The length of the semi-major axis of the elliptical orbit of the planet is

$a=\frac{r+R}{2}$

If we assume that there is a hypothetical planet which moves around the sun in a circular orbit of radius $r_0=\frac{r+R}{2}$, then the time period of this hypothetical planet and our given planet will be same. The time period of a planet around the sun in circular orbit is

$T=2\mathrm{\pi }\sqrt{\frac{{r^3}_0}{G{M}_{\mathrm{s}}}}=2\mathrm{\pi }\sqrt{\frac{{\left(\frac{r+R}{2}\right)}^3}{G{M}_{\mathrm{s}}}}$

$T=\mathrm{\pi }\sqrt{\frac{{\left(r+R\right)}^3}{2G{M}_{\mathrm{s}}}}$