Can a planet cover the whole sky as seen from its satellite

Question

Sorry if this is a trivial question, but I do not know enough physics to answer this on my own.

Can there exist a satellite that revolves around a planet so large such that the planet covers the entire sky as seen from at least one point on the satellite?

Added 1 I am sorry for being unclear earlier. But assume human eyes can't resolve less than $0.02^\circ$.

Added 2 Assuming both the planet and satellite (ignoring atmosphere to make things simpler) are spheres and since spheres are locally euclidean, for large enough radii a planet could cover the whole sky as it appears to the eye. Consider this picture:

Answer 1

If the planet and satellite are perfect spheres, or any convex shape then the answer is NO. If the planet is close to the satellite and you stand on the point nearest to it then you will only be able to see a small band around the horizon, but the whole horizon cannot be blocked.

If the satellite is not convex and you stand in a hole or crater on the satellite so that your view of the sky is reduced then the planet can fill the rest of the visible sky, so the answer is YES.

If the satellite itself is a sphere then the planet cannot obscure the whole horizon unless the satellite somehow passes through a tunnel or at least a gorge in the planet, not very likely

Update: Since the question has been updated there are a couple of extra points to be made

If the observer on the satellite is limited by the resolution of his vision then a sufficiently big planet could obscure the whole sky with the only band of sky left near the horizon being too small for him to see.

Also, regarding Carl's comment on the effect of GR. If the planet is sufficiently massive, but not the satellite, then light will bend towards the centre of the planet. In this case it is possible for the planet to cover the whole sky in the most extreme circumstances.

As mentioned in the comments on this answer, an atmosphere on the satellite would bend the light towards the satellite making it harder for a plenet to cover the whole sky.

If the atmosphere is on the planet it could only help if the satellite was inside the atmosphere, in which case the drag would slow it down so that it would not remain in orbit for very long.

Answer 2

I think if the satellite gets that close you have to consider tidal drag (as well as atmospheric drag it there is one present), which would mean any super close orbit would decay on a timescale that is small compared to astronomical timescales. The planet must be rotating slower than the orbital speed at its equatorial radius, otherwise it would be unstable, and mass/angular momentum would be shed -presumably forming a ring which might condense into a moon. Also if there are any other bodies nearby, so that it isn't governed by two body dynamics, the orbit will vary with time, and unless the near grazing condition was the innermost approach of an oscillation, it probably wouldn't avoid an impact for long. Now if you want to select a special time, just before the satellite impacts the planet, then yes it can happen. In fact a satellite in a wrong way orbit will lose momentum due to tidal drag and spiral in until it impacts. I think that is your best scenario for reaching your scenario.

Answer 3

No, because, if you assume spherical shapes for both satellite and main body, this would only be (geometrically) possible if they touch at the point where you stand.

It would be possible if you stand in a hole on the satellite, the walls of which obscure part of the sky.

As for the case of main body and satellite orbiting each other and nearly touching, I think this is theoretically possible (if neither has an atmosphere), but not a stable configuration. I'm no astronomer, though.