Answer:
Mp= 1.48×10^23 Kg and M = 4.47×10^30 Kg
Step-by-step explanation:
Given that
Diameter of planet D = 1.8×10^6m
Radius of planet Rp = 0.9×10^6m
Period of rotation of planet = 22.3 hrs = 80280s
Radius of orbit r = 2.2 × 10^11 m
Period of revolution around star T =432days = 432×24×60×60 = 37324800s
Acceleration of gravity on the surface of planet gp = 12.2m/s^2
gp = GMp/(Rp)^2
Mp = gp×(Rp)^2 /G
= 12.2 * (0.9*10^6)^2 ÷ 6.67×10^-11
9.882×10^12 ÷ 6.67×10^-11
Mp= 1.4×10^23 Kg
To determine the mass of the star, we consider the revolution of the planet around the star with period T
T^2 = (4π^2/GM)r^3
M = 4π^2r^3 ÷ GT^2
M = 4π^2* (2.2×10^11)^3 ÷ 6.67×10^-11 × ( 37324800)^2
M= 4.47×10^30 Kg