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:

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

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

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

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

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

A red giant star has a temperature of 3,000 K and a luminosity 10^510^5 solar luminosities. How do you calculate the radius of the red giant in terms of the radius of the sun?