Question

A neutron star and a white dwarf have been found orbiting each other with a period of 26 minutes. If their masses are typical, what is their average separation? Compare the separation with the radius of the sun, 7 ✕ 10⁵ km. (Hints: Use the version of Kepler's third law for binary stars,

M_A + M_B =

a3

P2

;

make sure you express quantities in units of AU, solar masses, and years. Assume the mass of the neutron star is 2.0 solar masses and the mass of the white dwarf is 0.7 solar masses.)

Ans:
______________ solar radius

Answer 1

Let and be the masses of the neutron star and white dwarf respectively.

Let and be the distances of neutron star and white dwarf from the barycenter respectively.

If be the distance between the neutron star and the white dwarf then

and

The gravitational force balances the centripetal force.

where is the velocity of the neutron star.

If be the period then

Given and  

Substituting in the expression of r, we get

Thus the average separation between the neutron star and the white dwarf is