A planet in another solar system orbits a star with a mass of $4\mathrm{.}00$ x $1030$ kg$.$ At one point in its orbit,

when it is distance $250\mathrm{.}0$ x $106$ 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.