Answer :
A red supergiant with a temperature of 3000 K and a total luminosity of 60000 times that of the Sun, using the radius-luminosity-temperature relationship the radius is 700 AU (to two significant figures).
The radius-luminosity-temperature relation can be used to calculate the radius of a red supergiant. Given a temperature of 3000 K and a total luminosity of 60000 times that of the Sun, the radius can be calculated as follows:
R = (L/Lsun)[tex]^{\frac{1}{2} }[/tex]* (Teff/Teff,sun)⁻²
where R is the radius of the star, L is the luminosity, Teff is the effective temperature, and Lsun and Teff, sun are the luminosity and effective temperature of the Sun, respectively.
Substituting the given values, we get:
R = (60000)[tex]^{\frac{1}{2} }[/tex] * (3000/5777)⁻²
R = 4657.88 AU
Therefore, the radius of the red supergiant is approximately 4700 AU (two significant figures).
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