Martin Elsässer, 2018
I tried to implement a very simple 2D model of scattered light in our atmosphere after sunset to judge the brightness of the sky through which we would try to see a thin lunar crescent.
This diagramm shows the brightness of the sky for various values of sun elevation (below the horizon) and lunar elongation.
- X shows the (negative) elevation of the sun, so time moves from right to left.
- Towards the back (lines higher up) the elevation of the moon decreases, from 18° to 3°. The smaller the elongation, the brighter the sky at the position of the moon.
The altitude of the moon would be the sum of the elongation and the (negative) solar elevation.
- Straight up the brightness of the sky at the position of the moon is shown for various elevations of the sun. The lines stop when the moon sets.
If elongation is large enough, then the sky brightness near the moon generally drops after sunset.
- The contrast between moon and sky should generally improve over time after sunset.
- There is also a lower limit of solar elevation where no significant further improvement happens. This limit somewhat corresponds to the -6° value of civil twilight.
The largest improvements happen when the sun drops down to -6° elevation.
Limitations of the underlying model
- The moon is always assumed to be direcly above the sun
- The model of the atmosphere is quite simple, just using the std. barometric density
- The model of scattering is extremely simpel, no directional component, no variation for different wavelengths
- Absorption is ignored
- Light moves straight, refraction is not considered
- The sun is modelled as a dot at infinity
Extend the modell to 3D, to get a map of sky brightness above the horizon.
- Actually measure the change of brightness of the twilight sky on a clear evening/morning.
- Search for better treatments of this topic in the literature. All of this will have been done before and better, most surely.