An extrasolar planet in the HD 4308 system orbits its parent star at a distance of 17.1 million kilometers and takes 15.56 Earth days to complete one orbit. Given this and assuming that planet has a negligible mass compared to the parent star, what is the mass of the parent star? A) 3.25 ×10³⁰ kg B) 2.00 × 10³⁰ kg C) 1.25 × 10³⁰ kg D) 1.64 × 10³⁰ kg

Question

Quizplus · Accepted Answer

We can use Kepler's Third Law to solve this problem: $T^2=\frac{4\pi^2a^3}{GM}$, where $T$ is the orbital period, $a$ is the orbital radius, $G$ is the gravitational constant, and $M$ is the mass of the parent star. Rearranging this equation to solve for $M$, we get $M=\frac{4\pi^2a^3}{GT^2}$.

Plugging in the given values, we get $M=\frac{4\pi^2(1.71	imes10^{10})^3}{6.67	imes10^{-11}(15.56	imes24	imes60	imes60)^2} \approx 1.64	imes10^{30}$ kg, which is closest to choice (D).

An Extrasolar Planet in the HD 4308 System Orbits Its