great circle
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great circle
hi!!
i dunno how but m a little confused regarding great circles and small circles.
The shortest path between two points on a plane is a straight line. However, on the surface of a sphere there are no straight lines. Instead, the shortest distance between any two points on a sphere is a segment of a circle.Ok.
So between 2 points where a great circle ain't formed,we have a small circle.
Now the smaller arc of this small circle would be the shortest distance between these 2 points.
so y do we say that only the great circle distance is the shortest distance between 2 points,
Shouldn't it be that a circular distance(great circle or small circle) represents the shortest distance.
thnx in advance
i dunno how but m a little confused regarding great circles and small circles.
The shortest path between two points on a plane is a straight line. However, on the surface of a sphere there are no straight lines. Instead, the shortest distance between any two points on a sphere is a segment of a circle.Ok.
So between 2 points where a great circle ain't formed,we have a small circle.
Now the smaller arc of this small circle would be the shortest distance between these 2 points.
so y do we say that only the great circle distance is the shortest distance between 2 points,
Shouldn't it be that a circular distance(great circle or small circle) represents the shortest distance.
thnx in advance
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Forget the circle word and use sphere instead.
Sit inside the SPHERE and draw lines on the outside wall.
The GREAT CIRCLE is not the literal meaning.
The circle does not exist.
Sit inside the SPHERE and draw lines on the outside wall.
The GREAT CIRCLE is not the literal meaning.
The circle does not exist.
Per Ardua ad Astraeus
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on the surface of a sphere there are no straight lines.
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BOAC yes indeed when we use a paper map it is flat..uses two dimensions x and y..
I can remembr the formula for the volume of a sphere think that is 4/3PI R to the cube.
so we have 1,34 x 3.142 x the cube of the radius
but thats all I can remember. The surface equation I can't remember. Think one nautical mile is that distance subtended by one minute..or have I got that wrong?
I can remembr the formula for the volume of a sphere think that is 4/3PI R to the cube.
so we have 1,34 x 3.142 x the cube of the radius
but thats all I can remember. The surface equation I can't remember. Think one nautical mile is that distance subtended by one minute..or have I got that wrong?
Last edited by DERG; 1st Mar 2011 at 15:03.
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Originally Posted by flyer by the wire
So between 2 points where a great circle ain't formed,we have a small circle.
regards,
HN39
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GCT
Great Circle TRACK - track.
The shortest line from a to b over the Earth.
Shorter than this one would need Thunderbird 4. (was it TB4 the one with the drill on it. . ?)
You can work out the Great Circle TRACK using one of many internet GCT thangs and they will do it for you.
There is formula for working out the Great Circle Track . .which is:
The shortest line from a to b over the Earth.
Shorter than this one would need Thunderbird 4. (was it TB4 the one with the drill on it. . ?)
You can work out the Great Circle TRACK using one of many internet GCT thangs and they will do it for you.
There is formula for working out the Great Circle Track . .which is:
Last edited by Upper Air; 1st Mar 2011 at 16:34. Reason: ran out of ink
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A Great Circle is any line of Longditude, and, the Equator. A Small Circle is any line of Latitude (excluding the Equator).
Don't get confused by straight lines on a chart... dependant upon the Chart Projection a straight line could be anything... a Rhumb Line or a great Circle Track.
Good luck... it's a less than easy science to understand.
In simplistic terms, stretch a piece of string between any two points on a football... that's a Great Circle! If you were to have a piece of string (tied from end to end) that was any less (in length) than the circumference of the football and that you laid it onto the surface of the football... that's a Small Circle.
Cheers
TCF
Don't get confused by straight lines on a chart... dependant upon the Chart Projection a straight line could be anything... a Rhumb Line or a great Circle Track.
Good luck... it's a less than easy science to understand.
In simplistic terms, stretch a piece of string between any two points on a football... that's a Great Circle! If you were to have a piece of string (tied from end to end) that was any less (in length) than the circumference of the football and that you laid it onto the surface of the football... that's a Small Circle.
Cheers
TCF
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Hi Fly by the wire,
Stretch an elastic band between any two points on a Globe. It will be on the great circle between those points.
As HN39 mentioned, the centre of any great circle is at the centre of the sphere. An orbiting satellite moves around a great circle.
Stretch an elastic band between any two points on a Globe. It will be on the great circle between those points.
As HN39 mentioned, the centre of any great circle is at the centre of the sphere. An orbiting satellite moves around a great circle.
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I'm not sure that I fully understand the OP's problem, but I think it might help to point out that the shortest distance between two points is only PART of a great circle. The full great circle goes all the way round the sphere, not just along the shortest line between the points.
Psychophysiological entity
Chop the world in two equal halves - at any angle.
Travel over however much of the cut-line you need, and Voilŕ, you have it.
Travel over however much of the cut-line you need, and Voilŕ, you have it.
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So between 2 points where a great circle ain't formed,we have a small circle.
Now the smaller arc of this small circle would be the shortest distance between these 2 points.
Now the smaller arc of this small circle would be the shortest distance between these 2 points.
A great circle, also known as a Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere, as distinct from a small circle. Any diameter of any great circle coincides with a diameter of the sphere, and therefore all great circles have the same circumference as each other, and have the same center as the sphere. A great circle is the largest circle that can be drawn on any given sphere. Every circle in Euclidean space is a great circle of exactly one sphere.
For any two points on the surface of a sphere there is a great circle through the two points. The minor arc of a great circle between two points is the shortest surface-path between them. In this sense the minor arc is analogous to “straight lines” in spherical geometry. The length of the minor arc of great circle is taken as the distance of two points on a surface of a sphere, namely great-circle distance. The great circles are the geodesics of the sphere.
When long distance aviation or nautical routes are drawn on a flat map (for instance, the Mercator projection), they often look curved. This is because they lie on great circles. A route that would appear as a straight line on the map would actually be longer.
For any two points on the surface of a sphere there is a great circle through the two points. The minor arc of a great circle between two points is the shortest surface-path between them. In this sense the minor arc is analogous to “straight lines” in spherical geometry. The length of the minor arc of great circle is taken as the distance of two points on a surface of a sphere, namely great-circle distance. The great circles are the geodesics of the sphere.
When long distance aviation or nautical routes are drawn on a flat map (for instance, the Mercator projection), they often look curved. This is because they lie on great circles. A route that would appear as a straight line on the map would actually be longer.
I think the point to understand is that it is the "minor arc" of the great circle that presents the shortest route between two points. Other circles can be drawn, but will result in a longer minor arc (least that's what I understand).
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wiki
Great circle - Wikipedia, the free encyclopedia
A great circle, also known as a Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere, as distinct from a small circle.
For any two points on the surface of a sphere there is a great circle through the two points. The minor arc of a great circle between two points is the shortest surface-path between them.
Strictly speaking the Earth is not a perfect sphere (it is an oblate spheroid or ellipsoid – i.e., slightly compressed at the poles), which means that the shortest distance between two points (a geodesic) is not quite a great circle. Nevertheless, the sphere model can be considered a first approximation.
Great circle routes are used by ships and aircraft where currents and winds are not a significant factor. Flight lengths can therefore often be approximated to the great-circle distance between two airports. For aircraft travelling west between continents in the northern hemisphere these paths will extend northward near or into the Arctic region, however easterly flights will often fly a more southerly track to take advantage of the jet stream.
A great circle, also known as a Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere, as distinct from a small circle.
For any two points on the surface of a sphere there is a great circle through the two points. The minor arc of a great circle between two points is the shortest surface-path between them.
Strictly speaking the Earth is not a perfect sphere (it is an oblate spheroid or ellipsoid – i.e., slightly compressed at the poles), which means that the shortest distance between two points (a geodesic) is not quite a great circle. Nevertheless, the sphere model can be considered a first approximation.
Great circle routes are used by ships and aircraft where currents and winds are not a significant factor. Flight lengths can therefore often be approximated to the great-circle distance between two airports. For aircraft travelling west between continents in the northern hemisphere these paths will extend northward near or into the Arctic region, however easterly flights will often fly a more southerly track to take advantage of the jet stream.
From the original post
There are no two points on the earth which cannot be joined by a great circle.
Try testing this argument on a football or other suitably small sphere.
Draw a circle with a diameter that is less than that of the sphere. Draw dots at two points on this circle.
Draw a straight line across the circle joining the two points.
You now have three paths between the two points. One is the straight line and the other two are arcs of the circle.
If you measure these paths you will find that the shortest is the straight line.
Now extend the straight line until the two ends meet. You will find that you have drawn a circle that has its centre at the centre of the sphere. This is the great circle on which the two points lie.
So the shortest distance between the two points is part of the great circle on which the two point lie.
So between 2 points where a great circle ain't formed,we have a small circle.
Now the smaller arc of this small circle would be the shortest distance between these 2 points.
Draw a circle with a diameter that is less than that of the sphere. Draw dots at two points on this circle.
Draw a straight line across the circle joining the two points.
You now have three paths between the two points. One is the straight line and the other two are arcs of the circle.
If you measure these paths you will find that the shortest is the straight line.
Now extend the straight line until the two ends meet. You will find that you have drawn a circle that has its centre at the centre of the sphere. This is the great circle on which the two points lie.
So the shortest distance between the two points is part of the great circle on which the two point lie.
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@ all above
thank u so much for your valuable input.
@Keith
But i really don't get the idea as to how you can draw a great circle between any two points.Consider two places placed @ the same lattitude(eg.15 degrees N) but different longitudes(say 18 degree east and 20 degree east)..
Now these two places are joined by the same parallel of lattitude(which is a small circle).
So how can a great circle be drawn through these 2 points?A small circle joins these 2 places.And hence the shortest distance b/w these 2 should be the small circle!
thank u so much for your valuable input.
@Keith
But i really don't get the idea as to how you can draw a great circle between any two points.Consider two places placed @ the same lattitude(eg.15 degrees N) but different longitudes(say 18 degree east and 20 degree east)..
Now these two places are joined by the same parallel of lattitude(which is a small circle).
So how can a great circle be drawn through these 2 points?A small circle joins these 2 places.And hence the shortest distance b/w these 2 should be the small circle!
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Hi flyer by the wire.
You can join two points with an infinite number of curved lines (including a Line of Latitude). However, only one line is the shortest distance, and it will lay on a Great Circle. (Lines of Longitude & the Equator are NOT the ONLY Great Circles.)
I suggest you buy yourself a globe of the world, and an elastic band. It will only take you a couple of minutes to see the difference.
You can join two points with an infinite number of curved lines (including a Line of Latitude). However, only one line is the shortest distance, and it will lay on a Great Circle. (Lines of Longitude & the Equator are NOT the ONLY Great Circles.)
I suggest you buy yourself a globe of the world, and an elastic band. It will only take you a couple of minutes to see the difference.
Last edited by rudderrudderrat; 2nd Mar 2011 at 15:01. Reason: extra text & can't spell
@Keith
But i really don't get the idea as to how you can draw a great circle between any two points.Consider two places placed @ the same lattitude(eg.15 degrees N) but different longitudes(say 18 degree east and 20 degree east).. Now these two places are joined by the same parallel of lattitude(which is a small circle). So how can a great circle be drawn through these 2 points?A small circle joins these 2 places.And hence the shortest distance b/w these 2 should be the small circle!
But i really don't get the idea as to how you can draw a great circle between any two points.Consider two places placed @ the same lattitude(eg.15 degrees N) but different longitudes(say 18 degree east and 20 degree east).. Now these two places are joined by the same parallel of lattitude(which is a small circle). So how can a great circle be drawn through these 2 points?A small circle joins these 2 places.And hence the shortest distance b/w these 2 should be the small circle!
Take an apple or some similar sperical(ish) fruit. The moreaccuarte will be the results.
Draw your line of latitude on it and draw two dots on that line to represent your two positions.
Place the apple on a table and roll it across the surface until one of the dots is at the top of the apple. Place a knife on that dot and while keeping the knife on the top dot, move the knife until it is also directly above the other dot. Now cut straight down through the apple to the table.
You will find that you have cut through both dots and also through the centre of the apple. The edges of the cut surfaces are the great circle on which the two dots lie.
small circles
If you 'chop' the sphere perpendicular to the N-S axis you will get the small cicle line of latitude route. If you angle the cut downwards so it passes through the centre of the earth you will get the great circle track. In the northern hemisphere the line where the surface is sliced for the great circle will lie north of the constant latitude line. You can make any number of 'cuts' you want taking in both points by angling the blade.
?