A red giant star has a temperature of 3,000 K and a luminosity #10^5# solar luminosities. How do you calculate the radius of the red giant in terms of the radius of the sun?

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Answer 1 · 2018-04-13T18:37:00

#=>R approx 33.33 " R"_ "sun"#

When you are dealing with solar units, the luminosity-radius-temperature relationship is simplified to:

#=>L = R^2T^4#

Solving for #R#:

#=>R = sqrtL/T^2 #

We are given #T = 3000 "K"# and #L = 10^5 "L"_ "sun"#. #R# in units of #"R"_ "sun"# is then:

#=>R = sqrt((10^5)^2)/3000 "R"_"sun"#

#=>R = 10^5/(3 xx 10^3) "R"_ "sun"#

#=>R = (1/3 xx 10^2)"R"_ "sun"#

#=>R = (100/3)"R"_ "sun"#

#=>color(green)( R approx 33.33 " R"_ "sun" )#