Rapid rotation o neutron star

Neutron stars spin very fast, lets fid in what time it completes on revolution.

$Formula P_{ns} = P_c(\frac{R_{ns}}{R_c})^2$

$P_{ns} = period of neutron star$

$P_c = period of core$

$R_{ns} = radius of neutron star$

$R_c = Radius of core$


Ans::

Cross-section of neutron star. Densities are in terms of ρ₀ the saturation nuclear matter density, where nucleons begin to touch.

                                  

So the radius of the core will be taken as 3Km and radius of neutron star is 17Km, period of core is say 0.000007seconds

$ P_{ns} = 0.0007(\frac{17}{3})^2 = 0.000335sec$

now 

$R_c = 0.7Km, R_{ns} = 20Km, P_c=3.6e-6sec$

so

$ P_{ns} = 3.6e-6(\frac{20}{0.7})^2 = 0.0029sec$

Now I exagerate:

$R_{ns} = 15.5Km, R_c = 0.06Km, P_c = 0.000000006sec$

so:

$P_{ns} = 0.000000006(\frac{15.5}{0.06})^2 = 0.0004sec$