The equation the governs the relationship between the mass of a star and its lif
ID: 1427314 • Letter: T
Question
The equation the governs the relationship between the mass of a star and its lifetime is given by:
t=8*10^9(M/Mx)^-2.5 years where Mx=mass of sun
a. Calculate the lifetime of a massive star that is 120 times more massive than the Sun (M = 120 Mx). It took 4.5 billion years (4.5×10^9) for intelligent life to develop on Earth. If this is a typical timescale, what does the lifetime of this star tell us about the possibility of intelligent life around massive stars?
b. Assume it always takes 4.5 billion years for intelligent life to develop. What is the most massive star that might support an advanced civilization?
Explanation / Answer
Here,
t = 8*10^9*(M/Mx)^(-2.5) years
a)
as M = 120 Mx
for the life time
t = 8*10^9*(M/Mx)^(-2.5)
t = 8*10^9*(120)^(-2.5)
t = 50715 years
hence, there will be No intelligent life on the planets around this star.
b)
let the mass is M
for
t = 8*10^9*(M/Mx)^(-2.5)
4.5 *10^9 years = 8*10^9*(M/Mx)^(-2.5) years
4.5 *10^9 = 8*10^9*(M/Mx)^(-2.5)
solving
M = 1.26 Mx
the maximum mass of star can be 1.26 times mass of sun
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