A planet in another solar system orbits a star with a mass of $4\mathrm{.}00$x $10^30$kg$.$At one point in its orbit, when it is distance $250\mathrm{.}0$x $10^6$km away from the star, its speed is $35\mathrm{.}0$km$/$s$.($a$)$Determine the semi$-$major axis of the elliptic orbit and the period. $($b$)$If the eccentricity of the orbit is $0\mathrm{.}4,$determine the speed of the planet in aphelion and at perihelion.