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The gnomonic map projection maps into straight lines all Great Circles, even those not passing through the central point, but can present even less than one hemisphere (unless the map were of infinite size with corresponding distortions, which is obviously not possible).
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What is the shortest line between any two points?
In plane geometry it is a straight line. If you want to know the shortest line between two points on a globe, it will be the intervening section or arc of the great circle route that connects the points. The great circle will be a circle that cuts the globe into exactly equal parts, like the equator.
Does every great circle of a sphere have to pass through its center?
Let's be very careful here: The "great circle" of a sphere is a circle that lies on the surface ofthe sphere, so there's no way the great circle can "pass through" the sphere's center.However, in order for the circle to be a "great circle", its center must be the center of the sphere.
Can anyone explain the great circle formula in layman terms?
Yes the great circle formula is the same formula for any other circle.
What is the difference between a small circle and a great circle?
A small circle is a simple circle on a two dimensional plane. The great circle is the circle around a sphere that is on the plane that intersects with the center of the sphere. It is the reason that on a flat map the paths of planes seem to curve to go to and from Europe and the North American continent.
What line that goes from one side of the circle to the other?
In geometry it is called the "Great Circle".
Mercator projection maps are used to determine great-circle routes?
No. A straight line on a mercator map is a path of constant bearing, but this will not generally be a great-circle route.
What is used by navigators to plot great circle routes?
Navigators use a Mercator projection chart to plot great circle routes. This chart allows them to draw a straight line, which represents the shortest distance between two points on a curved surface such as the Earth. By following this route, ships and planes can save time and fuel compared to following a rhumb line route.
Why do airline pilots use great circle routes to a plot airline flight paths?
Airline pilots use great circle routes to a plot airline flight paths because they are often the shortest distance between take off and destination. Great circle routes take into account the curvature of the Earth.
Why do airline pilots use great-circle routes to plot airline flight paths?
Airline pilots use great circle routes to a plot airline flight paths because they are often the shortest distance between take off and destination. Great circle routes take into account the curvature of the Earth.
Compare a straight route with a great circle route?
A straight route is the path taken in a straight line while the shortest distance between two points on a circle is known as the great circle route. However, while travelling the great circle around the globe, the path ahead will look like the straight route.
Why is a great circle route often navigation?
Since the earth is a globe, some air routes are shorter when the flight goes over the Arctic. Those flights take a part of the "great circle" and shave off hours of distance. In fact great circle routes are applicable anywhere on the globe because they are the shortest routes between any two points.
Is a straight line between two points on Mercator Projection a great circle route?
In general, no ... only if the two points are on the equator. The Mercator is probably the worst possible projection on which to try and identify great-circle routes and distances, true directions, and true sizes or shapes of anything.
Why is a great- circle route often used in navigation?
Great Circle routes are used because they are the shortest route between two points on the globe.
How much shorter is the great circle route then the straight route?
The great circle route is the shortest route.It is just that if you plot a great circle path on a flat map (unless it is the equator or a line of longitude) it will look bent - this is an artifact of map projection.The actual difference in route lengths depends on the routes you are comparing.---------------------------------------------------------------------------------------The great circle route is the shortest route between two locations on a "roughly" spherical object like the earth. It is in effect the straight line between two locations along the surface of a sphere.By the straight route - I assume you mean a straight line on a 2D map. This usually does not coincide with the great circle route. The difference in length between a so-called straight route and a great circle route would then vary based on both the map projection selected and the location of the two endpoints of the journey.-----------------------------------------------------------------------------The SHORTEST line between two points on a sphere IS a GREAT CIRCLE.Also, by definition, the shortest line between two points IS the straight route.
Are great circle routes used to calculate distance for air passenger duty?
yes they are
Why great-circle routes are commonly used in navigation?
Great-circle routes are the shortest distance between two points on a sphere, making them the most efficient for long-distance navigation. They also help conserve fuel by reducing the total distance traveled. Additionally, great-circle routes are utilized by aircraft to take advantage of the Earth's curvature for faster travel times.
What does the great-circle route represent?
It is the shortest distance between two points on a sphere, where the sphere in question is the earth. Particularly long airline flights follow great circle routes.
