Question

In a certain binary-star system, each star has the a mass of 1.20 1030 kg, and they revolve about their center of mass. The distance between them is 2.0 108 km. What is their period of revolution in Earth years?

Answer 1

Their period of revolution is 1.408 years

Step-by-step explanation:

Given data:

G = gravitational constant = 6.67x10⁻¹¹Nm²/kg²

M = mass of star = 1.2x10³⁰kg

D = distance between stars = 2x10⁸km = 2x10¹¹m

The radius of each star is:

`r=(D)/(2) =(2x10^(11) )/(2) =1x10^(11) m`

The gravitational force between stars is equal to:

`(V^(2) )/(r) =(GM)/(D^(2) ) \\V=\sqrt{(GMr)/(D^(2) ) } =\sqrt{(6.67x10^(-11)*1.2x10^(30)*1x10^(11) )/((2x10^(11))^(2) ) } =14145.671m/s`

The period is:

`T=(2\pi r)/(V) =(2\pi 1x10^(11) )/(14145.671) =44417725.445s=1.408years`