A planet has been discovered orbiting the sun$-$like star HD $209458.$ From

the period and velocity measured by the Doppler method, its mass was

calculated to be $0\mathrm{.}69$ times that of Jupiter. The plane of the planet$$s orbit is

edge$-$on and it has been observed to transit across the face of the star. The

light from the star was seen to drop by $1\mathrm{.}7\%$ when the planet$$s disc lay fully

within that of the star which has a radius of $8105$ km$.$ Assuming that

the brightness of the star is constant across the observed face, estimate

the diameter of the planet and hence it density in comparison with that of

Jupiter which has a radius of $7\mathrm{.}1104$ km$.$