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2.18 Solar Eclipse

 

Frank L. Preuss

 

MySolarEclipse

This diagram shows a solar eclipse.

We want to use an example, to discuss details of an eclipse. Further down are data of this example of a solar eclipse as a demonstration. You can have a look at it, but we actually want to only discuss interesting details of this eclipse.

This solar eclipse was seen in the USA. It started in the west und moved right across that country to the east. The following pictures show this:

Eclipse20170821

EclipseCourse20170621USA2

EclipseCourse20170621USA2

Now these pictures show that the eclipse did not stop at the east coast, but carried on and moved over the Atlantic.

So there is a beginning, and then a high point, and then an end.

The high point is right in the middle of the course of the eclipse. It is the time when astronomical tables show the time of the new moon.

The third picture shows that the middle of the path of the eclipse is somewhere west of the east coast and the table below confirms this.

Solar eclipses occur at new moon. Then the moon is right between the sun and the earth and the moon prevents light to fall upon very certain areas of the surface of the earth and causes a shadow on the earth and this shadow moves on the earth and the shadow, the cone shadow, is quite small, as shown on the above picture.

We must distinguish between two theoretical lines. On is the line from the centre of the sun going to the centre of the moon and then to the centre of the shadow. The second line does not go the centre of the shadow, but to the axis of the earth. Now when the first line goes through the axis of the earth, then it is the exact time of new moon. If the first line goes through the centre of the earth, then the shadow would be on the equator.

In our example we can see this:

 

Solar eclipse August 21, 2017
12345678910 11121314151617181920 21222324252627282930 31
No. Geography Astronomy Solar eclipse Calculation
Location Coor- dinates Distances Sun Moon New moon Beginning of totality Speed of shadow in km/minute
Place State, in USA Time zone La- ti- tu- de Lo- ng- it- ude Dist- ance in km Acc- umu- lated Dist- ance in km Sunrise Sunset Daylength Solar noon Moonrise Moonset Meridian passing Time Green- wich mean time Time Green- wich mean time Dif- fer- ence
Time An- gle in o Time An- gle in o Time Dif- fer- ence Time An- gle in o Mil. km Time An- gle in o Time An- gle in o Time An- gle in o Distance in km Illu- mina- tion in %
1 Madras Oregon -8 44o 36' N 121o 07' W 0 0 06:14 72 19:59 287 13:45:09 -2:50 13:07 57.2 151 322 06:04 72 20:09 285 13:11 56.8 372 377 0.0 11:30 19:30 10:19 18:19
2 Grand Teton National Park Wyoming -7 43o 36' N 110o 50' W 835 835 06:34 73 20:16 287 13:42:05 -2:45 13:26 58.1 151 232 06:21 72 20:25 285 13:28 57.8 372 265 0.0 12:30 19:30 10:35 18:35 00:16 52
3 Orin Wyoming -7 835 11:44 18:44 00:09
4 Glendo Wyoming -7 42o 29' N 105o 01' W 483 1 318 06:13 73 19:51 287 13:37:56 -2:38 13:03 59.4 151 323 06:00 72 20:00 285 13:04 59.2 372 204 0.0 12:30 19:30 11:45 18:45 00:01 48
5 South of Crawford Nebraska -7 1 318 11:46 18:46 00:01
6 Homestead National Monument of America, west of Beatrice Nebraska -6 40o 15' N 96o 45' W 751 2 069 06:44 74 20:15 266 13:30:55 -2:25 13:30 61.6 151 324 06:30 73 20:23 285 13:30 61.5 372 117 0.0 13:30 19:30 13:02 19:02 00:16 44
7 Parkville Missouri -6 2 069 13:08 19:08 00:06
8 Weldon Spring Missouri -6 2 069 13:16 19:16 00:08
9 Paducah Kentucky -6 37o 04' N 88o 37' W 791 2 860 06:16 74 19:37 285 13:21:35 -2:09 12:57 64.8 151 325 06:01 73 19:45 284 12:56 64.9 372 030 0.0 13:30 19:30 13:22 19:22 00:06 40
10 Nashville Tennes- see -6 36o 09' N 86o 46' W 194 3 054 06:10 74 19:29 285 13:19:02 -2:05 12:50 65.7 151 325 05:54 73 19:36 284 12:49 65.8 372 010 0.0 13:30 19:30 13:27 19:27 00:05 39
11 40,000 feet above the Tennes- see/Geor- gia border -5 3 054 14:37 19:37 00:10
12 Nottely Lake Georgia -5 3 054 14:35 19:35 00:02
13 Greenville South Carolina -5 34o 50' N 82o 24' W 423 3 477 06:33 75 19:51 285 13:17:36 -2:02 13:12 66.3 151 326 06:16 73 19:57 284 13:10 66.5 371 912 0.0 14:30 19:30 14:38 19:38 00:03 28
14 Charleston South Carolina -5 32o 47' N 75o 56' W 324 3 801 06:47 75 19:57 285 13:10:16 -1:49 13:22 69.1 151 325 06:31 74 20:04 283 13:20 69.3 371 939 0.0 14:30 19:30 14:46 19:46 00:08 41
15 Total 3 801 01:31 42 km/minute = 2 520 km/h = 1 570 miles/h

 

With the speed of the shadow the speed of the moon on its orbit around earth is the decisive speed. This speed, calculated with the values from the above table for the distances of the moon from the earth, is 3299 km/h. See column 11 and row 3 of the following table.

The second speed, which must be taken into account, is the speed of surface of the earth around the axis of the earth. It is 1670 km/h at the equator.

For the speed of the shadow the speed of the surface of the earth must now be subtracted from the speed of the moon, therefore 3299 1670 = 1629 km/h.

The speed of the surface of the earth in Madras is 1189 km/h. The speed of the shadow there is then 3301 -1189 = 2112 km/h. That is first the actual value of the speed of the moon there und secondly, when the shadow would run parallel to the degree of latitude.

The speed of the surface of the earth in Greenville is 1371 km/h. The speed of the shadow there is then 3297 1371 = 1926 km/h. That is first the actual value of the speed of the moon there and secondly, when the shadow would run parallel to the degree of latitude.

A comparison of these speeds look then like this:

Comparison of speeds
1234567891011121314
1 Speed of Madras, Oregon, USA Greenville, South Carolina, USA Equator
2 km/ h miles/ h km/ minute miles/ minute km/ h miles/ h km/ minute miles/ minute km/ h miles/ h km/ minute miles/ minute
3 Moon 3301 2051 55 34 3297 2049 55 34 3299 2050 55 34
4 Earth 1189 739 20 12 1371 852 23 14 1670 1038 28 17
5 Shadow 2112 1312 35 22 1926 1197 32 20 1629 1012 27 17
6 Shadow from previous table 52 28
7 Difference -17 +4

In this table therefore speeds of the shadow are compared. The speeds in the coloured fields are speeds when the course of the shadow runs parallel to a line of latitude, a parallel. And the speeds below that are then the actual speeds, where the course of the shadow is inclined.

The value of 27 km/minute, in column 13 and row 5, for the speed of the shadow at the equator, can be taken as the basic speed of the shadow. The more the shadow moves further north, the more this value increases.

The speed of the moon is always the same, about 55 km/minute. That can be seen in columns 5 and 9 and 13 of row 3.

And at the equator the speed of the surface of the earth is about half that value, 28 km/minute, see column 13 row 4. And when this half of the value is subtracted, also half of the value remains, 27 km/minute.

Now the speed of the shadow changes according to the distance from the equator, but it also changes the more it deviates from following a parallel. And that is noticeable in the eastern part of the USA where the course of the shadow is more inclined than in the western part. But then close to the eastern coast it comes again less inclined, and consequently the speed increases.

Now coming back to the first table, the table called "Solar eclipse August 21, 2017," and there looking at column 28, we have the times, when the eclipse occurred at the different places, at their respective times, according to their time zone. And in the next column, column 29 we have the Greenwich times, which give us a better idea, about the course of the eclipse - time wise. Now in column 27 we have the time of the new moon and that is always and everywhere the same time: 19:30 Greenwich time. And that is because the exact time of the new moon does not depend on a certain place on the surface of the earth, but when the theoretical line from the centre of the sun via the centre of the moon goes right through the axis of the earth. And that happens irrespective of any place. When we now keep this time of 19:30 in mind and go down column 29, then we see that the times given in column 29 increase from place to place and come closer and closer to the time of 19:30. And in the place called Nashville in Tennessee we have the time 19:27, therefore 3 minutes before 19:30, and in the place called Nottely Lake in Georgia we have 19:35, therefore 5 minutes after 19:30. So between these two places there was new moon. And there was then also the high point of the solar eclipse and therefore also the centre of the course of eclipse, space wise.

 

This is the end of "2.18 Solar Eclipse"
To the German version of this chapter: 2.18 Sonnenfinsternis

 

 

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