a$)$ By how much would the Sun$-$Earth distance have to be increased in order to reduce the average

temperature on the Earth by about $2\mathrm{.}0$ K$?$

$($b$)$ By how much would the length of the year increase in the process? Assume that the Earth will

remain in a circular orbit, and use Kepler$$s third lawa $($simplified$,$ and assuming a circular orbit$)$:

P $2=4$$2$R$3$

GMSun

where P is the period, i$.$e$.$ time for one orbit of the Earth around the Sun, and G is the gravitational

constant.