Position of the sun
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Position of the sun
Late yesterday afternoon we flew into Perth, Western Australia on a track of 260 degrees with the sun setting directly in front of us.
Perth is 31'56 degrees south.
The furthest south the sun should come south is the tropic of capricorn. Ie, 23.5 degress south.
Therefore, why did the sun appear to be setting directly in front of us when we were tracking 260 degrees? Magnetic variation here is only around 2 degrees west so that doesn't account for all of the difference.
Should the sun not be setting somewhere north of 270 degrees?
Perth is 31'56 degrees south.
The furthest south the sun should come south is the tropic of capricorn. Ie, 23.5 degress south.
Therefore, why did the sun appear to be setting directly in front of us when we were tracking 260 degrees? Magnetic variation here is only around 2 degrees west so that doesn't account for all of the difference.
Should the sun not be setting somewhere north of 270 degrees?
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The azimuth limits of the setting Sun ([b]A{/B]) can be calculated from the relationship between the latitude of the observer (phi) and the declination of the Sun at the time of observation (delta). This relationship is expressed by the equation:
cos A = sin (delta) / cos (phi)
So at Perth with a latitude of phi= -31'56: cos (phi) = 0.8487. On the 19th of December delta = -23.80 degrees, thus sin delta = 0.4035. Hence cos A = 0.4035/0.8487 = 0.4754, giving A = 61.61 degrees at Sunrise and 298.39 degrees at Sunset.
cos A = sin (delta) / cos (phi)
So at Perth with a latitude of phi= -31'56: cos (phi) = 0.8487. On the 19th of December delta = -23.80 degrees, thus sin delta = 0.4035. Hence cos A = 0.4035/0.8487 = 0.4754, giving A = 61.61 degrees at Sunrise and 298.39 degrees at Sunset.
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Crash & Burn,
ZK DAN's formula is fine if applied correctly to get the right answer which certainly is not 298' or so.
Perhaps an easier way to get a grip on it may help.
If the Earth were flat your thoughts would be correct. But it is round so at 31'56 South your Sensible Horizon; that is the horizontal plane from the observer's eye is tilted 31'56 to the left of the Sensible Horizon at the Equator; so you see the sun "around the corner."
If you can imagine the sensible horizon at the Equator as a tangential line extending out past your position it would be 31'56 degrees above your sensible horizon. Fortunately the Earth is round, not flat, otherwise you would be flying underground.
[ 19 December 2001: Message edited by: pterodactyl ]
ZK DAN's formula is fine if applied correctly to get the right answer which certainly is not 298' or so.
Perhaps an easier way to get a grip on it may help.
If the Earth were flat your thoughts would be correct. But it is round so at 31'56 South your Sensible Horizon; that is the horizontal plane from the observer's eye is tilted 31'56 to the left of the Sensible Horizon at the Equator; so you see the sun "around the corner."
If you can imagine the sensible horizon at the Equator as a tangential line extending out past your position it would be 31'56 degrees above your sensible horizon. Fortunately the Earth is round, not flat, otherwise you would be flying underground.
[ 19 December 2001: Message edited by: pterodactyl ]
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My methods are based on sound Spherical Trigonometry applied to a Spherical Triangle, in this case the Earth. The equation in my above post is derived from the Cosine Formula. Essentially what it is saying is that if the declination of the Sun is negative (Southern Hemisphere summer) the azimuth of Sunset is between 270 degrees and 360 degrees, ie North of West. If the declination is positive (Southern Hemisphere winter) the azimuth of Sunset is between 180 degrees and 270 degrees, ie South of West. The value of the Sun's hour angle at setting for a given latitude is dependant upon the Sun's declination.
Dan
Dan
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ZK DAN,
You may want to consider your theory again. It would seem that you are out of phase with reality.
During the Southern Summer the Sun is at it's apparent most southerly point on Dec 22 of 23'27"(tilt of earth axis as I recall) and therefore at sunset would be at it's southmost point not most northerly as you suggest.
I chose not to resort to Spherical Trig because I felt that Crash & Burn wanted a concise and easily perceived explanation.
You may want to consider your theory again. It would seem that you are out of phase with reality.
During the Southern Summer the Sun is at it's apparent most southerly point on Dec 22 of 23'27"(tilt of earth axis as I recall) and therefore at sunset would be at it's southmost point not most northerly as you suggest.
I chose not to resort to Spherical Trig because I felt that Crash & Burn wanted a concise and easily perceived explanation.
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The formula's fine but you have to get the signs right. In this case both the angular values are negative. So is the sine of the declination. then the correct result appears as if by magic. Thank heaven for nav aids!
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While all good info, I think it may be simpler for the lay person to just take it to the extreme and imagine what the sun would look like as you approach the pole in the summer time. The closer you get, the farther towards the pole it "sets", until it just moves around the horizon in a complete circle when you're at the pole. That's how I explained it to my son when he was about 7 and he understood it -- I don't think I would have gotten far with any of the explanations above!
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As a non-mathematical analysis, and I may have the wrong end of the stick here so I'll beg your pardon in advance, but isn't it the case that as you move further south in the southern summer then the position of sunset moves ever further north until after passing the Tropic of Capricorn the sunset has moved so far north that the sun doesn't set at all? Indeed, the sun at its lowest point during the 24 hours of daylight will define true north. (And the reverse for the northern summer) Surely the secret lies in the angle of tilt of our home planet?
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BIK-116.8 has it right. Ignoring formulas it really is very simple. The further South you venture in Southern Summer the sun is in view for an even longer period till at the higher latitudes and at the pole we have a 24 hour daylight period for some months. That is why twilight periods get longer the further south you are.
Blacksheep,whatever you do, don't let the Pope hear of your theory. You will be burned at the stake!!
[ 20 December 2001: Message edited by: pterodactyl ]</p>
Blacksheep,whatever you do, don't let the Pope hear of your theory. You will be burned at the stake!!
[ 20 December 2001: Message edited by: pterodactyl ]</p>
Atlas 750 makes a very cogent point...you must pay attention to the signs of latitude and declination. As he points out, Southerly declinations are negative, as are longitudes East of the Prime Meridian (Greenwich), and southerly latitudes as well. The cosine formula is known by heart by all marine navigators worthy of the name.
The conscientious ones use it several times daily. I recall during my time as a merchant mariner, the Mate would take a bearing on the setting sun from the gyro-repeater on the bridge-wing, then compute from the almanac what the bearing should be given time and DR latitude of the observation.
The difference between the two gave a gyrocompass-error, and was a standard practice. Compass-errors are taken every watch, usually as soon as the watchkeeper assumes control, and about halfway through his watch. The sun or a star (or planet) can be used so observations of compass-error can be made at all times when celestial objects are visible. Best results are obtained with objects relatively low in the sky.
The compass-errors were recorded in a book kept readily to hand on the chart-table, and the Masters Night Orders usually contained the phrase "compass errors to be obtained."
"Simple sums for simple sailors" is the essence of celestial navigation. In this age of instant positions via GPS it is heartening to see someone looking to the heavens and thinking "why is this so"...and having sufficient interest to ask the question.
The conscientious ones use it several times daily. I recall during my time as a merchant mariner, the Mate would take a bearing on the setting sun from the gyro-repeater on the bridge-wing, then compute from the almanac what the bearing should be given time and DR latitude of the observation.
The difference between the two gave a gyrocompass-error, and was a standard practice. Compass-errors are taken every watch, usually as soon as the watchkeeper assumes control, and about halfway through his watch. The sun or a star (or planet) can be used so observations of compass-error can be made at all times when celestial objects are visible. Best results are obtained with objects relatively low in the sky.
The compass-errors were recorded in a book kept readily to hand on the chart-table, and the Masters Night Orders usually contained the phrase "compass errors to be obtained."
"Simple sums for simple sailors" is the essence of celestial navigation. In this age of instant positions via GPS it is heartening to see someone looking to the heavens and thinking "why is this so"...and having sufficient interest to ask the question.
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pterodactyl,
Are you responsible for those Spanish chaps in long robes and pointy hats who came round the manger and forced me to recant? Very painful having your hooves drawn you know, so weakling that I am, I confessed to using a fallacy to take the p*ss out of mathematicians. Now safely ensconced back in a Muslim country, far from papal oppression, I thumb my nose at both mathematics and the inquisition and insist that the solution lies in terrestrial tilt and the lands of the midnight sun. Consider if one will, the strange arctic/antarctic phenomena of sunset and sunrise coinciding at midnight and taking place at true north/south and work back from there to the tropical regions where the mid-day sun may be directly overhead and sunrise and sunset occur due east and due west. So far no-one has answered the gentleman's original question - Why was sunset taking place to the south of due west in the southern hemisphere during the southern summer...?
As one moves hubwards, doesn't the sun simply appear to move towards the relevant pole in summer, until eventually one moves so far hubwards that it is in view all the time? Being one who lives in a tree on the island of Borneo, on the rim as it were, it is so difficult to think in hubwards terms...
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Are you responsible for those Spanish chaps in long robes and pointy hats who came round the manger and forced me to recant? Very painful having your hooves drawn you know, so weakling that I am, I confessed to using a fallacy to take the p*ss out of mathematicians. Now safely ensconced back in a Muslim country, far from papal oppression, I thumb my nose at both mathematics and the inquisition and insist that the solution lies in terrestrial tilt and the lands of the midnight sun. Consider if one will, the strange arctic/antarctic phenomena of sunset and sunrise coinciding at midnight and taking place at true north/south and work back from there to the tropical regions where the mid-day sun may be directly overhead and sunrise and sunset occur due east and due west. So far no-one has answered the gentleman's original question - Why was sunset taking place to the south of due west in the southern hemisphere during the southern summer...?
As one moves hubwards, doesn't the sun simply appear to move towards the relevant pole in summer, until eventually one moves so far hubwards that it is in view all the time? Being one who lives in a tree on the island of Borneo, on the rim as it were, it is so difficult to think in hubwards terms...
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On the subject of solstices, can someone explain this? In London, at the summer solstice in June, both the earliest sunrise and the latest sunset occur pretty well on the same day, i.e. June 21st. Whereas at the winter solstice in December, the earliest sunset occurs a week or so before the shortest day, December 21st, and the latest sunrise about a week afterwards. Granted we're only talking about a few minutes here, but you'd think it might be symmetrical at both solstices....
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Max Continuous,
My terminology may be a little "old fashioned" as I am relying on facts studied nearly 50 years ago and the modern terms may be different.
We all know that the Earth orbits around the Sun although, to an observer on Earth, the sun apparently revolves around the Earth. The Apparent Solar day would be the time between two successive transits through the meridian of the observer and has been divided into 24 hours. In fact the Earth's angular speed of orbit varies and is not uniform so in arriving at the Mean Solar Day which is then divided into 24 hours the successive transits over a period of years was measured and then averaged to be divided into the 24 hour day we know. So the time between successive transits of the Sun is contantly varying and is not exactly 24 hours. The points where the apparent path of the Sun (The Ecliptic) intersect the Earth's Equatorial plane (The Celestial Equator)are about March 21st (First Point of Aries) with the Sun moving South to North and about 23rd September(First Point of Libra) with the Sun moving North to South.
According to Kepler's Law about orbital motion orbital speed increases when two bodies are closest and reduces with increased distance apart. If you calculate the days from March 21st to September 23rd you get 186 days and from September 23rd to March 21st you get 179 days. A difference of 7 days. So we have a cycle of slowing and then increasing orbital speed but not at a constant rate. This is easily confirmed as you would expect because the Earth is at Perihelion (closest to the Sun) about Jan 2nd and orbital speed is greatest, whereas it is at Aphelion (furthest from the Sun) about July 2nd and orbital speed slowest.
And the Solstices are the mid points on the Ecliptic halfway between the two points of intersection of the Ecliptic and the Celestial Equator.
Take half of the 186 days between 21st March and 23rd September...93 days after that is 22nd December; the Northern winter Solstice.
Take half of the 179 days from 23rd September to 21st March.....say 90 days after that is 22nd June the summer Solstice.
The usual typos!
[ 21 December 2001: Message edited by: pterodactyl ]</p>
My terminology may be a little "old fashioned" as I am relying on facts studied nearly 50 years ago and the modern terms may be different.
We all know that the Earth orbits around the Sun although, to an observer on Earth, the sun apparently revolves around the Earth. The Apparent Solar day would be the time between two successive transits through the meridian of the observer and has been divided into 24 hours. In fact the Earth's angular speed of orbit varies and is not uniform so in arriving at the Mean Solar Day which is then divided into 24 hours the successive transits over a period of years was measured and then averaged to be divided into the 24 hour day we know. So the time between successive transits of the Sun is contantly varying and is not exactly 24 hours. The points where the apparent path of the Sun (The Ecliptic) intersect the Earth's Equatorial plane (The Celestial Equator)are about March 21st (First Point of Aries) with the Sun moving South to North and about 23rd September(First Point of Libra) with the Sun moving North to South.
According to Kepler's Law about orbital motion orbital speed increases when two bodies are closest and reduces with increased distance apart. If you calculate the days from March 21st to September 23rd you get 186 days and from September 23rd to March 21st you get 179 days. A difference of 7 days. So we have a cycle of slowing and then increasing orbital speed but not at a constant rate. This is easily confirmed as you would expect because the Earth is at Perihelion (closest to the Sun) about Jan 2nd and orbital speed is greatest, whereas it is at Aphelion (furthest from the Sun) about July 2nd and orbital speed slowest.
And the Solstices are the mid points on the Ecliptic halfway between the two points of intersection of the Ecliptic and the Celestial Equator.
Take half of the 186 days between 21st March and 23rd September...93 days after that is 22nd December; the Northern winter Solstice.
Take half of the 179 days from 23rd September to 21st March.....say 90 days after that is 22nd June the summer Solstice.
The usual typos!
[ 21 December 2001: Message edited by: pterodactyl ]</p>
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Blacksheep,
So that was you! Now I remember. You were the quite rotund chappie we had trussed up on the spit.
The dungeon was very cold but we were well clothed in our flowing robes. You were most disrespectful and uncooperative so we had decided to apply a little heat.
After several revolutions on the spit we observed that you were well done in the middle but your extremities had ice forming on them.
A really innovative monk devised a method of tilting the spit axis about 20 degrees or so hoping to spread the effect more evenly. This was quite effective in melting the ice from your balding pate which seemed to be continuously illuminated by the flickering flames but we then noticed that your feet seemed to be continually in darkness and ice was forming on them again.
So it was decided that we should continuously tilt the rotor equally in each direction. In the end you didn't know whether you were coming or going and did finally agree with us that the Earth is FLAT.
And about time too, the Mother Superior was getting impatient.
So that was you! Now I remember. You were the quite rotund chappie we had trussed up on the spit.
The dungeon was very cold but we were well clothed in our flowing robes. You were most disrespectful and uncooperative so we had decided to apply a little heat.
After several revolutions on the spit we observed that you were well done in the middle but your extremities had ice forming on them.
A really innovative monk devised a method of tilting the spit axis about 20 degrees or so hoping to spread the effect more evenly. This was quite effective in melting the ice from your balding pate which seemed to be continuously illuminated by the flickering flames but we then noticed that your feet seemed to be continually in darkness and ice was forming on them again.
So it was decided that we should continuously tilt the rotor equally in each direction. In the end you didn't know whether you were coming or going and did finally agree with us that the Earth is FLAT.
And about time too, the Mother Superior was getting impatient.
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Crash & Burn,
This might be helpful.
Go to <a href="http://www.heavens-above.com/" target="_blank">http://www.heavens-above.com/</a> and you can enter the observer's location and it will give you the Sun's Azimuth at Sunrise and Sunset.
Information below is for Perth Australia on 24 Dec 01
Observer's Location: Perth ( -31.9330°N, 115.8330°E)
Local Time: Universal Coordinated Time -8 (GMT + 8:00)
Apparent geocentric position
Right ascension 18h 10m 46s
Declination -23° 24' 58"
Range 0.9835708 AU
Constellation Sagittarius
2001
Autumn equinox 21:30, 20 March
Winter solstice 15:37, 21 June
Spring equinox 07:04, 23 September
Summer solstice 03:21, 22 December
Event Time Altitude Azimuth
Astronomical twilight starts: 03:28 -18.0° 134°
Nautical twilight starts: 04:06 -12.0° 128°
Civil twilight starts: 04:40 -6.0° 123°
Sunrise: 05:08 -0.8° Azimuth 119°
Sunset: 19:23 -0.8° Azimuth 242°
Civil twilight ends: 19:51 -6.0° 238°
Nautical twilight ends: 20:26 -12.0° 232°
Astronomical twilight ends: 21:03 -18.0° 226°
Maximum altitude: 12:16 81.5° 0°
Minimum altitude: 00:16 -34.6° 180°
I have highlighted the Sun's Azimuth at sunrise and sunset. You can see that the Sun's bearing at Sunset is 242' almost 20' to the left of a track of 260'
[ 24 December 2001: Message edited by: pterodactyl ]</p>
This might be helpful.
Go to <a href="http://www.heavens-above.com/" target="_blank">http://www.heavens-above.com/</a> and you can enter the observer's location and it will give you the Sun's Azimuth at Sunrise and Sunset.
Information below is for Perth Australia on 24 Dec 01
Observer's Location: Perth ( -31.9330°N, 115.8330°E)
Local Time: Universal Coordinated Time -8 (GMT + 8:00)
Apparent geocentric position
Right ascension 18h 10m 46s
Declination -23° 24' 58"
Range 0.9835708 AU
Constellation Sagittarius
2001
Autumn equinox 21:30, 20 March
Winter solstice 15:37, 21 June
Spring equinox 07:04, 23 September
Summer solstice 03:21, 22 December
Event Time Altitude Azimuth
Astronomical twilight starts: 03:28 -18.0° 134°
Nautical twilight starts: 04:06 -12.0° 128°
Civil twilight starts: 04:40 -6.0° 123°
Sunrise: 05:08 -0.8° Azimuth 119°
Sunset: 19:23 -0.8° Azimuth 242°
Civil twilight ends: 19:51 -6.0° 238°
Nautical twilight ends: 20:26 -12.0° 232°
Astronomical twilight ends: 21:03 -18.0° 226°
Maximum altitude: 12:16 81.5° 0°
Minimum altitude: 00:16 -34.6° 180°
I have highlighted the Sun's Azimuth at sunrise and sunset. You can see that the Sun's bearing at Sunset is 242' almost 20' to the left of a track of 260'
[ 24 December 2001: Message edited by: pterodactyl ]</p>
