It's possible... sort of. The closest distance two identical planet-sized bodies in a hypothetical binary system can be together without destroying each other i

It's possible... sort of. The closest distance two identical planet-sized bodies in a hypothetical binary system can be together without destroying each other is about 2.5 radii, which is pretty close and the other planet would take a noticeable chunk of the sky. At that distance they'd be very oblate and tidally locked to each other; not exactly a world friendly to biological life, and won't look like your picture either.