-years.
Why are distant stars harder to measure with parallax?
Their parallax angles are tiny. A star 1,000 parsecs away shifts by only 0.001″, so even a small measurement error is a large fraction of the angle. Space telescopes such as Gaia measure these angles above Earth’s blurring atmosphere.
Explain where the parallax shift comes from. Add a quick sketch if it helps.
As Earth orbits the Sun, we view a nearby star from different places. Six months apart we are 2 AU apart, so the nearby star appears to shift against much more distant background stars. The parallax angle p is half of that total shift.