orbit of close binary stars

[shirin]

in analysis of close binary stars, it is assumed that their orbits is circular and then by a rotating coordinate system, potential is obtained and then lagrangian points and so on...
Is the orbit of CLOSE binary stars nearly circular in reality or is it assumed circular because otherwise it is hard to solve ?

[harcel]

Yes the equations are easier to solve in a circular orbit, as many things become time independent (separation between the two components, shape of the equipotential surfaces and so on), but I think a more physical reason is:
Close binaries interact through tidal forces, which circularize the obit. So after a bit of evolution and interaction the orbits will be very close to circular.

[shirin]

two more questions;
Does the location of lagrangian points differ when mass trasfer is happening?
For a binary star, is the mass transfer always from one star to another or may it change?
Thanks in advance

[harcel]

When mass transfer is happening the Lagrangian points indeed change (as the mass ratio between the object changes) and it will even change the orbits of the stars. The donor star and receiving star may reverse their roles. It usually is a big star that is the donor. Say you have a red giant and a normal sun-like star. The red giant can transfer mass to the other. When it evolves and becomes a white dwarf it may later receive mass when the sun-like star becomes a red giant.

[shirin]

I've heard something about locating astroids in lagrangian points. Which binary system do these lagrangian points belong to? earth and what?
There is no mass transfer between earth and its companion. But it were so, what would happen to these astroids? I mean, as these lagrangian points differ due to mass trasfer, do the astroid move toward the new lagrangian point or whatelse happans?