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2.14 Angle measurement and time measurement


Frank L. Preuss


Extracts from the book "dtv-Atlas zur Astronomie" follow:

Page 43
For the calculation of the day length or generally of the time period, which a heavenly body stands above the horizon, the so-called half day arc T is introduced, therefore half of the arc going above the horizon, which a heavenly body describes. It is approximately and without consideration of refraction (see page 87)
cos T = - tg δ x tg φ
Thereby is δ the angle distance of the heavenly body from the celestial equator (the declination), φ the geographic parallel. One gets T in the angle measurement, what still must be converted into the time measurement. It is 15o = 1h; 1o = 4m; 15' = 1m; 1' = 4s usw.

Page 87

The refraction and extinction

Apart from the absorption of certain wave length areas of the electromagnetic radiations coming from outside (see page 36) the light rays also experience a ray refraction, which leads to an apparent lifting of the location of the heavenly body above the horizon. With astronomical position identifications this is to be taken into account. Only for the case that a heavenly body stands exactly in the zenith, the refraction disappears. With a position at the horizon it is (for 760 mm atmospheric pressure and +10o C temperature) at any rate 35'24". That means that the sun disk, which has about a diameter of half a degree, appears to have just risen, although it is in fact still under the horizon. The amount of refraction increases with rising atmospheric pressure and sinking temperature and vice versa. With the refraction also a mostly oval distortion of the sun and moon disk at the horizon is connected, which again only disappears, when the heavenly body moves higher above the horizon.

Moreover the light rays penetrating through the earth atmosphere experience a waning or extinction, which is for the case of the zenith position of a star only about one tenth size class. But towards the horizon the extinction increases more and more. In general one relates the amount of extinction to the brightness in the zenith, i.e. one ignores the mentioned zenith extinction of approximately 0m1. Strictly speaking the extinction is again depending on wave lengths. The strongest it has an effect on the short wave rays, therefore blue rays, less on the other hand on the reddish light, by which also the red change of colour of the heavenly bodies near the horizon is explained. Moreover page 86 b expresses only the average extinction. With strong smoke (industrial areas!) or with fog it can still be considerable above these values.


Now follows a table for the conversion from angle measurement and time measurement:


Angle measurement and time measurement
Angle measurement Time measurement
Angle Angle Degrees hh:mm:ss Time Hours
360o00'00"360o36024:00:0024 h24
180o00'00"180o18012:00:0012 h12
 90o00'00" 90o 9006:00:00 6 h 6
 45o00'00" 45o 4503:00:00 3 h 3
 15o00'00" 15o 1501:00:00 1 h 1
 01o00'00"  1o  100:04:00 4 m 0.06666667
 00o15'00" 15'  0.25000000 00:01:00 1 m 0.01666667
 00o01'00"  1'  0.0166666700:00:04 4 s 0.00111111
 00o00'15" 15"  0.00416667 00:00:01 1 s 0.00027778
 00o00'01"  1"  0.00027778 0.00001852


Now follows an example.

38o 16' 37.48" means 38 degrees, 16 arc minutes and 37.48 arc seconds.

Expressed in degrees this is:
38 + 16/60 + 37.48/3600 =
38 + 0.26666667 + 0.01041111 =
38.27707778 degrees.

38 + 16 x 0.01666667 + 37.48 x 0.00027778 =
38 + 0.27707791 + 0.01041119 =
30.27707791 degrees.

Expressed in hours this is:
38.27707778 x 0.06666667 =
2.55180531 hours.

38.2770778 / 15 =
2.55180519 hours.


Now still something to the ray refraction, which leads to an apparent rising of the position of the heavenly body above the horizon.

An extract follows from Jakob Lorber‘s work "Das große Evangelium Johannes" (The great Gospel of John) and that is from Volume 10 and there beginning with Chapter 178, Verse 16, to Chapter 179, Verse 04, jl.ev10.178,16 to jl.ev10.179,04.

   16] The best is to recognize God, the only one and alone true, and to love him above all and one’s neighbour like oneself.

   17] Now the sun will rise immediately, and you will see so a number of things, which will take you aback!«

   01] At the same moment one saw already a sun, but standing quite high above the horizon, which actually was quite alike the sun.

   02] And the head town judge asked me, saying: »Lord and master, how had then the sun been able this time to climb so fast over the horizon, that we noticed nothing of it, until it appeared to us already at a sizeable seeing level? And still we see no clouds, which could have prevented the sun to become visible to us immediately at the rising!«

   03] Said I: »But that is also no real sun, but a copy of the sun still standing under the horizon in the mirror of a layer of air having become completely still; but this sun will soon pass, when the real one rises.

   04] See, this sun image is like the natural intellectual light of men, which will also soon pass, so in me also soon for them the true sun of life will rise and to a small part has already risen!«


And now still something from Joshua, Chapter 10, Verses 6 to 15.

Jos 10:6 And the men of Gibeon sent unto Joshua to the camp to Gilgal, saying, Slack not thy hand from thy servants; come up to us quickly, and save us, and help us: for all the kings of the Amorites that dwell in the mountains are gathered together against us.

Jos 10:7 So Joshua ascended from Gilgal, he, and all the people of war with him, and all the mighty men of valour.

Jos 10:8 And the LORD said unto Joshua, Fear them not: for I have delivered them into thine hand; there shall not a man of them stand before thee.

Jos 10:9 Joshua therefore came unto them suddenly, and went up from Gilgal all night.

Jos 10:10 And the LORD discomfited them before Israel, and slew them with a great slaughter at Gibeon, and chased them along the way that goeth up to Bethhoron, and smote them to Azekah, and unto Makkedah.

Jos 10:11 And it came to pass, as they fled from before Israel, and were in the going down to Bethhoron, that the LORD cast down great stones from heaven upon them unto Azekah, and they died: they were more which died with hailstones than they whom the children of Israel slew with the sword.

Jos 10:12 Then spake Joshua to the LORD in the day when the LORD delivered up the Amorites before the children of Israel, and he said in the sight of Israel, Sun, stand thou still upon Gibeon; and thou, Moon, in the valley of Ajalon.

Jos 10:13 And the sun stood still, and the moon stayed, until the people had avenged themselves upon their enemies. Is not this written in the book of Jasher? So the sun stood still in the midst of heaven, and hasted not to go down about a whole day.

Jos 10:14 And there was no day like that before it or after it, that the LORD hearkened unto the voice of a man: for the LORD fought for Israel.

Jos 10:15 And Joshua returned, and all Israel with him, unto the camp to Gilgal.




This is the end of "2.14 Angle measurement and time measurement"
To the German version of this chapter: 2.14 Winkelmaß und Zeitmaß



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