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 ρ. 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 ρ and radius R, assuming uniform density and luminosity L 0.02Lo.a) A star has a temperature T = 15000K, mass M = 0.25MSketch the position of this star on the Hertzsprung-Russell diagram relative to the mainsequence.b) Using the given properties of the star, derive expressions for the star's radius R and meandensity 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 forthe central pressure P. of the star in terms of its density p and radius R, assuming uniformdensity.

a) Based on the given properties, the star falls in the blue-white region of the Hertzsprung-Russell…

Answered: a) A star has a temperature T = 15000K,…

Applications and Investigations in Earth Science (9th Edition)

9th Edition

ISBN:9780134746241

Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

Chapter1: The Study Of Minerals

Section: Chapter Questions

Problem 1LR

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Question

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 ρ. 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 P_c of the star in terms of its density ρ and radius R, assuming uniform density