Consider a pair of double planets. They are roughly the same size and also roughly earth-sized, but their orbital plane around each other is tilted with respect to the ecliptic (see sketch below). The planets are tidally locked to each other. I'm having some trouble figuring out the appearance of the planets in each other's sky depending on the tilt.
Distances obviously not to scale
It seems to me that with a large tilt (upper image) there would be a situation where the shadow of planet 1 (P1) does not fall onto planet 2 at all. So P2 would appear full in the sky of P1 at inner-side night, and I guess P1 would be fully in darkness during inner-side day of P2. But given i.e. the appearance of the new moon on Earth, would it be visible at all?
Then if the tilt is lesser (lower part) such that the shadow of P1 actually does fall onto P2, what would they look like respectively? I guess P2 would be a crescent with the lower part in darkness, the size of which depends on exactly how much of it is in P1's shadow. But what does P1 look like to P2?
Sorry if I'm missing something obvious.
Sizes and distances in case that is helpful:
- Radius P1 ~ radius P2 ~ 6300 km (Earth radius)
- Semi-major axis of orbit around each other: 53000 km (assume roughly circular orbit since they have similar size and mass)
- Orbital period of planets around each other: 24h
- Semi-major axis of orbit around the star: 26.9 million km (it's a red dwarf, that's why they are so close)
- Orbital period around star: 50 days