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24. Problem 12.55E (HRW) Suppose that the Sun run out of nuclear fuel and suddenly collapses to form a white dwarf star, with a diameter equal to that of the Earth. Assuming no mass loss, what would be then the Sun’s new rotation speed, which currently is about 25 days? Assume that the Sun and the White dwarf are uniform, solid spheres. |
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Solution: Click For PDF Version We note down the following astronomical data: Mass of the Sun
Mean radius of the Sun,
Mean radius of the Earth,
The moment of inertia of a sphere of mass M and radius R,
Angular speed of the Sun,
Angular momentum of the Sun
This gives
Let the period of rotation of the white dwarf be T. As
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. Let
be the
angular speed of the Sun when it has become a white dwarf of radius
.
As there is no external torque on the Sun when it collapses, its angular
momentum will be a constant of motion. Therefore,
.
, we find
the rotational period of the Sun when it has become a white dwarf of radius
,