You are the science officer on a visit to a distant solar system. prior to landing on a planet you measure its diameter to be 1.8×107m and its rotation period to be 22.3 hours . you have previously determined that the planet orbits 2.2×1011m from its star with a period of 407 earth days. once on the surface you find that the free-fall acceleration is 12.2m/s2.
what is the mass of the planet? what is the mass of the star?

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