I'm asking this question as a reference for use in worldbuilding when developing world size, atmospheric content, or alien optometric abilities (aka, vision).
While I'm specifically asking two questions, their relevance is so close that it's more practical to ask them once, together.
- A sphere 10 Km in diameter
- It's homogeneous (the material isn't relevant)
- Having an albedo of 70% (similar to fresh snow)
How far away can that sphere be...
A) In space, with Sol at the observer's back, the observer 1 AU from Sol?
B) In space as in (A), but assuming for the purposes of this question, that space is filled with an aether in all ways equivalent to Earth's atmosphere at sea level?
And still be seen (even if its shape cannot be clearly distinguished, i.e., a "point") by the average human eye?
1. I understand that eye sensitivity to light and focus vary between people. I don't know how to specify the "average." If someone can provide metrics that would clarify this issue, please leave a comment and I'll add them into the question.
2. For the purpose of this question, please ignore the lack of ground. I understand that light reflecting from surfaces between the oberserver and the observed will contribute (substantially, I suspect) to whether or not an object can be seen at a distance. I could be wrong, but I believe the basic setup I've proposed represents a best-case scenario.
3. For the purpose of this question, please ignore the fact that the sun isn't above the observer. In other words, it's shining from behind the observer rather than above or on top of the observer. This effects the amount of Rayleigh Scattering that would also contribute to visibility. Once again, I suspect this makes the setup a best-case scenario.
4. Ignore the fact that our hapless observer is sans-spacesuit. In other words, there's nothing about his/her environment as the observer that's affecting his/her vision (no faceplate). Lucky dude, as otherwise the eyes would have a bit of trouble in the vacuum of space.
5. The atmosphere between the oberver and the observed is uniform. This is different from the conditions of a planet (convex) or the inner surface of a Dyson sphere or ringworld (concave) where the atmosphere density is not uniform along the sight path.
6. Please ignore the field of stars (assume they aren't there). This isn't a test of how well a human can identify one tiny mote from a field of tiny, shining motes.
A curious thought...
Please note that there may be a considerable difference between the sun behind the observer and the sun above and midway between the observer and the observed as the reflection off the sphere may (may...) be greater in the later case. However, it would only be greater on the top half of the sphere (closest to the sun) while it would be lower on the bottom half (and all the Rayleigh scattering issues come into play... and the sun's in your eyes...). At this time, I'm thinking that placing the light source behind the observer produces the highest reflectivity and lowest optical distortion for the greatest distance. If the math says I'm wrong, please let me know.