Assuming an identical Solar system except for the strange sun(s) and that
- the binary star system's barycentre coincides with the Sun's centre of mass
- mass of the combined star system is equal to the mass of the Sun
- the stars are identical with a radius 2-1/3 times that of the Sun (assuming density same as the sun: is this possible, given the other constraints?)
- combined surface luminosity when the stars are equidistant from the earth (as felt from the earth) is equal to the surface luminosity of the Sun
- rotational period of the binary star system is of the order of a few days, say a week
how would things like day and night, seasons, eclipses etc. change?
I hope the orbit of the binary star system being coplanar with the planets would be enough for stability. Please correct me if I'm wrong.
There is a similar question on WBSE, but with different premises. I can't seem to find my answer there anyway.
EDIT: I did the calculations for relations between sequence star size, mass, temperature and luminosity and it turns out that selecting any one parameter fixes the rest as well. So such a system cannot be identical to the solar system and even if it was in terms of geometry, the suns would be too cold to allow any life on Earth.