## Examples

Example 14.1 Assume that the Sun collapses into a neutron star with a radius of 20 km. a) What will be the mean density of the neutron star? b) What would be it rotation period? a) The mean density is

2 x 1030 kg

One cubic millimetre of this substance would weigh 60 million kilos.

b) To obtain an exact value, we should take into account the mass distributions of the Sun and the resulting neutron star. Very rough estimates can be found assuming that both are homogeneous. Then the moment of inertia is I = |MR2, and the angular momentum is L = Io>. The rotation period is then obtained as in Example 11.1:

20 x 103 m

The Sun would make over 550 revolutions per second.

Example 14.2 What should be the radius of the Sun if the escape velocity from the surface were to exceed the speed of light?

The escape velocity exceeds the speed of light if

Fig. 14.14. Observed outburst of the microquasar GRS 1915+105 on 9 September, 1997. The disappearance of the internal part of the accretion disc (decrease in the X-ray flux) is followed by an ejection of relativistic plasma clouds (oscillation in the infrared and radio). (S. Chaty, astro-ph/0607668)

For the Sun we have

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