Answer key: Star Color & Luminosity Worksheet
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Goal: Explain how a star’s surface temperature sets its color and peak wavelength, and how temperature and size together set its luminosity.
Completed results table
| Setting | Luminosity | Peak wavelength | Apparent color |
|---|---|---|---|
| Sun-like (5,772 K, 1 Sun) | 1 Sun | 502 nm | Yellow-white |
| Cool dwarf (3,000 K, 0.2 Suns) | 0.00292 Suns | 966 nm | Orange-red |
| Hot star (15,000 K, 5 Suns) | 1,140 Suns | 193 nm | Blue-white |
| Sirius A (9,940 K, 1.71 Suns) | 25.72 Suns | 292 nm | White |
| Twice as hot (11,544 K, 1 Sun) | 16 Suns | 251 nm | White |
| Twice as wide (5,772 K, 2 Suns) | 4 Suns | 502 nm | Yellow-white |
Answers
Look at your table. As surface temperature goes up, what happens to the peak wavelength and to the star’s color?
The peak wavelength gets shorter as temperature rises (Wien’s law: λ = 2,897,772 nm·K ÷ T). The 3,000 K cool dwarf peaks at 966 nm (infrared) and looks orange-red, the 5,772 K Sun peaks near 502 nm and looks yellow-white, and the 15,000 K hot star peaks at 193 nm (ultraviolet) and looks blue-white.
When you doubled the temperature and kept the radius the same, by what factor did the luminosity change? Use the formula L/L☉ = (R/R☉)² × (T/5,772 K)⁴ to explain why.
It rose 16 times, from 1 Sun to 16 Suns. Luminosity depends on T⁴, so doubling T multiplies L by 2⁴ = 2 × 2 × 2 × 2 = 16.
What happened to the luminosity when you doubled the radius? What about at 10 times the radius? Explain.
Twice the radius gives 4 Suns; ten times the radius gives 100 Suns. Luminosity depends on R² because a star shines from its whole surface, and surface area grows with the square of the radius.
Predict: a red giant is cooler than the Sun (3,500 K) but 40 times wider. Will it be more or less luminous than the Sun? Then press “Red giant” and record its luminosity.
More luminous: about 216 Suns. Each square meter of its cooler surface gives off less light, but 40 times the radius means 40² = 1,600 times the Sun’s surface area, which more than makes up for it.
Sirius A gives off about 26 times as much light as the Sun. Use your table to give two reasons why.
It is hotter (9,940 K), so each square meter radiates (9,940 ÷ 5,772)⁴ ≈ 8.8 times as much power, and it is larger (1.71 Suns), with 1.71² ≈ 2.9 times the surface area. Together: 8.8 × 2.9 ≈ 25.7 Suns.
Challenge: a star has a surface temperature of 3,000 K. What radius would it need to be exactly as luminous as the Sun? Calculate it, then check in the lab.
R = (5,772 ÷ 3,000)² ≈ 3.70 Suns. Setting L = 1 in the formula gives R² = (5,772 ÷ 3,000)⁴. With Star radius 3.7 and 3,000 K, the lab shows 0.999 Suns.