Color suggests temperature
B and V are brightness measurements through two filters. Their difference, B−V, is converted here with a classroom color–temperature approximation.
B−V = 1.820 → T ≈ 3,300 KCatalog teaching sample
Equation Lab / Observational astronomy
Measure the impossible.
Earth’s orbit turns one tiny apparent shift into a geometric distance. Select a real nearby star, reconstruct its annual parallax, and follow the observations from color to temperature, distance, luminosity, and an explicitly model-dependent size estimate.
04 / From observation to answer
One star. Four connected measurements.
The catalog supplies what an observatory measures. Each step below shows what can be inferred—and where assumptions enter.
Earth supplies the baseline
Observations six months apart are separated by about 2 AU. The defined annual parallax angle is half the total apparent displacement.
Total six-month shift ≈ 1,536.133 masParallax supplies distance
One parsec is the distance at which one astronomical unit subtends one arcsecond. That definition makes the reciprocal relation possible.
1 / 0.7680665″ = 1.3020 pcDistance reveals luminosity
Distance and apparent V magnitude give absolute magnitude: how bright the star would appear from exactly 10 parsecs away.
mV = 11.13 → MV = 15.56
05 / From distance to size
Distance unlocks the next question.
A direct physical radius requires distance plus angular diameter. Most stars are too small on the sky for a simple classroom measurement, so this lab instead shows a rough model estimate from color, absolute magnitude, and a spectral-type bolometric correction.
This estimate assumes one dominant star and a simplified temperature and bolometric-correction calibration. It is not a substitute for interferometry, eclipsing-binary analysis, or a published catalog radius.
Absolute V magnitude15.56
Adopted bolometric correction−2.50 mag
Classroom radius estimate0.15 R☉
L = 10⁰·⁴⁽⁴·⁷⁴⁻Mbol⁾ L☉ · R/R☉ = √(L/L☉)/(T/5772 K)²
Catalog values are not screen geometry.
Right ascension, declination, parallax, uncertainty, spectral type, and B/V photometry are sourced values. Every star sphere, glow, orbit, and triangle on screen is scaled for legibility.
Inverse parallax is used deliberately.
For this nearby, high-signal sample, d = 1000/p is an excellent teaching approximation. Low-significance or negative catalog parallaxes require statistical distance inference instead.
Color is not distance.
Color constrains temperature after accounting for calibration, extinction, metallicity, and multiplicity. Geometric parallax determines the distance independently.
Trace the numbers.
06 / Selected record provenance
Proxima Centauri
- Catalog identifier
- NAME Proxima Centauri
- Astrometry source
- Gaia EDR3
- Parallax reference
- 2020yCat.1350....0G
- Photometry reference
- 2014AJ....147...21J
- Teaching snapshot
- 2026-07-23 · SIMBAD database