Question

Problem 4 The mass of a star 25 pt We see a very low mass star in orbit around an unseen star. We can assume that we have additional information that tells us the unseen star has almost all of the mass in the system. The star we see has a period of 5 years and a semi-major axis of about 4.5 x 10% km. What is the mass of the unseen star?

Answer 1

21.54 × 10³⁵ kg

Step-by-step explanation:

Given:

Period = 5 years

semi-major axis = 4.5 × 10⁸ km

Now,

According to the Kepler's third law

we have,

`T^2=(4\pi^2)/(GM)r^3`

Here,

T is the period

G is the gravitational force constant = 6.67 × 10⁻¹¹ m³/kg⋅s²

M is the mass of the star

on substituting the respective values, we get

`5^2=(4\pi^2)/(6.67*10^(-11)M)(4.5*10^8)^3`

or

M = 21.54 × 10³⁵ kg