Astronomers have observed an asteroid orbiting a planet in another planetary system. They have estimated the radius of the orbit of the asteroid around the planet to be 1.5 × 10⁷ m and the gravitational force on the asteroid due to the planet to be 230 N. They calculated that, if the radius of the orbit was 4.0 × 10⁷ m instead the orbital period of the asteroid would have been 3.0 h. Determine the planet's mass.