E.5 · IB Physics
Stellar parallax
Watch Earth orbit the Sun while a nearby star appears to shift against distant background stars. Change the star's distance and the measuring precision to see where the parallax method stops working.
d = 1 / p
d in parsecs (pc), p in arcseconds (″)
1 pc = 3.09 × 10¹⁶ m = 3.26 ly
1″ = 1/3600 °
d in parsecs (pc), p in arcseconds (″)
1 pc = 3.09 × 10¹⁶ m = 3.26 ly
1″ = 1/3600 °
- Parallax p
- Six-month shift 2p
- Distance
- Distance
- Δd/d ≈ Δp/p
Try this
- Set d = 1.30 pc (about the distance of the nearest star) and read p. Now double d: what happens to p?
- With the ground-based uncertainty, increase d until the status says the method fails. Switch to Gaia and find the new limit.
- Watch the magnified view for a full orbit: compare the total shift between the two ghost positions with p.
Common error: p is half of the total angular shift seen six months apart, and d = 1/p gives parsecs only when p is in arcseconds, so convert before using metres or light-years.