A selenelion is a rare lunar eclipse where the Sun and the Moon are both visible at the same time. An even rarer form of selenelion occurs if it is a partial lunar eclipse, and the upper part of the Moon is eclipsed. Some call this an “impossible eclipse.”
Flat-Earthers claim that such an eclipse should not be possible to occur because the Earth’s shadow is in the wrong position. In reality, it is possible to happen because the observer is looking slightly downward due to the dip of the horizon and atmospheric refraction.
For our calculation, we will use the average figures of the diameter of the Sun and the Moon, which are 0.53° and 0.52°, respectively.
During a lunar eclipse, the Sun, Earth, and the Moon are practically in a straight line. Therefore, if we can observe the Sun and the Moon simultaneously, then they must be close to the horizon, during either sunrise or sunset, with the eclipsed Moon appears in the opposite direction.
Because Earth is a sphere, the horizon is not at eye level or the astronomical horizon, but slightly below it. If the observer is 200 m above the surface, then the dip of the horizon is γ = acos(R/(R+h)) = acos(6371 km / (6371 km + 200 m)) = 0.45°. Therefore, the observer can see 0.45° below the eye level.
Due to atmospheric refraction, we can also observe the Sun and the Moon even if geometrically they are slightly below the horizon. Atmospheric refraction raises celestial objects close to the horizon upward by about 34 arcminutes or 0.57°. In the case of our lunar eclipse, atmospheric refraction raises the Sun, and the Moon upward by 0.57°. To simplify things, we add it to the figure of the dip of the horizon above.
If the Sun, Earth, and the antisolar point are in a straight line, then, geometrically, the observer must be slightly off the straight line, and we need to account for the lunar parallax. Due to this, it will lower the position of the Moon as seen by the observer by atan(Earth’s radius / Moon’s distance) = atan(6371 km / 384400 km) = 0,95°.
From all of these numbers, we can explain how the so-called “impossible eclipse” can occur in the spherical Earth model, with plenty of wiggle room.
- Horizon – Wikipedia
- Atmospheric refraction – Wikipedia
- Parallax#Lunar parallax – Wikipedia
- Moon, Sun, and eclipses – Kevin Krisciunas
- Lunar standstill – Wikipedia