$7.$ Consider a planet orbiting a star in a circular orbit with a radius of $5$AU $($astronomical units$),$

where $1$AU is the average distance between the Earth and the Sun $(1$AU$1\mathrm{.}5\backslash$times $1011$ m$).$ The star

has a mass of $2\backslash$times $1030$ kg$.$

$($a$)$ Calculate the gravitational force exerted by the star on the planet.

$($b$)$ Using Kepler's laws, determine the period of the planet's orbit.

$($c$)$ The star explodes in a supernova and loses $90\%$ of its mass. Assuming the distance from the star

to the planet is unchanged, calculate the planet$$s new period.