PHY074 · Astronomy & Space · Classes 11–12 + College
Parallax distance
Objective: To measure the distance to a nearby star from its parallax shift as the Earth orbits the Sun.
🧰 Apparatus
- (Simulation) Earth orbit and star field
- Classroom model: a pencil held at arm's length, viewed with each eye
- Protractor
📐 Formulas and SI units
d (pc) = 1 / p (arcsec)
1 pc = 3.26 ly = 3.086 × 10¹³ km
💡 Theory
A nearby star seems to shift against distant background stars when seen from opposite sides of the Earth's orbit, six months apart. Half of this angular shift is the parallax p. A star with p = 1 arcsecond is 1 parsec away (3.26 light-years): d (pc) = 1/p (arcsec).
🪜 Procedure
- Classroom: hold a pencil up and look with one eye, then the other; note the shift.
- Move the pencil closer: the shift grows.
- In the simulation, set p and read the distance.
- Compare Proxima Centauri (0.768″) with farther stars.
📋 Observations Simulated values
✅ Result and conclusion
Proxima Centauri's parallax of 0.768″ puts it 1.30 pc (4.25 light-years) away.
🔬 In a real lab
Parallax angles are tiny, so the atmosphere blurs them; satellites like Gaia measure them to millionths of an arcsecond.
⚠️ Safety
Never point telescopes or binoculars towards the Sun.
❓ Quick check
1. A larger parallax means the star is…
2. Parallax is measured six months apart because…
3. 1 parsec is about…
🏋️ Practice
Easyp = 0.1″. d?
Answer: 10 pc
Mediumd = 4 pc. p?
Answer: 0.25″
ChallengeConvert 10 pc to light-years.
Answer: 32.6 ly