AST 341 Homework 4 Due Monday 5 November 2012 C&O questions are from Carroll & Ostlie, 2nd edition (the big orange book). 1. Derive the homologous form of the luminosity equation, df dx = Dp2 tν−2 x2 . 2. C&O 10.3 3. C&O 10.5 4. C&O 10.7 5. C&O 10.17 6. C&O 11.2 7. C&O 11.3 8. T Tauri stars collapse quasi-statically, converting gravitational potential energy into heat. If you could measure the radius of a T Tauri star very accurately, how much smaller would it be after a year? Assume a mass of 1 M⊙ , a radius of 3 R⊙ , and Tef f =4500K. If you had a photometer capable of measuring the brightness with 0.001 magnitude accuracy, how long would it take before you noticed the star fading (ignore the fact that all T Tauri stars are stochastically variable on timescales of days to years)? 1