Answer :
Final answer:
The mass of a star, given the orbital radius and period of its planet, can be calculated using Kepler's third law. In this case, the star with a planet having an orbital radius of 6 AU and a period of 6 years has a mass of 6 solar masses (MSun).
Explanation:
The mass of a star, given the orbital radius (D) and period (P) of its planet, can be calculated using a modified version of Kepler's third law: D³ = M₁ * P². D is in units of astronomical units (AU), P is in years, and the mass of the star M₁ is in solar masses (MSun). We have D = 6 AU and P = 6 years for this situation.
Substituting these values in the equation: 6³ = M₁ * 6² which simplifies to: 216 = 36M₁, from this, the mass of the star M₁ = 216/36 = 6 MSun. Thus, the star has a mass of 6 solar masses (MSun).
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