After the Sun exhausts its nuclear fuel, its ultimate fate will be to collapse t

Question

After the Sun exhausts its nuclear fuel, its ultimate fate will be to collapse to a white dwarf state. In this state, it would have approximately the same mass as it has now, but its radius would be equal to the radius of the Earth.

(a) Calculate the average density of the white dwarf.

(b) Calculate the surface free-fall acceleration.

(c) Calculate the gravitational potential energy associated with a 5.49-kg object at the surface of the white dwarf

Five stars for correct answers and explanations

Explanation / Answer

a) solve for density mass/volume
volume of sphere = 4/3 ? r^3
mass of sun = 1.991E30
volume = 4/3? * (6.43E6)^3 = 1.11E21
density = 1.991E30 / 1.11E21 =
1.84e9kg/m^3
b) g = G* (M/r^2)
g = 6.67E-11 * 1.991E30 / (6.43E6 ^2)
g =3.212E6m/s^2
c) PE = - G (M*m/r)
= - 6.67E-11* ( 1.991E30 *5.49/ 6.43 E6)
=-1.1337E14J

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