Answer
(a) The orbital speed is $8.27\times 10^4~m/s$.
(b) The orbital period of the planet is 14.5 days.
Work Step by Step
(a) We can find the mass of the star.
$M = (0.85)(1.989\times 10^{30}~kg)$
$M = 1.69\times 10^{30}~kg$
We can find the orbital radius of the planet.
$R = (0.11)(1.50\times 10^{11}~m)$
$R = 1.65\times 10^{10}~m$
We can find the orbital speed of the planet.
$v = \sqrt{\frac{G~M}{R}}$
$v = \sqrt{\frac{(6.67\times 10^{-11}~m^3/kg~s^2)(1.69\times 10^{30}~kg)}{1.65\times 10^{10}~m}}$
$v = 8.27\times 10^4~m/s$
The orbital speed is $8.27\times 10^4~m/s$
(b) We can find the orbital period of the planet.
$T = \frac{distance}{speed}$
$T = \frac{2\pi~R}{v}$
$T = \frac{(2\pi)(1.65\times 10^{10}~m)}{8.27\times 10^4~m/s}$
$T = 1.25\times 10^6~s = 14.5~days$
The orbital period of the planet is 14.5 days.
