Answer:
Mass of the planet = 1.48 × 10²⁵ Kg
Mass of the star = 5.09 × 10³⁰ kg
Explanation:
Given;
Diameter = 1.8 × 10⁷ m
Therefore,
Radius = =
or
Radius of the planet = 0.9 × 10⁷ m
Rotation period = 22.3 hours
Radius of star = 2.2 × 10¹¹ m
Orbit period = 407 earth days = 407 × 24 × 60 × 60 seconds = 35164800 s
free-fall acceleration = 12.2 m/s²
Now,
we have the relation
g =
g is the free fall acceleration
G is the gravitational force constant
M is the mass of the planet
on substituting the respective values, we get
12.2 =
or
M = 1.48 × 10²⁵ Kg
From the Kepler's law we have
T² =
on substituting the respective values, we get
35164800² =
or
= 5.09 × 10³⁰ kg