Using the same temperatures as in the previous question, but equal radii. What is L_B/L_R?

Two stars have the same luminosity. Red: T_R = 3000 K; blue: T_B = 30 000 K. What is R_R/R_B? (Use L ∝ R²T⁴.)

Predict first. If the Sun burned coal for its luminosity, would its lifetime be of order days, years, or millions of years? Choose your prediction before calculating.

Calculate. One kilogram of coal releases about 8×10⁶ J when burned. If the Sun (M⊙ ≈ 2×10³⁰ kg) were made of coal, how long (in years) could it provide luminosity L⊙ ≈ 4×10²⁶ W? Enter an approximate number of years.

 Given R⊕ = 6371 km and R⊙ = 695 510 km, how many Earth volumes fit in the Sun? Enter an approximate number (in exponential notation, e.g. 1.4e5).

A star has 25% more mass than the Sun. What is M/M⊙?

If L/L⊙ = 10⁴, what is log₁₀(L/L⊙)?

A right-angled triangle has opposite side 3 and adjacent side 4 (same units). What is the length of the hypotenuse?

Density has dimensions of mass per unit volume. Which expression has the same dimensions as density?

Wien's law states that λ_peak = σ/T. Find the temperature (in K) when λ_peak = 5.0×10⁻⁷ m and σ = 2.90×10⁻³ m K.