Don McCarthy's Questions of the Week

Problem #1: Follow up from last week.

The following equation characterizes “main sequence” stars: (L/L_⊙) = (M/M_⊙)^α

The letters “L, M” refer to a star’s luminosity and mass, respectively. The symbol “⊙” refers to the Sun. The symbol “α” is a number greater than zero.

After being sure you understand the terms, reflect on what this equation is saying and write a sentence describing a trend you notice. Do not use Google, etc.; just look at the equation and think about it.

Does the equation work for the star Sirius (2 M_⊙ and 25 L_⊙) in the Club’s scale model downstairs?

Problem #2: In case you already know about problem #1. Do this problem without a calculator.

Jack drives a gas-guzzling SUV 15,000 miles a year. It averages 10 mpg. His wife Jill drives an economy car the same distance. It gets 30 mpg.

The couple wants to use less gasoline. They can afford to trade Jack’s clunker for an SUV that gets 13 mpg or trade Jill’s sensible car for a hybrid that gets 60 mpg.

Which trade would save the most gasoline?