If a white dwarf star has a radius two-thirds as large as the Earth’s, what is the mass of the star?

Question

If a white dwarf star has a radius two-thirds as large as the Earth’s, what is the mass of the star?

Answer 1

Can't say.

You can use formula V = 4/3(pye)r^3 for working out the mass inversely proportionate to the volume. The radius of a white dwarf is inversely proportional to the cube root of its mass.It will be a fairly inaccurate answer; even while the volume is comparable to that of Earth. White Dwarfs are highly dense & in mass distribution they peak at 0.6 Solar mass& majority are between 0.5 & 0.7 solar mass.  As white dwarfs have mass comparable to the Sun's and their volume is comparable to the Earth's, they are very dense. The relation of volume & mass will not be linear as we know White Dwarfs have varying density. In fact it is a converse relation, the the radius of a white dwarf decreases as its mass increases.

Compression of a white dwarf will increase the number of electrons in a given volume. Applying either the Pauli exclusion principle or the uncertainty principle, we can see that this will increase the kinetic energy of the electrons, causing pressure.

And then you will need to apply Chandrashekhar Limit of approximately 1.4 solar masses. It is a close call for this size.

Answer 2

It depends on the density, but if the radius is caused by gravity, the white dwarf star should have the mass of the sun.  

Answer 3

I didn't know how to calculate it, so I looked it up in wiki.  It was pretty involved, having to take into consideration things like degeneracy states, equilibrium, and relativistic effects.  The article in wiki will give you all the information you need, and probably a lot more, that you will have to sift through.

Edit: On the other hand, there is a less technical way to approximate this. The size you gave is fairly typical for a white dwarf and the average density of this kind of star is about 10^6 g/cm^3.

The radius of the earth is about 6.37 x 10^8 cm. Your white dwarf then, would have a radius of 4.25 x 10^8 cm. Its volume would be 3.2 x 10^26 cu.cm.  Multiply by the density and you get 3.2 x 10^32 grams.  The mass of the sun is about 2 x 10^33 g, so this white dwarf is about 16% of the mass of the sun. That's about 53,000 times the mass of the earth.

To which, a white dwarf would say, "Duhhh, I'm not FAT, I'm DENSE."

Answer 4

You have to know the density!

Answer 5

larger than earth's