Isogonals and great circles
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Great circles are of significance because they represent the shortest distance between two points on the earth's surface. A great circle is the path that a light or radio beam would follow. Most long flights approximate great circle routes.
Isogonals are just lines of equal variation.
I guess I could say that they are not necessarily the same.
Isogonals are just lines of equal variation.
I guess I could say that they are not necessarily the same.
A great circle is the path that a light or radio beam would follow.
A great circle is the shortest distance between two points along the surface of the Earth ignoring any mountain ranges. A great circle taken all the way round between said two points effectively divides the Earth into two equal hemispheres -- the Equator being one case; others being any line of longitude paired with its opposite number (+ or - 180 degrees).
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Originally Posted by RatherBeFlying
Not quite so sure about that as, with the exception of lasers, electromagnetic radiation likes to propagate on a spherical wavefront.
A great circle is the shortest distance between two points along the surface of the Earth ignoring any mountain ranges. A great circle taken all the way round between said two points effectively divides the Earth into two equal hemispheres -- the Equator being one case; others being any line of longitude paired with its opposite number (+ or - 180 degrees).
A great circle is the shortest distance between two points along the surface of the Earth ignoring any mountain ranges. A great circle taken all the way round between said two points effectively divides the Earth into two equal hemispheres -- the Equator being one case; others being any line of longitude paired with its opposite number (+ or - 180 degrees).
On a sphere, two points are connected by 1 shortest path, which is an arc of the great circle in the plane of those two points and the centre of Earth. Except two antipodeal points, in which case all great circles through either point are equally shortest connecting paths.
But the Earth is not a sphere... 2 poles are connected by infinite number of equally shortest paths (all meridians), but 2 opposite points of equator are connected by 2 equally shortest paths - the meridians. The arcs of equator between those points are longer!
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Originally Posted by chornedsnorkack
But is Earth a sphere?
And I think that great circle plots are done with the simplifying assumption of spherical geometry - unless some huge leap forward has been made.
barit1
never failing to find the great circle route to the corner pub
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Hey,
the physical shape of the earth is probably best resembled as a geoid (equipotential surface approximating mean sea level)...
For Nav Systems an ellipsoid model is used (e.g. WGS84), since the assumption of earth being a sphere is much too inaccuarte to navigate precisely. The shortest distance between two points on the suface of the ellipsoid is called geodatic line. (The same as the great circle on a sphere)
Spherical geometry on an ellipsoid is really not something you want to get involved with
Trust me.... ;-)
LF and MF follow the curvature of the earth at least to some extent, due to refraction (lower air density in the higher atmosphere) and diffraction from the ground.
VLF uses the surface of the earth and the ionosphere as a wave guide, so there is some truth in your statement about great circular propagation of radio waves. Everything upwards of MF frequency range definitely propagates in the line of sight.
cheers
the physical shape of the earth is probably best resembled as a geoid (equipotential surface approximating mean sea level)...
For Nav Systems an ellipsoid model is used (e.g. WGS84), since the assumption of earth being a sphere is much too inaccuarte to navigate precisely. The shortest distance between two points on the suface of the ellipsoid is called geodatic line. (The same as the great circle on a sphere)
Spherical geometry on an ellipsoid is really not something you want to get involved with
Trust me.... ;-)LF and MF follow the curvature of the earth at least to some extent, due to refraction (lower air density in the higher atmosphere) and diffraction from the ground.
VLF uses the surface of the earth and the ionosphere as a wave guide, so there is some truth in your statement about great circular propagation of radio waves. Everything upwards of MF frequency range definitely propagates in the line of sight.
cheers
The Earth is ana oblate spheroid, fatter at the equator due to rotation.
The shortest track between two points is actually a rhumb line.
A great circle is the largest circle that can be made on the earth. This is if you think about it, the same as a rhumb line. Although, now we know the Earth is an oblate spheroid, this would technically have to be drawn along the eqatuor.
I must get out more
The shortest track between two points is actually a rhumb line.
A great circle is the largest circle that can be made on the earth. This is if you think about it, the same as a rhumb line. Although, now we know the Earth is an oblate spheroid, this would technically have to be drawn along the eqatuor.
I must get out more
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Originally Posted by Dan Winterland
The Earth is ana oblate spheroid, fatter at the equator due to rotation.
The shortest track between two points is actually a rhumb line.
A great circle is the largest circle that can be made on the earth. This is if you think about it, the same as a rhumb line. Although, now we know the Earth is an oblate spheroid, this would technically have to be drawn along the eqatuor.
I must get out more
The shortest track between two points is actually a rhumb line.
A great circle is the largest circle that can be made on the earth. This is if you think about it, the same as a rhumb line. Although, now we know the Earth is an oblate spheroid, this would technically have to be drawn along the eqatuor.
I must get out more
Just so we are not confusing program, What do you mean the shortest track? I am not putting words in your mouth, but I just want to say that the rhumb line isn't the shortest distance between two points.
A Great circle is essentially the circumference of the earth, assuming the earth is round.
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Originally Posted by Dan Winterland
The Earth is ana oblate spheroid, fatter at the equator due to rotation.
The shortest track between two points is actually a rhumb line.
A great circle is the largest circle that can be made on the earth. This is if you think about it, the same as a rhumb line. Although, now we know the Earth is an oblate spheroid, this would technically have to be drawn along the eqatuor.
I must get out more
The shortest track between two points is actually a rhumb line.
A great circle is the largest circle that can be made on the earth. This is if you think about it, the same as a rhumb line. Although, now we know the Earth is an oblate spheroid, this would technically have to be drawn along the eqatuor.
I must get out more
well, this only true in two cases:
You are flying along the equator (Track 090/270) or your track is 000/180, when flying along a meridian...
Rumbline distance is always greater or equal to GC (geodetic line, to be precise) distance.
cheers
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Well assuming a spherical Earth
'India-Mike
pilotezulu
Perhaps not, but has anyone got a definitive answer? Things seem to have gone off topic after 2nd post, interesting as it may be.
If isogonals are indeed not great circles, is the agonic line a special case? I've not seen this marked on a worldwide map before. I'm drawing a comparison with parallels of lattitude, all small circles except the one that's neither North nor South. I'm assuming a spherical Earth of course.
Cheers
PS - 'India-Mike, you'll need to change your name
'India-Mike
Is an isogonal a great circle?
Isogonals are just lines of equal variation.
I guess I could say that they are not necessarily the same
I guess I could say that they are not necessarily the same
If isogonals are indeed not great circles, is the agonic line a special case? I've not seen this marked on a worldwide map before. I'm drawing a comparison with parallels of lattitude, all small circles except the one that's neither North nor South. I'm assuming a spherical Earth of course.
Cheers
PS - 'India-Mike, you'll need to change your name
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I wonder if there's a magnetic declination chart on the NOAA website? That might help to answer the original question. I'd check that myself, but don't really care to know.
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Originally Posted by microburst8265
Hey,
the physical shape of the earth is probably best resembled as a geoid (equipotential surface approximating mean sea level)...
For Nav Systems an ellipsoid model is used (e.g. WGS84), since the assumption of earth being a sphere is much too inaccuarte to navigate precisely. The shortest distance between two points on the suface of the ellipsoid is called geodatic line. (The same as the great circle on a sphere)
Spherical geometry on an ellipsoid is really not something you want to get involved with Trust me.... ;-)
the physical shape of the earth is probably best resembled as a geoid (equipotential surface approximating mean sea level)...
For Nav Systems an ellipsoid model is used (e.g. WGS84), since the assumption of earth being a sphere is much too inaccuarte to navigate precisely. The shortest distance between two points on the suface of the ellipsoid is called geodatic line. (The same as the great circle on a sphere)
Spherical geometry on an ellipsoid is really not something you want to get involved with
Trust me.... ;-)Consider this:
If you look at a pair of points both exactly at the equator and exactly opposite, then the shortest distance is the meridian through a pole. Either pole, those distances are equal. The arcs of equator either side are appreciably longer, though they also are "great circle". One would expect that the other "great circles" would be longer than the pair of meridians, too.
Now look at the pair of points still both exactly at the equator but not precisely opposite - such that the shorter equator arc between them is still longer than the pair of meridians to a pole.
Obviously there is a path which is shorter than the great circle, yet makes an angle at a pole. Therefore, you should also have a non-angled continuous line which does not follow either the great circle at equator (having the equatorial bulge) or meridians with an angle at a pole, but smoothly passes through higher latitudes. Actually a pair of such lines, on either hemisphere.
Now consider a pair of points which are also slightly off the equator, in the same hemisphere. Obviously, now, the continuous line across one hemisphere would be longer than the line across the other hemisphere - but still shorther than the paths in between, spending too much time on the equatorial bulge...
What can be said generally about "shortest" or "straight" lines on Earth?
"the physical shape of the earth is probably best resembled as a geoid"
Good one!!
Definition of Geoid - the shape of the Earth!
Therefore if the shape of the Earth is a geoid then the Earth is..... Earth shaped!!!!
Good one!!
Definition of Geoid - the shape of the Earth!
Therefore if the shape of the Earth is a geoid then the Earth is..... Earth shaped!!!!
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The isogonal contours are complex shapes influenced by continents, oceans and the earth's core.
Have a look at this to see what I mean:
http://www.geomag.bgs.ac.uk/images/c...pdf/merc_d.pdf
As I understand it, a GC track is defined as the intersection of a plane that passes through two points on the surface plus the earth's centre, and the earth's surface. This may differ minutely from the shortest distance definition, but is practically identical.
Have a look at this to see what I mean:
http://www.geomag.bgs.ac.uk/images/c...pdf/merc_d.pdf
As I understand it, a GC track is defined as the intersection of a plane that passes through two points on the surface plus the earth's centre, and the earth's surface. This may differ minutely from the shortest distance definition, but is practically identical.
An isogonal is not a great circle. Nothing follows an isogonal from one place to another. It does not represent the shortest distance anywhere.
Isogonals merely represent the points on the earth's surface where the magnetic variation is exactly XX deg E. Move a smidgin to the side of that line, and the variation is now XX-bee'sdick.
What governs that is rather complex, due to the earth's core content mixing.
There is also more than one magentic pole at each end of the earth, but that's another story
Isogonals merely represent the points on the earth's surface where the magnetic variation is exactly XX deg E. Move a smidgin to the side of that line, and the variation is now XX-bee'sdick.
What governs that is rather complex, due to the earth's core content mixing.
There is also more than one magentic pole at each end of the earth, but that's another story
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Hmm, ok, you got me 
But still, the geoid approximates a surface of equal gravitational potential, and therefore differs from the earth's topographic structure... Or shall I say earth is potato shaped ;-) This is a physical model. Mathematically you will still end up with the ellipsoid...
ch.....:
Good point, going back to the spherical model with the same situation (both points on exact opposite sides) you will end up with an infinite number of "shortest" distance between the two...
So for some layouts you will get multiple solutions, nevertheless if you go to smaller scale I think there will only be one, since the circular circumference of the ellipsoid largens with decreasing latitude. Probably somebody should just do the Math and show us
Back to topic: Agonic line: Variation = 0
But still, the geoid approximates a surface of equal gravitational potential, and therefore differs from the earth's topographic structure... Or shall I say earth is potato shaped ;-) This is a physical model. Mathematically you will still end up with the ellipsoid...ch.....:
Good point, going back to the spherical model with the same situation (both points on exact opposite sides) you will end up with an infinite number of "shortest" distance between the two...
So for some layouts you will get multiple solutions, nevertheless if you go to smaller scale I think there will only be one, since the circular circumference of the ellipsoid largens with decreasing latitude. Probably somebody should just do the Math and show us
Back to topic: Agonic line: Variation = 0
is the spherical model implied?
Can we even talk about great *circles* outside of a surface of a sphere? All these other shapes have exactly 1 great circle which doubles as their respective equator.
Just wondering.
(A blatant attempt to divert the off-topic thread to question its very reason for existance.)
Just wondering.
(A blatant attempt to divert the off-topic thread to question its very reason for existance.)
More bang for your buck
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good definition and info on great circles http://mathworld.wolfram.com/GreatCircle.html
