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Calculator: Great Circle Distance

Computing great circle distance between points P1 and P2 on a sphere width Radius R:

Used Formulas

The points are given in polar coordinates latitude and longitude :

(1)
(2)
where'
' =' 'Latitude in degrees Nord. Negativ values for South.
' =' 'Longitude in degrees East. Negativ values for West.

Converting into cartesian vector format using the center of the sphere as (0,0,0):

(3)
(4)
width
where'
' =' 'Unit vector from center of the sphere to point
' =' 'Lengt of vector
' =' 'Radius of the sphere

The unit vectors to the 2 points are:

(5)
(6)
where'
' =' 'Unit vector from center of the sphere to point
' =' ' = Latitude in radian. Negativ values for South.
' =' ' = Longitude in radian East. Negativ values for West.

The cosine of the angle between the vectors is:

(7)

And the great circle distance between the Points is:

(8)
where'
' =' 'Great circle distance between and
' =' 'Radius of the sphere (earth)
' =' 'X component of the unit vector from center to
' =' 'X component of the unit vector from center to
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Created Mittwoch, 29. März 2017
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Changed Freitag, 20. November 2020