In the near future, we will begin to find Earth-like planets around other stars.

Question

In the near future, we will begin to find Earth-like planets around other stars. We will then start to search those planets for signs of life. Let us assume that the full lifetime of our Sun, from its birth to its death, is 12.8 billion years. If we assume that it would take life 970 million years to become sufficiently well-established on a given planet that we could detect it from the Earth, what is the mass of the most massive star that could host a detectably habitable planet? times the mass of the Sun. Note: One million = 1 000 000 = 1 x 106 One billion = 1 000 000 000 = 1 000 million = 1 x 109 Check

Explanation / Answer

As we know the lifetime of a star is proportional to the (mass of the star/consumption rate)
The consumption rate is the rate it burns up its fuel (luminosity)
Luminosity of star is proportional to M^4
Therefore lifetime of a star is proportional to (1/M^3)
Hence T(sun)/T(planet) = (1/M(sun)^3)/(1/M(planet)^3)
12800/970 = (M(planet)/M(sun))^3
M(planet)/M(sun) 2.363
M(planet) = 2.363 times the mass of the sun

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