## Increasing Luminosity of the Sun

The Sun is getting bigger and brighter, very slowly. It's temperature is stable, has been so for billions of years and will be so for billions more, but because of the luminosity, temperature radius relationship
$L=4 \pi \sigma R^2T^4$
where
$R=Radius \: of \: Star$

$T=Surface \: Temperature$

$\sigma = Stefan's \: Constant =5.67 \times 10^{-8} W/K^4 /m^2$

if the size of the star increases, so does it's power output. In fact, through the Sun will be a main sequence star for maybe 4.5 billion years, the Earth will be a burnt piece of rock in far less than that - after only about 1 billion years.