Horizons: Exploring the Universe (MindTap Course List)
Horizons: Exploring the Universe (MindTap Course List)
14th Edition
ISBN: 9781305960961
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 9, Problem 13P
To determine

What is its radius if a T Tauri star is the same temperature as the Sun but is ten timesmore luminous?

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If a T Tauri star is the same temperature as the Sun but is eighteen times more luminous, what is its radius relative to the Sun? (Hint: Use the luminosity-radius-temperature relation: L L  =    R R   2     T T   4   .) R R  =
The origin of the above quote (with "flame" or "candle" sometimes substituted for "light") is unclear. It is often attributed to either Lao Tzu or to the character Eldon Tyrell from the 1982 movie Blade Runner.   Stars follow a similar law, although the factor isn't precisely 1/2. In this problem, you will figure out the precise factor that the quote should have to apply to stars. Using the proportionality relationships for stellar luminosity as a function of mass and stellar lifetime as a function of mass, combine the two equations to arrive at a proportionality for stellar lifetime as a function of luminosity. Consider a star with luminosity twice that of the Sun's. Compute the star's main sequence lifetime as a multiple of the Sun's main sequence lifetime. Enter your result below as a decimal. For example, if you found TT⊙=0.3, enter "0.3". (Here T is the star's lifetime and T⊙ is the Sun's main sequence lifetime.
Using solar units, we find that a star has 4 times the luminosity of the Sun, a mass 1.25 times the mass of the Sun, and a surface temperature of 4090 K (take the Sun's surface temperature to be 5784 K for the sake of this problem). This means the star has a radius of....................  solar radii and is a .................... star (use the classification).
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