$7.$ After Ceres was promoted to a dwarf planet, we now recognize the largest known asteroid to be Vesta, with a mass of $2\mathrm{.}671020$ kg and a diameter ranging from $578$ km to $458$ km$.$ To make the calculation easier, we can that Vesta is spherical with radius $520$ km$.($a$)$ Find the approximate escape velocity from its surface. $($b$)$ What would be the orbital period for a space probe in a circular orbit of $10\mathrm{.}0$ km from its surface?