In about six billion years our suns luminosity aka power out

In about six billion years, our sun\'s luminosity (a.k.a. power output) will be 2000 times more than it is now. At this stage, our sun will be considered a \"red giant\" star. The surface temperature of a red giant is only about two thirds of our sun\'s current temperature. Between what two famous celestials objects will be the location of our sun\'s surface in six billion years?

Solution

Luminosity,L = k*R^2 * T^4
so, L2/L1 = [R2/R1]^2 * [T2/T1]^4
2000 = [R2/R1]^2 * 0.1975
R2 = 100.62 * R1 = 100.62 * 6.96*10^8 = 7.003 * 10 ^10m
Radius of orbit of mercury = 4.6*10^10 m - 7 * 10 ^ 7m
Radius of orbit of venus = 1.08*10^11 m

Hence sun\'s surface will be between venus amd mercury