Question A4 a) A star has a temperature T = 15000K, mass M = 0.25M and luminosity L = 0.02L. Sketch the position of this star on the Hertzsprung-Russell diagram relative to the main sequence. b) Using the given properties of the star, derive expressions for the star's radius R and mean density p. Calculate values for these in units of R. and kg m-³, respectively. c) Starting from the equation for hydrostatic equilibrium, derive an approximate expression for the central pressure Pc of the star in terms of its density p and radius R, assuming uniform ρ density. d) Assuming that the star is made of ordinary gas material such as the Sun, calculate an estimate of the central temperature of the star. From this value and the luminosity, briefly explain what can be inferred about the nuclear processes in the star. Discuss very briefly why your estimate for the central temperature may be too large.

Question A4 a) A star has a temperature T = 15000K, mass M = 0.25M and luminosity L = 0.02L. Sketch the position of this star on the Hertzsprung-Russell diagram relative to the main sequence. b) Using the given properties of the star, derive expressions for the star's radius R and mean density p. Calculate values for these in units of R. and kg m-³, respectively. c) Starting from the equation for hydrostatic equilibrium, derive an approximate expression for the central pressure Pc of the star in terms of its density p and radius R, assuming uniform ρ density. d) Assuming that the star is made of ordinary gas material such as the Sun, calculate an estimate of the central temperature of the star. From this value and the luminosity, briefly explain what can be inferred about the nuclear processes in the star. Discuss very briefly why your estimate for the central temperature may be too large.