I've been thinking about this and why the particular Starlink satellite is flaring and how we can further demonstrate why it is flaring at that moment in time. Simply - they are flaring by reflecting the light from the the sun using the satellite chassis as a mirror, not their solar array. The chassis always points towards directly down towards the earth as it orbits in order to broadcast its radio signal (internet) to the closest subscribers
Bearing in mind reflection theory, the suns's position which should therefore be directly on the other side of the earth of the satellite as the axis. (This was initially proposed by Reddit user danse-macabre-haunt). I have checked this on In-The-Sky.org using the example above and in the stitched image below which lets us see through the ground it confirms that the sun is almost directly below the horizon in line with the flaring satellites.
(you'll need to set the date & time & view on that link if you wanna see an accurate prediction)
The image here shows the "On Station" satellite with its chassis parallel to the surface of the Earth, visible because it is scattering light.
However to get a flare or glint, the light has to reflect off a surface (not simply scatter). Something I did not immediately recognize is that this means such glints will generally not be visible from the ground.
Consider this simplified representation:
The green disk is the Earth (viewed from the side, with the North Pole at the top).
The Sun's rays come in essentially parallel from the right.
The Satellite orbits with the chassis parallel to the surface to the surface of the Earth.
So, if the Earth were perfectly spherical, and all the angles are perfect, then any ray from the sun reflecting off the chassis would miss the Earth.
However for a viewpoint above the surface, there's specific latitudes where you can get a direct reflection off the bottom the chassis, but only at certain latitudes.
These latitudes will change with the seasons.
It gets a little more complicated with three dimensions. Things to consider:
- The Earth is an oblate spheroid - i.e. it's flatter at the poles.
- The Earth's surface is not smooth, it has mountains.
- The Earth's atmosphere curves light down and around the horizon
- The above three all gives a bit more potential for visibility from the ground.
- The sun also needs to be roughly in line with the satellite
It also suggests that the ideal view latitude is 45* plus the tilt of the Earth's axis towards the sun. This is complicated though by the elliptical (oblate spheroid) nature of the Earth. The window will be wider with the altitude of the plane.