For antipodal points there are an infinite number of great circles between the two points and the length is half the circumference of the earth. But for the ellipsoid al earth there are just two paths for antipodal points that have opposite directions.
Full Answer
What is the distance along a great circle?
The great-circle distance, orthodromic distance, or spherical distance is the distance along a great circle . It is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior).
What is the distance between two points in Euclidean space?
The distance between two points in Euclidean space is the length of a straight line between them, but on the sphere there are no straight lines. In spaces with curvature, straight lines are replaced by geodesics. Geodesics on the sphere are circles on the sphere whose centers coincide with the center of the sphere, and are called 'great circles'.
What is the length of the shorter arc of a circle?
The length of the shorter arc is the great-circle distance between the points. A great circle endowed with such a distance is called a Riemannian circle in Riemannian geometry . , where r is the radius of the sphere.
How accurate are great circle distance formulas for Earth's surface?
The Earth is nearly spherical, so great-circle distance formulas give the distance between points on the surface of the Earth correct to within about 0.5%. The vertex is the highest-latitude point on a great circle.
How do you find the distance of the great circle?
The great circle formula is given by: d = rcos-1[cos a cos b cos(x-y) + sin a sin b]. Given: r = 4.7 km or 4700 m, a, b= 45°, 32° and x, y = 24°,17°.
Why is a great circle the shortest distance?
Planes travel along the shortest route in 3-dimensional space. This route is called a geodesic or great circle. While map projections distort these routes confusing passengers, the great circle path is the shortest path between two far locations. This is why pilots fly polar routes saving time and distance.
What is great circle distance in aviation?
The great-circle distance or orthodromic distance is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere.
What is the shortest distance between two points on the Earth surface?
Credit: US Geological Survey – Online Earthquake Glossary: Great circle. The shortest distance between any two points on the surface of a sphere is called the Great Circle, a part of which is shown in the diagram as a dashed line. This circle is concentric with the center of the sphere.
What is the length of the great circle?
Great circles on Earth are roughly 40,000 kilometers (24,855 miles) all the way around. The Earth isn't a perfect sphere, however. It is an oblate spheroid, meaning it stretches out a little around the Equator in a form called an equatorial bulge.
Which is the largest circle on the Earth?
The equator is the circle that is equidistant from the North Pole and South Pole. It divides the Earth into the Northern Hemisphere and the Southern Hemisphere. Of the parallels or circles of latitude, it is the longest, and the only 'great circle' (a circle on the surface of the Earth, centered on Earth's center).
How many miles are in one great circle degree?
One-degree of longitude equals 288,200 feet (54.6 miles), one minute equals 4,800 feet (0.91 mile), and one second equals 80 feet.
What is the distance between points?
Distance between two points is the length of the line segment that connects the two given points. Distance between two points in coordinate geometry can be calculated by finding the length of the line segment joining the given coordinates.
What is the maximum distance between two points on Earth?
Along any truly straight line As the variable circumference of the Earth approaches 40,000 kilometres (25,000 mi), such a maximum "diametrical" or "antipodal" line would be on the order of 13,000 kilometres (8,000 mi) long.
Why is the great circle the shortest route between two places?
(iii) Great Circles are the shortest routes between two places as we can connect any two places on the earth's surface by the curvature line of the great circle. And this curvature is the smallest possible route between those two places, because this curvature directly connects those places or points.
What is the fastest distance between two points?
A straight lineA straight line is the shortest distance between two points.
Why great circle has a shorter distance than rhumb line in a long ocean passages?
Overall? Over a longer oceanic passage, it makes sense to travel on a Great Circle Circle than the Rhumb Line due to the extra time and energy involved.
Why is a great circle route often used in navigation?
Why are great circles important in navigation? Because they show us the shortest routes between two points on a sphere. If we want to travel the shortest distance across any sphere, Earth being the obvious choice for most of us, you actually need to head towards the point on the opposite side of that sphere.
What is the difference between great circle and rhumb line?
In other words, a great circle is locally "straight" with zero geodesic curvature, whereas a rhumb line has non-zero geodesic curvature. Meridians of longitude and parallels of latitude provide special cases of the rhumb line, where their angles of intersection are respectively 0° and 90°.
How do you find the shortest distance in Earth geometry?
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