Question

When the Sun ends up as a white dwarf, billions of years from now, it will contain about 40 percent of its present-day mass and have the same radius as Earth. What will be its density? How many times more dense is that than the present-day Sun?

Answer 1

We are going to have to have to look up some numbers. You can use Google for that.
Solar mass (now): 1.989*10^30 kg = M1
Solar mass (future): 0.4*M1 = 7.956*10^29 kg = M2
Solar radius (now): 6.96342*10^5 km = R1
Earth radius (now): 6378.1 km
Solar radius (future): 6378.1 km = R2

Solar density increase factor:
(M2/M1)*(R1/R2)^2 = 4769

Future solar density as white dwarf:
= M2/[(4/3)*pi*R3^3]= ____
Your turn.

Answer 2

I used the wrong exponent for R

Solar density increase factor:
(M2/M1)*(R1/R2)^3 = 0.4*1.30*10^6
= 5.2*10^5

Currently, the sun's density is 1.4 times that of water: 1.4 g/cm3.
It will become nearly 1 million times more dense as a white dwarf.

Answer 3

thanks