Answer to Question #97534 in Mechanics | Relativity for Mimo

Question

Two double neutron stars, one having mass 1.0 MSun and the other 3.0 MSun rotate about their common center of mass. Their separation is 6 light years. If they in circular orbit, what is their period of revolution. Use this context to explain the dynamics of the merger of two neutron stars in NGC4993 observed recently (17 Aug 2017) that led to a kilonova and another direct observation of gravitational wave (Nobel Prize in Physics 2017).

Answer 1

Period of revolution

We need to find the Period of revolution

Solution:

We have a formula to find the Period of Revolution,

(i,e)

$$T = 2 \pi \sqrt {\frac {L^3 }{G ( M_1 + M_2)}}$$

Here, L is the distance of first start from the common centre of mass

$$L = 6 \space light \space years = 6 \times 9.4607 \times 10^{15} m \\$$

G is the universal gravitation constant

$$G = 6.67 \times 10^{-11} N.m^2 /kg^2$$

And $M_1 \space and \space M_2 \space are \space the \space masses \space of \space the \space starts$

$M_1 + M_2 = 1.0 M_{sun} + 3.0 M_ {sun} = 4 M_ {sun} = 4 \times (1.989 \times 10^{30})kg$

Plug all these values in the formula

$$T = 2 \pi \sqrt {\frac {( 6 \times 9.4607 \times 10^{15})^3 }{ 6.67 \times 10^{-11} (4 \times (1.989 \times 10^{30}))}}$$

= $116.9 \times 10^6 \space years$

Answer: period of revolution = $116.9 \times 10^6 \space years$