12/11/2023 0 Comments Umbra vs penumbra![]() The killing factor here is that on this situation the only way to have Penumbra is when the same size Sun is far away from the Moon, it can be calculated, measured, simulated on any optical lab or kitchen table. Considering only a closer to 90° Sun & Moon position, then both must have 120km in diameter. The problem here is that the Umbra diameter changes even at 90° (round Umbra), in different eclipses according to factors, one is the actual distance Moon-Earth at the moment of eclipse, another is the angle of shadow casting over Earth surface. With the same measurement date for the Penumbra, one could calculate the size proportions between Sun & Moon and the proportional distances between them and Earth.Ĭonsidering (B), both Moon and Sun must have 120km in diameter in order to cast a same size shadow. The cone would increase in diameter as it distances from the Moon, blocking solar light in vast area, in such way that the entire Andromeda galaxy could be in this inverted cone shadow.Ĭonsidering history and records, close to 90° of Sun's position where Umbra happens on total eclipse, the Umbra diameter was never smaller than 120km in diameter.Ĭonsidering (A) above, the Moon must be way larger than 120km in diameter, the Sun must be way larger than the Moon and they are not close at all. The shadow diameter would be the same as the Moon and will be projected at far distances without changing size.Ĭ) If the Sun is smaller than the Moon, it will projects a Moon shadow with an inverted cone, apex on the Sun. The apex distance from the Moon is directly proportional to the sizes Sun & Moon and the distance between them.ī) If the Sun and the Moon has the same size, it will projects a Moon shadow in a conical form with infinite apex, known as "cylinder". If anything comes inside such dark cone, it will intercepts and shows the shadow. If nothing intercepts this cast conical shadow, it just disappears in the space, nobody sees the cone. That is pure optics and shadow casting.Ī) If the Sun is bigger than the Moon (what it is), it will projects a Moon shadow in a conical form, smaller the diameter as far it gets from the Moon, until the distance is such that the cast shadow reach the apex, a very narrow point. The Umbra and Penumbra round shape can tell us the conical result of projection, with 5 and 7 we can calculate the proportions between 3 and 4 and between 1 and 2 above. As the umbra (the small disc of total shadow where you can not see the Sun during the eclipse) is a conical projection, it assumes a round shape if casting close to 90° angle to Earth's surface, or an ellipsoid when this angle decreases.Ħ.) The Umbra dimensions (length and width) if an elipseĨ.) The Shadow casting Angle on Earth's surface ![]() As an interesting topic for improving general knowledge about light and shadow casting, I am starting here a discussion about how to calculate the Total Solar Eclipse Umbra and Penumbra sizes, angles of projection, etc, in order to calculate the proportional Sun and Moon sizes and respective distances.
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