Answer:
82780.42123 m/s
14.45 days
Explanation:
m = Mass of the planet
M = Mass of the star = [tex]0.85\times 1.989\times 10^{30}\ kg=1.69065\times 10^{30}\ kg[/tex]
r = Radius of orbit of planet = [tex]0.11\times 149.6\times 10^{9}\ m=16.456\times 10^{9}\ m[/tex]
v = Orbital speed
The kinetic and potential energy balance of the planet and star system is given by
[tex]\frac{GMm}{r^2}=\dfrac{mv^2}{r}\\\Rightarrow v=\sqrt{\dfrac{Gm}{r}}\\\Rightarrow v=\sqrt{\dfrac{6.67\times 10^{-11}\times 1.69065\times 10^{30}}{16.456\times 10^{9}}}\\\Rightarrow v=82780.42123\ m/s[/tex]
The orbital speed is 82780.42123 m/s
The orbital period is given by
[tex]t=\dfrac{2\pi r}{v}\\\Rightarrow t=\dfrac{2\pi \times 16.456\times 10^{9}}{82780.42123}\\\Rightarrow t=1249040.48419\ seconds[/tex]
Converting to days
[tex]\dfrac{1249040.48419}{24\times 60\times 60}=14.45\ days[/tex]
The orbital period is 14.45 days
