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 Post subject: Surface Tempuratre of our sun in 5 Billion Years?
PostPosted: Sat Apr 19, 2014 8:00 am 
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Joined: Sun Oct 11, 2009 7:59 am
Posts: 811
In about 5 billion years, the Sun will become a red giant, increasing in radius
by a factor of 50, and increasing in luminosity by about a factor of 100. Find the surface
temperature of the Sun in this red giant phase. (Hint: this is a ratio problem.)


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 Post subject: Surface Tempuratre of our sun in 5 Billion Years?
PostPosted: Sun Jul 23, 2017 9:14 am 
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Joined: Thu Apr 02, 2009 10:45 am
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Stars luminosity is given by the following relation:
L=A * * T^4

So you can build the following equation that relates luminosity, radius and surface temperature

L2/L1 = (4 * r1^2 * T1^4)/(4 * r2^2 * T2^4) = (r1 / r2)^2 * (T1 / T2)^4

From there you have

T1 / T2 = [(L1 / L2) / (r1 / r2)^2]^(1/4)

T1/T2 = [(100 / 1) / (50 / 1)^2]^(1/4) = 0.45

Assuming that Suns surface temp. is about 5700 K, in 5 billion years its temperature will be approx. 2500 K



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