Astrophysics - Can there be a contact binary from white dwarfs

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Question:

A typical white dwarf has a mass of 1 solar mass and a radius of 10 thousand km. A typical neutron star has a mass of 1.5 solar masses and a radius of 30km. Given that there's a natural speed limit in Nature, namely the speed of light, is it possible to have a contact binary consisting of two white dwarfs (each identical to one another in size and mass)? Same question for two neutron stars.

I was thinking about:

E= (1/2) (mu) (v^2) - GM (mu) /r

I used this with v= speed of light and came up with positive numbers for each set of binaries.

However, considering E= -GM (mu) /2a one would expect the total energy to be negative.


Am I completely wrong in what I have done which leads me to say that no, neither binary is possible because E is not negative?

Any help would be greatly appreciated. Thanks.
 

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