Answer:
M=4.736×10³⁰kg
Explanation:
Given Data
Diameter of planet= 1.86×10⁷m
Radius R=Diameter/2=1.86×10⁷/2⇒0.93×10⁷m
Period of rotation of planet t=22.3 hr⇒80280 seconds
Period of revolution around star T=422 earth days⇒3.646×10⁷ seconds
Radius of orbit r=2.2×10¹¹m
Acceleration of gravity on surface of planet g=12.2 m/s²
To Find
Mass of star
Solution
To find mass of star.For that we will consider the revolution of planet around the star with given period
[tex]T^{2}=\frac{4\pi ^{2}r^{3} }{GM}\\ M=\frac{4\pi ^{2}r^{3} }{GT^{2}}\\M=\frac{4\pi ^{2}(2.2*10^{11} )^{3} }{(6.67*10^{-11} )(3.646*10^{7} )^{2}}\\M=4.736*10^{30} kg[/tex]
