Umbra Size Calculator

Orbital mechanics determine size of umbra, and that, in turn, tells us how large a shadow will be. That means you can use the umbra size calculator to calculate where a solar eclipse will be either an annular event (just a ring) or a total event (darkness). It’s frequently a matter of a couple thousand kilometers. Either you get a ring of fire…or you don’t.

It’s a race: a geometric race between curvature of the planet and reach of shadow. That’s because it use the idea that similar triangles have proportional sides. A big triangle is formed by Sun, Moon, and a point on Earth. The Sun is big but distant. The Moon is small but near.

How to Calculate Eclipse Shadows

There’s also a shadow cone projected from the Moon away from the Sun. The length of that cone depend on ratio between the Moon’s diameter and the Sun’s diameter, which change depending on how much farther or closer each one is. If the Moon are nearer to Earth, then its cone gets longer; if further away, then shorter. It’s what accounts for whether certain eclipses is annular or total.

The size (diameter) of the blocking body. This is the size (diameter) of the light source. These two objects is separated by a distance. The tool will tell you length of cone. That’s how far away end of shadow is from the occulter. That means any target beyond that point will be in antumbra.

This is the portion of the shadow where the blocking object are smaller than light source. It look like a ring of fire. And if the target is closer then the tip, then it’s inside the umbra: Total shadow. And the tool will let you know if your geometry support annularity or totality.

The size of the shadow itself get a lot of attention. Some might think the shadow has the same width as Moon all over. It doesn’t. As it travels farther out from the source, the umbra grow narrower. By the end, tip of the shadow is basically just a single point.

Because Earth is bigger than the Moon, the Earth’s shadow will be wider when casting onto the Moon (hence a lunar eclipse). That means moon is in the dark longer then the earth is during a total solar eclipse. You can see that with coverage fraction output. That is comparing shadow’s width at some given distance to diameter of object being covered. How much of target is covered?

These ratios are illustrated in preset buttons. Mars’s small moon Phobos is too small to produce complete shadow on the Martian landscape. The moon’s shadow cone does not reach all the way down to surface. From view of Mars, observers witness an annular eclipse. (More precisely, this is a transit since the shadow doesn’t touch them at all.)

Jupiter’s large moon Io produce a wide shadow that easily touches tops of gas giant’s clouds. What makes these illustrations important is lesson that it isn’t always so much about size as it is proportion. If a moon is near its primary body, even a small moon can throw a lengthy shadow. Conversely, a moon that orbits far out may be physically larger but fall short.

Exact means exact. It’s not enough for people to say, “I measured X distance from this point and Y distance from that.” That won’t work because you’re measuring from surfaces rather than from center to center. The calculator use the standard definition of astronomical terms. You should of be equally careful with what you enter into it.

A small error in your input will cause calculator to shift position of shadow’s tip. In turn, that may make the difference between an annular eclipse situation and a total eclipse situation. Distance and alignment determine what part of space is umbra. And it’s a dynamic region defined by alignment and distance.

Knowing how long cone is provides a predictive advantage. You won’t have to guess where that dark spot will be. Now you know. The math lead to shadow following. Predictability increase when you know the triangle.