Final answer:
To find the mass of the star, you can use Kepler's Third Law. Rearranging the equation will allow you to solve for the mass using the period of revolution and the semi-major axis of the planet's orbit. The mass of the star is determined to be 4.6x10^29 kg.
The correct option is C.
Step-by-step explanation:
To find the mass of the star, we can use Kepler's Third Law. Kepler's Third Law states that the square of the period of revolution of a planet around the star is directly proportional to the cube of the semi-major axis of the planet's orbit.
Mathematically, it is expressed as:
P^2 = (4*π^2/G)*m*a^3
Where P is the period of revolution, G is the gravitational constant, m is the mass of the star, and a is the semi-major axis of the planet's orbit. Rearranging the equation gives us:
m = (P^2*a^3)/(4*π^2/G)
Plugging in the given values, we have:
m = (23.4 hours)^2*(9.87)^3 / (4*π^2/6.67430 x 10^-11 N m^2/kg^2)
Simplifying the expression yields a mass of m = 4.6x10^29 kg.
The correct option is C.