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Frank L. Preuss

How fast is the shadow of the moon?

The answer 244 had the example of the shadow of the man, which the sun casts upon a truck.

The first case, when both have the same speed, would then be, when with a solar eclipse the earth would not turn around itself and when the moon would not orbit the earth.

With the second case the rotation of the moon around the earth is added; the earth also now does not turn around itself, but the moon revolves around the earth.

With the third case also the earth rotation is added. The earth revolves around itself and the moon revolves around the earth.

The shadow of the moon moves along the surface of the earth in an eastward direction. Since the earth also turns eastwards, the speed of the shadow of the moon along the earth is equal to the speed of the moon on its orbit minus the speed of the surface of the earth from the rotation of the earth around its own axis.

The moon has a speed of about 3 544 km/h, see 242. The surface of the earth one of 1 667 km/h, see 43.

The speed of the shadow of the moon on the surface of the earth is then 3 544 km/h minus 1 667 km/h = 1 877 km/h.

That would be at the equator. The more it is towards the poles, the more the second number, 1 667 km/h, gets less, and consequently the speed of the shadow greater.

1 877 km/h in km per minute converted, gives 1 877 km/h / 60 minutes/h = 31 km per minute.

The speed of the surface of the earth must be deducted, because the earth indeed turns from west to east, but exactly because of this the light travels from east to west. Sunrise, for example, wanders from east to west, therefore in westerly direction, and consequently against the direction of the shadow of the moon, which wanders in easterly direction.

Here once again the picture:

The picture shows that the centre of the cone shadow is on that line, which goes from the centre of the sun to the centre of the moon and then to the centre of the earth. That would be the situation at the exact time of the new moon. This point of time is valid for all places on the surface of the earth. One can obtain it from astronomical tables.

This point of time would then be the time, when the cone shadow has reached the centre of the course of the shadow.

Now this line must not go through the centre of the earth, when there is a solar eclipse, but when it is in the middle of the course of the shadow, it will go through the axis of the earth, and that will be the time of the new moon.

But the beginning of the course of the shadow is further westerly, therefore on a line from the centre of the sun to the centre of the moon and then not to the centre of the earth, but to the edge of the earth. In the picture therefore to the upper edge of the earth.

From there the shadow wanders to the other edge of the earth, to the end of the course of the shadow.

This looking at the shadow would apply to a course of the shadow at the equator. There the course of the shadow is the longest, but the shadow also the slowest. The further we come to a pole the shorter the course of the shadow gets, but the shadow then also gets the faster.

For the just made contemplation a picture would therefore be more helpful, where the shadow of the new moon does not aim for the centre of the earth, but for a place on the surface of the earth, away from the centre of the earth.

The shadow of the moon wanders from the west of the earth to the east of the earth, because the moon also does it. See the red arrow.

On the next picture one can see the courses of the shadow just discussed:

In the centre, there where the North Pole is, are the courses the shortest and most curved, and the more it gets to the equator the longer they get and the straighter.

This picture also shows very nicely that these shadow courses only cover very limited areas of the surface of the earth.

That a certain place on the surface of the earth is covered by a cone shadow is therefore a very rare thing.

"A solar eclipse, especially a total one, can be seen from only a limited part of the earth, while the eclipsed Moon can be seen at the time of the eclipse wherever the Moon is above the horizon."

"Any point on Earth may, on the average, experience no more than one total solar eclipse in three to four centuries."

"A total lunar ellipse can last as long as an hour and three-quarters, but for a solar total eclipse maximum duration of totality is only 7½ minutes."

This is the end of "Astronomical question and answer 245"
To the German version of this chapter: Astronomische Frage und Antwort 245

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