# Determining inclination angle of interacting binaries

Consider an interacting binary system. If the plane of their orbits is inclined by some angle $$\theta$$ around its semi major axis $$a$$ and some angle $$\phi$$ around its semi minor axis, is there a situation that when observed from earth it is not possible to determine whether the orbital plane is inclined or not?

As far as I know inclination angle is determined by determining the displacement in the foci of the ellipse relative to the center of ellipse therefore I thought if $$ae$$ is not changed then it is not possible to determine inclination angle, using the following relation in ellipses:$$(ae)^2 = b^2 + a^2$$ $$a^2 + b^2 = a^2\cos^2(i) + b^2\cos^2(n)$$ $$\therefore \frac{a}{b} = \frac{\sin(n)}{\sin(i)}$$

I conclude if the above condition holds then it is not possible to determine whether the observed ellipse is inclined or not, I was wondering whether this conclusion is valid or not.

Also I wanted to know if Kepler's second and third law are affected by inclination angle and if they are can one determine the inclination angle using Kepler's laws?

• Can you be clear about what sort of binaries you are talking about. Interacting binaries are far too close to each other for their orbits to be directly observed. Jul 12 '21 at 15:16
• You may find it helpful to play with the interactive 3D plot linked in my answer here: astronomy.stackexchange.com/a/43350/16685 Jul 14 '21 at 16:59