Show that the surface temperature, T$,$ of a rotating spherical body at a

distance R from the Sun falls as the inverse square root of R$.$

Knowing that a spacecraft in Earth orbit prior to orbital insertion

towards the Sun reached a stable temperature of $260$ K$,$ fi nd the constant

of proportionality in the relationship between R and T$,$ where T is in kelvin

and R is in astronomical units.

How close $($in AU$)$ could this spacecraft be allowed to approach the Sun

if it could withstand a surface temperature of $1000$ K$?$