After the Sun exhausts its nuclear fuel, its ultimate fate may 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.  ?kg/m3 (b) Calculate the surface free-fall acceleration.  ?m/s2 (c) Calculate the gravitational potential energy associated with a 1.88-kg object at the surface of the white dwarf.  ?J

a) b) Electron degeneracy pressure in a white dwarf star, of uniform density p, in the nonrela- tivistic case is given by Pwd ħ² 3memp 25/305/3 where symbols have their usual meanings. Using the result that the central pressure in a star, of radius R and uniform density, under gravitational attraction is given by Pc = Gp² R², derive an expression for the radius Rwd of a white dwarf in terms of its mass M, in the case of nonrelativistic electron degeneracy. Using your result, briefly discuss the limitations of your expression for the radius, in the context of white dwarfs of increasing mass. Consider a white dwarf, mass M, radius Rwd and temperature T, consisting entirely of helium nuclei and electrons. Show that the internal thermal energy of the ions alone is given by 3 M Eth= -kT, 8 mp where mp is the proton mass. White dwarfs initially have a very high temperature when they form, and then cool by radi- ation. Derive a differential equation for the rate of change of the temperature…

After the Sun exhausts its nuclear fuel, its ultimate fate may 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.Calculate the average density of the white dwarf.Calculate the surface free-fall acceleration.Calculate the gravitational potential energy associated with a 6.69-kg object at the surface of the white dwarf.

International Astronomical Union reported on 24 Feb 1987: An object was discovered on Feb. 24.37 UT (position R.A. = 5h35m.8, Decl. = -69 18'), obtained m = 4.8 on Feb. 24.454 UT. This object proved to be the most famous supernova (SN) in the 20th Century and the brightest visible from Earth since 1604. It is classified as a SN of the type Il in the Large Magellanic Cloud (SN1987A). Its brightness peaked in May 1987, with an apparent magnitude of m = 2.8. a) Find the absolute magnitude M of the SN1987A at maximum. Distance of the LMC is 51,400 pc. b) The progenitor (before SN explosion) star was a blue supergiant of the apparent magnitude m = 12.8. How much brighter (in terms of flux density) this SN was at maximum compared to the progenitor star. Find the ratio FSN / Ebefore