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 very low 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 find the mass of the parent star:

(T₁/T₂)² = (M₁/M₂)
where T₁ is the period of the planet's orbit, T₂ is the period of the star's rotation (which we assume is equal to the planet's orbital period), M₁ is the mass of the star, and M₂ is the mass of the planet.

We know that T₁ = 15.56 Earth days, and we can assume that T₂ is also 15.56 Earth days. We also know that the planet has a very low mass compared to the parent star, so we can assume that M₂ is negligible. Therefore:

(15.56/15.56)² = (M₁/1)

M₁ = (15.56/15.56)²
M₁ = 0.9999999999999986 solar masses

Using the conversion factor 1 solar mass = 1.99 x 10³⁰ kg, we get:

M₁ = 1.64 x 10³⁰ kg

Therefore, the best choice is D.

An Extrasolar Planet in the HD 4308 System Orbits Its