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[Home]>[Miscellaneous]>[8. Astronomy]>[1. Astronomical questions and answers]>[1.2 Astronomical questions and answers, Part 2]
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Frank L. Preuss
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1.2 Astronomical questions and answers, Part 2
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No.  Question  Answer  
^ 51  When are the rays of the sun tangent to earth at the Antarctic Circle?  On the 22nd of December.  
^ 52  How can it be that the rays of the sun are tangent to earth at the Antarctic Circle on the 21st of June and also on the 22nd of December?  On the 21st of June the rays of the sun are tangent to earth at the near side of the Antarctic Circle and on the 22nd of December at the far side.
On the 21st of June there is no sunshine between the Antarctic Circle and the South Pole. On the 22nd of December there is sunshine in that area the whole day long. 

^ 53  When this thing with degrees west longitude and degrees east longitude was introduced, the whole thing was determined by the English. Or the Englishman asserted himself. The French also tried it, to determine Paris as zero, but were then not so successful. What would have been an easier system?  The English wanted to see themselves as the centre of the world, there were west and east meets. It would have been easier, when they would have seen themselves as beginning and end, as alpha and omega. Then London would also have zero degrees, but also 360 degrees, but then the division in west and east would have fallen away.  
^ 54  Which location lies on 180^{o} east and also on 180^{o} west?  Fiji.  
^ 55  For the man on the Fiji Islands, what is for him in the west and what is for him in the east?  For him the east, the far east, is west of him, and for him the west, the far west, is east of him. Very assuring!  
^ 56  Since the Americans are now more in the driving seat, they could determine Washington as zero and as 360. What advantage would that have?  Incredible many school books would have to get printed anew. That would bring a great impetus to that part of industry.  
^ 57  In winter a man sees the sun rise in the east. Then he observes, how the sun finds its way in an arch to the right upward, reaches its zenith at midday and then further in an bow to the right and downwards and then sets in the west. Where is the man?  On the northern hemisphere.  
^ 58  How could one set out the north direction on a piece of land in a simple way?  One determines the geographic longitude of the piece of land. Is this for example 116^{o} E, for example in Perth in Australia, and the sun shines at 12 o'clock midday from north on 120^{o} E, time zone 8, then the sun shines 4^{o} after that in Perth directly from north. In 60 minutes the sun moves 15^{o} and for one degree it needs 4 minutes and 16 minutes for 4 degrees. A survey rod has been placed vertically into the ground and at 16 minutes after 12 o'clock midday a second survey rod is placed into the shadow of the first and with the two rods one has the north direction.
But since the true time can differ from the mean time, it is to be recommended to determine the north direction with the help of local coordinates. The difference between the true time and the meantime can reach globally up to a maximum of above a quarter of an hour. 

^ 59 
A man stands on the South Pol.
1. Where is north? 2. Where is the North Pole? 3. In what direction is London? 4. In what direction is New Orleans? 5. If the man wants to turn around in the opposite direction, without moving, what must he do? 
1. Everywhere.
2. Down below. 3. In the direction of the Prime Meridian. 4. Perpendicular to the direction of the Prime Meridian. 5. Just stand still for 12 hours. 

^ 60 
A man stands on the equator and looks in the direction west.
1. What must he do to look in the opposite direction, without moving? 2. In what direction does he then look? 
1. Just stand still for 12 hours.
2. Also in the direction west. 

^ 61  Johannesburg is in the subtropics. In summer it can get quite hot there. In winter it can get quite cold, particularly also because it is high up, more than 1½ km above sealevel. Towards which direction should the windows of a building be directed, so that in summer practically no sun shines into the rooms, but in winter very much?  To the north.  
^ 62 
A ship sails west on the equator. For one degree longitude, from 48^{o} to 47^{o}, it needs 10 hours.
a) How fast does the ship travel? b) Where is the ship? 
a) The equator is 40 000 km long. One degree on the equator is 40 000 km / 360^{o} = 111 km long. 111 km / 10 h = 11 km/h.
b) Eastern hemisphere  Indian Ocean. 

^ 63 
A ship travels on the equator. It travels from 30^{o} to 20^{o} longitude.
a) In what direction does the ship travel? b) Where is the ship? c) Why? 
a) East.
b) Western hemisphere  Atlantic Ocean. c) Because there is no waterway there in the eastern hemisphere. 

^ 64 
The Okavango River comes from Angola and flows a short distance through Namibia, through the Caprivi Strip. It is the only river within Namibia, which has always water. It then flows into Botswana and flows there into the Okavango Delta, a basin without outlet. There the water drains into the sand.
a) What is under the Okavango Delta? b) Who was Caprivi? 
a) Hawaii.
b) Successor of Bismarck as German Reichskanzler. 

^ 65  What is under Taiwan (Formosa)?  Rio de Janeiro.  
^ 66  With what speed does the earth move around the sun? 
The earth has a distance from the sun of 1 Astronomical Unit, AU. That are 149 600 000 km. The orbit is then 1 AU x 2 x 3.14 = 939 500 000 km long and for that the earth needs 1 year or 365 days. That are
2 600 000 km per day or per 24 hours. And that are 107 000 km/h. And that are 1 800 km/minute. And that are 30 km/second. 

^ 67  With what speed does the solar system move around the centre of the Milky Way? 
The sun has a distance from the centre of the Milky Way of 25 000 light years.
The orbit is then 25 000 x 2 x 3.14 = 157 000 light years long. The time of rotation of the sun around the galactic centre can be assumed to be 200 million years. In one year the covered distance is then
0.000785 light years. And that are 0.000785 x 9.46 x 10^{12} = 0.0074 x 10^{12} km per year. And that are
7 400 000 000 km per year. And that are 20 274 000 km per day. And that are 845 000 km/h. And that are 14 080 km/minute. And that are 235 km per second. 

^ 68  With what speed does the Milky Way move around the centre of that group of galaxies? 
Good question.
"Strikingly many nebulae lie on the connection line to the Virgo heap. This has led to the supposition, all these groups and heaps would together again form a super heap, at which edge is the local nebula group and in which middle the Virgo heap. According to DE VAUCOULEURS the galaxies of this super heap are to run around once in 50 to 200 billion years the »Virgo centre«. But this is just as well controversial as the question, whether there are super heaps in the universe at all or whether the joining together of smaller to larger units stops with nebula heaps."


^ 69  With what speed do we move around the centre of the Milky Way? 
< 1 667 km/h around the axis of the earth. Plus
107 000 km/h around the sun. Plus 845 000 km/h around the centre of the Milky Way. That is together 953 000 km/h. 

^ 70  What do spiritual writings say about such speeds? 
"An above mentioned middle sun of the third order flies through such an orbit of course only in at least ten times thousand years; but because the orbit is a so very enormously far stretched one, so such a sun must in a moment have already a thousand times so far distance behind it, as from here to that star, which we have visited first!"
jl.ev02.141,11, 18511864.
"It is of greatest importance to know, with which enormous speed all world bodies fly through the universe. An extraordinary atmosphere is formed through friction exactly there, where certain resistances become apparent, because friction produces heat and consequently an isolated standing body does not necessarily need to give off this heat. It is therefore only an unusual moving body necessary to set off certain degrees of heat, and consequently the sun could just as well be a cold mass, so the earth would nevertheless produce so much heat through its own speed in its rotations that the requirements would be covered completely." 

^ 71  What is a middle sun of the third order? 
"All now took their bed and slept until broad daylight; I also rested and slept a few of hours. But the two angels performed their worlds leading business in the night and were with the rising of the sun also already again with us, got up to me, thanked and said: »Lord, everything is in the greatest order in the whole large worlds man. The prime middle suns stand unmoved in their places, and their rotations are equal: the orbits of the second middle suns are unmoved; the orbits of the third class of middle suns around the second are precisely also in the greatest order, just as well the middle suns of the fourth class with their ten times hundred thousand planet suns, here and there more and here and their less,  as you, oh Lord, has laid the measure from the original beginning! But the countless many planet suns with their small, in the main lightless planets and moons depend anyway on the order of the large lead suns, and consequently in this hull globe, given to both of us for supervision, is
(»Hull globe is the naming of the summary of decillion times decillion suns, which all move around a common immeasurable large centre, which is also a close to endless large prime middle sun, in large and far stretched orbits, as central suns of first, second, third and fourth class with countless many planet suns, as the one of our earth is.  But countless many such hull globes, which for us men are away in unthinkable far distances of each other and fill the eternal infinite space, have the common name »the large worlds man«. This for the easier understanding of the morning report of the two angels to Jesus, the Lord of infinity; Jakob Lorber) everything in the greatest and best order, and we are for that reason allowed to spend a bright day with you, holy father, and with your children very dear to us!«"
jl.ev02.057,01, 18511864. A middle sun of third order is then probably for example the centre of the group of galaxies, to which our galaxy belongs, the Milky Way. And the centre of our galaxy, the Milky Way, is therefore a middle sun of the fourth order. 

^ 72  What is under Hawaii?  The Okavango Delta in Botswana.  
^ 73  Does Hawaii get its groundwater from the Okavango Delta?  Probably not.  
^ 74  How can one measure, how fast the earth rotates around itself? 
Measuring is done at equinox.
1. Method: One has a board in that plane, in which the sun orbits the earth, that means, the plane of the board is in the plane of sun orbit. On the board one fastens a sheet of paper. Through the sheet of paper and the board one knocks in a nail, which cast a shadow. A second nail is knocked in through the sheet of paper, where the shadow is and draws a pencil line on the paper between the two nails. One hour later one knocks in a third nail, also again into the shadow of the first nail and draws a second line, this time also again from nail 1, but now to nail 3. Then one measures the angle, which the two lines form at nail 1. The angle should be 15^{o}. The earth rotates therefore 15^{o} in one hour and 360^{o} in 24 hours. The sheet of paper is kept as document that one has proved to oneself, how fast the earth rotates around itself. 2. Method: One has a point casting a shadow and a piece of thread is stretched from this point to the shadow of this point. One hour later a second piece of thread is stretched, again from the point casting a shadow to its shadow, which it now casts. Then the angle between the two threads is measured. It should also be 15^{o}. The angle one can also be determine by making a drawing of it. The lengths of the three sides of the triangle are measured and then one draws a triangle on a piece of paper and then measures the angle. When instead of taking one hour, three hours are taken, one should get as result an angle of 45^{o}. An angle of 45^{o} is produced, by folding a square piece of paper diagonally. One can also calculate the angle. One calls the soughtafter angle A. One calls the length of the triangle between the two shadow points a and the lengths of the two pieces of thread b and c. Then one uses the law of cosines: a^{2} = b^{2} + c^{2}  2bc cosA. The cosine of the angle A is then: cos A = (a^2 + b^2 + c^2)/2*b*c. That one calculates once in a row of a spreadsheet and then needs for further calculations only to enter the 3 lateral lengths and immediately has the angle. In my spreadsheet calculation the formula is A =DEGREES(ACOS(H6)), when the value for cosA is in the cell H6. 3. Method: One has a point giving a shade, for example 1 m above the floor. On the floor the shade is marked. After one hour the shade of the point is marked again. One measures the distance of the two points and calls it c, the one lateral length of the triangle. Then one measures the two other sides, therefore from the point casting a shadow to the respective shadow. These values are entered into the spreadsheet calculation and the angle is given. 

^ 75  When the sun stands in the sky in the west in the afternoon, how can one then predict, where the sunset will be, where therefore the course of the sun will cut the horizon? 
When one wants to record, where a celestial body is, then one takes the sight on it and records this position. When one wants to record, how a celestial body moves, then one does it at least twice.
But with the sun this is not advisable. For that reason one should work with the shadow of the sun. Before sunset, when therefore the sun is already not too high in the west, one sticks a shadow casting point on the window pane and marks the shadow on a vertically fixed paper. A second marking gives one already the inclination of the course of the sun. With this inclination one can find the future place at the horizon, where the sun will set. 

^ 76 
a) How great is the angle of the course of the sun to the vertical at the equator on the 20th of March and on the 23nd of September?
b) How great is the angle of the course of the sun to the horizontal at the poles on the 20th of March and on the 23nd of September? 
a) Zero degree.
b) Zero degree. 

^ 77  How does on build a sundial? 
One has a vertical stick or pillar. The end of the shadow is marked on the ground and the date and the time is added. For the sake of simplicity on each full hour. The more marked points are available, the more exactly one can draw a system of lines, which make a checking of time possible.
One can fix a point to the window pane and mark the shadow of the point on the floor. And at every next full hour one then marks a further point. Now follows the description of a not so simple sundial: Pocket Sundial. This portable folding German sundial has a string gnomon (pointer), adjustable for accuracy at any latitude. As shadows fall across the sundial, the smaller dials show Italian and Babylonian hours. The dial also indicates the length of the day and the position of the sun in the zodiac. 

^ 78  How does one calculate the angle against the vertical by which the plane of the orbit of the sun is the tilted or inclined? 
It is the angle of the parallel. The angle of the parallel on which Berlin is located, is 52^{o}30' and therefore the looked for angle is 52^{o}30'.
But normally this angle is given as measured to the horizontal. So the formula is 90^{o} minus the angle of the parallel and that is then 90^{o} minus 52^{o}30' and therefore the looked for angle is 37^{o}30'. 

^ 79  In what direction should we look?  "I try to avoid looking forward or backward, and try to keep looking upward." English novelist and poet Charlotte Brontë (18161865).  
^ 80 
How great is the angle measured against the vertical with which the sun stands in the sky at midday on the following degrees of latitude?
1. +50 2. +40 3. +30 4. 30 5. 40 Near the parallel +50 are places like the island Sakhalin north of Japan, Irkutsk in Russia, Kiev, Krakau, Prag, Frankfurt, Luxemburg, Amiens in France, the southern end of the British island, Newfoundland, Winnipeg, Vancouver. Near the parallel +40 are places like North Korea, Beijing, Samarqand, Azerbaijan, Yerevan, Ankara, Istanbul, Thessaloniki, the island Sardinia, the island Mallorca, the Azores, New York, Denver. Near the parallel +30 are places like Shanghai, Mount Everest, Delhi, Kuwait, Eilat in Israel, Cairo, Agadier in Marocco, Canary Islands, New Orleans, Houston. Near the parallel 30 are places like Perth in Australia, Durban in South Africa, Porto Alegre in Brasilia. Near the parallel 40 are places like the North Island of New Zealand, the island Tasmania, Bahia Blanca in Argentina. 

For the 20. March and the 23. September, equinox, the angle of the parallel is also the angle of the rays of the sun. For the 21. June, solstice, the angle of 23.5 degrees is subtracted from the angle of the degree of latitude, to get the angle of the rays of the sun. And for the 22. December, solstice, the angle of 23.5 degrees is added, to get the angle of the rays of the sun. The angle difference between the 21. June and the 22. December is always 47 degrees. That is twice 23.5 degrees. 

^ 81  How can a board be so aligned in a simple way that the plane of the board is in that plane, in which the sun orbits earth? 
Bourke in Australia is taken as example und the 23. September, therefore equinox. The latitude there is 30^{o}. The angle against the vertical, with which the rays of the sun arrive there is then 30^{o}. The board is arranged on a table so that it has this angle of 30^{o} to the vertical.
The vertical is produced with the help of a pendulum. A 30^{o} angle one can get in the following way. The long side of an A4 sheet of paper is folded into half of its length. From this halflength and from the length of a second A4 sheet a rightangled triangel is produced. The hypotenuse is the long side of the second sheet and the short leg is the halflength of the first sheet. The right angle is produced with a third sheet. The angle, which is oposite the short leg, is the 30^{o} angle. This arrangement stands on a table. And now the whole thing is turned horizontally so that the rays of the sun are parallel to the board. The correct alignment of the board is adjusted so that one places oneself between the sun and the board and one aligns one's sight to the straight line between the board and the shadow of the board. 

^ 82  How can one measure the vertical engle of a ray of the sun?  One lets for example the rays of the sun fall on a door, which is opened so far that the rays of the sun are parallel to the door.  
^ 83  What does it mean "looking upward" in the statement "I try to avoid looking forward or backward, and try to keep looking upward."? 
An example might help, excerpts from a news item:
Old uncle is 114 and smoking Secret to his long life is a gift from God, says Fredie Blom To fellow neighbours he is just Oom Fredie. Fredie Blom is no ordinary man. At 114, he is possibly older than all the 56 million people in South Africa and possibly the oldest man alive in the world. The walls are adorned with posters of Bible verses. Apart from using a cane when he walks, Blom is fit and strong  and sharpeyed  he's never seen a doctor for ailment treatments. "I have no secret to living long. It's a gift from God. He's the crown of my life. I am grateful and thank Him every moment," says Blom. His is a life of respect and acknowledging the creator, "respect both the older and younger, and listen to advice, this was ingrained in me by my parents," he says. "I am now waiting for the day when the angel will come." 

^ 84  How does one know when it is midday? 
It is midday, when the sun is in the plane determined by three points: The observer, the North Pole and the South Pole.
So the sun is either in the south, or in the north, or directly above the observer or in any point between these 3 points. Or the sun is in a vertical plane in northsouth direction. Or the sun is in a plane determined by the observer and the axis of the earth. 

^ 85  How does a man know at what clock time is midday? And that means, at what clock time is the sun in the plane determined by the axis of the earth and his position? 
Let us take Cairo in Egypt.
The man establishes the time zone he is in. It is time zone +2. This time zone is also called East European Time. Now he establishes on which meridian this time zone is based. It is 30^{o} E. Now he finds out on which longitude he is. Let's us say he is on 30^{o} 59' 17" E. 30^{o} 59' 17" = 30 + 59/60 + 17/3600 = 30 + 0.9833 + 0.0047 = 30.9881^{o}. The difference between the longitude of the time zone and his longitude is 30.9881  30 = 0.9881^{o}. The sun travels 360^{o} in 24 hours or 15^{o} in 1 hour or 15^{o} in 60 minutes or 1 degree in 4 minutes. For 0.9881 degrees it needs 0.9881 x 4 = 3.9524 minutes. That is 3 minutes plus 0.9524 x 60 = 3 minutes + 57.14 seconds. Therefore 3 minutes and 57 seconds. When it is midday on the 30th longitude, then it was 3 minutes and 57 seconds before that time midday with the man, therefore 11:56:03 o'clock. Every day at 11:56:03 o'clock it is true midday with the man; the sun stands the highest. The 12:00:00 o'clock time is only the true time for a certain longitude in his time zone, for the longitude of 30 degrees. Every place in that time zone, which is not on the 30th longitude, has another true time of midday. Or when it is midday on the 45th longitude, then it is 14^{o} 00' 43" later midday with the man. One gets that, when one subtracts from 30^{o} 59' 17" the angle of 15 degrees. That is 14.0119 degrees and for that the sun needs 14.0119 x 60 / 15 = 56.05 minutes and that is 56 minutes and 3 seconds. That would then be 12:56:03 in accordance with time zone 3 and 11:56:03 in accordance with time zone 2. Midday is therefore 56 minutes and 3 seconds after 11 o'clock and that is the time in which the sun stands in the south and gives him the direction, in which north is. So at 11:56:03 o'clock it would be the easiest time to measure the angle of the sun and with it of the rays of the sun. And when he does this always on those days, where the sun shines at 11:56:03, he receives information about the course of the sun during the year. And this allows him to compare the data with those, which he has calculated or received in another way. 

^ 86  The man measures the angle of the sun against the vertical on 21. June and compares this with the theoretical angle of 53.5 degrees on the 30th parallel. He now wants to know the effect of him not being exactly on 30 degrees. What must he do? 
He establishes the latitude of his position and finds it to be 29^{o} and 51' and 8". That is 29 + 51/60 + 8/3600 = 29 + 0.8500 + 0.0022 = 29.8522^{o}.
He now calculates the angle of the rays of the sun and that is 29.8522 + 23.5 = 53.3522^{o}. The difference to 53.5^{o} is 0.1478^{o}. As for his purpose he only measures in full degrees, he decides that the difference too small an amount and ignores it. 

^ 87  There are different possibilities to measure how fast the earth turns around itself. What would be a method to also measure this, but to also observe at the same time, how fast the sun orbits the earth? 
One takes for example graph paper ruled in millimetre squares or squared paper with a line distance of 5 mm, and arranges it perpendicular to the direction of the rays of the sun. Then one takes a shadow giving edge, which is sideways to that direction, which the sun travels. Then one lines up the lines of the paper so, that they are parallel to the shadow. The distance of the edge is so chosen, that the shadow travels 1 mm in each second.
The earth rotates in 24 hours by 360 degrees, in one hour by 15 degrees and in one minute by 0.25 degrees and in one second by 0.00417 degrees. The reciprocal value of the sine or of the tangent of 0.00417 degrees is 13751 mm / 1 mm. And that is 13.75 m divided by 1 mm. When the edge giving the shadow is 13.75 m away from the graph paper ruled in millimetre squares, one can observe in second rhythm, how the shadow travels one millimetre in every second. 

^ 88  How does one establish, when it is midday, when one is on the equator at equinox or at solstice on the 21st of June on the Tropic of Cancer or at solstice on the 22nd of December on the Tropic of Capricorn?  One puts up a vertical rod. When the shadow changes from west to east, it is midday.  
^ 89  How does one establish, where is north, when one is on the equator at equinox or at solstice on the 21st of June on the Tropic of Cancer or at solstice on the 22nd of December on the Tropic of Capricorn?  One puts up a vertical rod. At the time of midday the rod casts no shadow. One waits until it casts a shadow. With that, one has the direction, where east is. And with that, one also has the north direction.  
^ 90  How does one establish, where is north, when the sun is not shining?  One takes a map or a street map and there finds the own position. Then one finds an object on the map, which is also visible in nature. Then one holds the map horizontally and turns the map so, until the alignment on the map agrees with the alignment in nature. Then the north direction on the map is also the north direction in nature.  
^ 91  An architect in Johannesburg wants to align his building to the north. At which time should he establish the north direction on the site through the casting of the shadow?  Johannesburg is on the 28th degree of longitude and in the time zone 2. In the time zone 2 the sun stands at 12 o'clock at midday on the degree of longitude +30. Therefore it stands on the 28th degree of longitude 2 degrees later in the north. The sun travels every 60 minutes 15 degrees further to the west. For one degree it needs 4 minutes and for 2 degrees 8 minutes. Eight minutes after 12 o'clock midday is therefore the right time.  
^ 92  It is sunshine and an aeroplane flies at midday over the equator and takes pictures downwards of the surface of the earth. How can one establish on the photos, where the point is, where a horizontal plane perpendicular to the aeroplane is tangent to the surface of the earth, where therefore the curvature of the earth is zero on the photos?  There, where the shadow of the aeroplane is.  
^ 93  In order to use a house for observatory purposes, the man wants to know, in which direction one side of the building is aligned to. How can he establish that? 
We assume, the side of the building is about in the north direction. He measures the time, when the vertical plane of the façade is in the same plane as the vertical plane determined by the façade and the sun, therefore when the plane of the façade casts no shadow, therefore the rays of the sun run parallel to the façade. We assume the measured point of time is one hour and 44 minutes before midday, therefore before the sun stands in the north.
That is 1 + 44/60 = 1 + 0.7333 = 1.7333 hours. In one hour the sun travels 15 degrees and for 1.733 hours it needs then 26 degrees. Now the man can in a simple way determine, where the north direction is. The side of the building is his base line. It deviates by 26 degrees from the north direction. 

^ 94  A man has a side of a building, which is in the direction of NNW. He has measured the time, by which this side of his building is parallel to the rays of the sun. The point of time is one hour and 44 minutes before midday. That is 1.7333 hours before midday. He has calculated that that corresponds to an angle of 26 degrees against north. Where is the man?  Northern hemisphere.  
^ 95  What helps are there to measure astronomical observations? 
They are for example disks, which can be turned around on axis, above all windows and doors.
A window, which can be turned around a horizontal axis, can be provided with a protractor next to the window, which measures the vertical angle of the window, and one that measures the horizontal angle of a ray of the sun. And when a paper is fixed next to the window, then the angle can also be drawn there. Another paper can be on the plane of the window, and be used there for the recording of the angle in the plane of the window. A door can have a horizontal protractor under the door, which is already aligned to north; the opening angle of the door can be checked there and also recorded. A vertical protractor is fixed to the door itself. An example would be to measure and to document the course of the sun in the sky. Sunrise can be recorded there chronologically, and where at the horizon it takes place; the place therefore at the horizon in the angle against north, and also the vertical angle, how far it is under the horizontal plane, when the observer sees the sun rise over the sea. Then the position of the sun can be recorded in any time intervals, including the midday elevation of the sun over the south point or over the north point, and then also the sunset. When one keeps records on the days where the sun is shining, one can get an idea, how the course of the sun is in the course of a year. Also the course of the moon, of a planet or a star one can so get recorded in a quite simple way. And this information can then be compared with data, which one has received from other sources. Does for example the midday elevation of the sun at equinox agree with the value of the latitude? 

^ 96  How does the man orientate himself? 
The man has a vertical rod standing on the floor and uses the upper end of the rod as a shadow giving point.
Shortly before midday he marks the shadow and writes the time or a number next to it, perhaps 1. After a short time, perhaps after 5 minutes, he again marks the shadow, and writes 2 next to it. With these two points he has already reached a fundamental orientation. Since the sun moves from east to west, the shadow moves from west to east, and the man now knows already the approximate west east direction, because the line from 1 to 2 goes in the approximate direction to the east and he has with it also the approximate north direction. In addition he has the speed with which the sun rotates around the earth, or with which the earth rotates around itself. He continues to mark points in short intervals. After a short time he has a curve which strives towards the rod and then away from the rod. The closest point gives, together with the foot point of the rod, the north direction. If he has written a time next to it, then he has at the same time also the time, when the sun sets the north direction. If the man is on the equator at the time of equinox, then the curve is a straight line. It gives the east west direction. The point of time of the change of the shadow from west to east gives him the time, when it is midday. It is the point of time, where the rod casts no shadow. But already with the second point he not only has the approximate north direction, but the exact. If the man is on the north pole, then the curve is the other opposite, not a straight line, but a circle. Every connection line of a point with the foot point of the rod gives him the north south direction. And since it is equinox, the radius of the circle is infinite. If the man continues to record things, he can build up a system of local and chronological orientation. At equinox he can get an exact hour measure. Sunrise and sunset is 6 o'clock. And that everywhere. Also in the two polar regions. On the equator the curve is a straight line; the radius of the curve is infinite, but the man is directly on the curve, and also the rod. On the 45th longitude the curve is so far away, as the rod is long, is high. On the pole the curve is again a straight line, a curve with an infinite radius, a circle with the radius infinite, but the curve is also infinitely far away. The curve therefore forms itself from a straight line always more to a circle, but also always moves more away from the rod. With the method of recording a series of markings around a shadow giving point during the time of midday one receives in a few minutes the north direction and also the point in time, when the sun is in north direction, when it is midday, therefore of place and time. In addition the man has the angle of the midday elevation of the sun and also its course with regard to time. He therefore can determine the horizontal speed of the sun. If he carries out the measurement during equinox, he also knows on which longitude he is. If he carries out the measurement in a room, he has the angle between the window front and the north direction. If the man does not only carry out this measurement on one day, but on several, then he also has the course of the sun in vertical direction, therefore on his meridian. The closer he is to the equator, this is also a horizontal course of the sun, only in the direction perpendicular to the previous horizontal direction. Actually two markings are enough with this measuring to be able to draw this curve, in the case it is a straight line. Therefore really only a few minutes are enough. Several measurements before and after midday result in a curve. When the man draws the perpendicular line onto this curve, which goes through foot point of the shadow giving point, then this line goes through the point of the curve, which gives him the direction to north and which also gives him the time, when the sun has reached its culmination point. 

^ 97  How can the man convince himself of the practical usefulness of the method of the recording of a series of markings around a shadow giving point during the time of midday? 
With this method he finds out at which time the true midday time is with him. This is his first method.
He then determines the true midday time through a second method. He determines the geographic longitude  where he is. And out of this he calculates his true midday time. Then he compares the two results. 

^ 98  What advantage has Germany had that it waged a war and experienced air raids? 
All windows had to be blacked out. Black roller blinds prevented light coming out at night from the homes. Street lights were not switched on. All artificial light was prevented from giving information to hostile aeroplanes. Cars travelled with strongly reduced lights. The lamps of coaches were anyway hardly negative.
And that brought about that no light pollution, air pollution through light, existed and that the starry sky was beautifully visible at night, also in the cities. 

^ 99  With which different results one has to reckon, when one compares a measurement of the midday time with a calculation of the midday time? 
A measurement of the midday time should be the real thing. That is the method of drawing a curve.
Because of the calculation I now bring an extract from the book "dtvAtlas zur Astronomie", 1976, page 47: "Since the true sun namely moves through the ecliptic unequally (at sun nearness in January faster, at sun farness in July slower), one lets a fictitious mean sun run uniformly through the sky equator and refers the mean sun time to this. As time equation it is denoted: True time minus mean time. It can reach maximum value to up to above a quarter of an hour. The diagram shows the course of the time equation during a whole year and with it also the correction, which is to be displayed for the true sun time on a normal sundial without additional equipment." The now following graphic comes from page 46 of the same book
"Sonnenuhr geht vor" = "Sundial is fast" "Die Zeitgleichung" = "The time equation" One should therefore not get different results, when one measures on 16. April or on 15. June or on 2. September or on 26. December. When there are therefore deviations of up to 18 minutes in the length of a day, then the length of an hour deviates of up to 45 seconds. And from this then also deviations result, when one measures the time, which the earth needs to rotate 15 degrees, or when one measures the angle by which the earth rotates in one "hour". 

^ 100  In what situation should one use the method of measuring the time of midday, and not the method of calculating the time of midday? 
When one wants for example to set out on a piece of ground the north direction, to align a building to be built towards south or towards north.
The man erects a survey rod vertically, and then he uses the end of the rod as shadow giving point and marks on the horizontal ground in time intervals at the time of midday the shadow points and then gets a curve, which first approaches the survey rod, then reaches that point, that is closest to the rod, and then moves away from the rod. The north direction is then the line from the survey rod to that point on the curve, which is closest to the rod. This line always results in the north direction, independently of the variation of the length of the day, which results from the unequal move of the sun through the ecliptic, which is faster at sun nearness in January, slower at sun farness in July. The north direction is determined by the piece of ground and the axis around which the earth rotates. This plane is the plane of the meridian of the piece of ground, and it is always the north south direction, therefore does not change, also then not, when the length of the day changes. Would the man use the calculation of the time of midday, he could also get the time, when the sun goes through the meridian. He only had to take in addition the time equation, but it does not give exactly the same values each year. 

^ 101  To the next question. 101  To the next answer. 101 
^
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