how to caculate geographic extension

I assume there's a point with the given coordinates, and it's at the centre of a rectangle with the given dimensions. And the poster wants to find the coordinates of the rectangle's coordinates.

(There must be another assumption about the orientation of that rectangle, otherwise there would be infinitely many possible answers.)

(And there must be some assumptions about what "rectangle" means. Evidently it's four lines on a spherical surface that meet at four corners, like its plane counterpart. But it isn't possible for all those corners to be right angles, since the sum of the angles of a quadrilateral on a sphere does not have to be 360 degrees and quadrilaterals whose angles are all 90 degrees do not have to have opposite sides with the length equal.)

DrClapa at 2007-7-13 11:25:20 >

DrClap is right, the curvature can be ignored, and in general life is, otherwise there would be no maps.

earth circumference D = 2*pi*R = 40 000 000 m, so R = ca. 11 000 000 m.

100 m bend on the surface woud give an angle in radians of 2pi * 100 / D.

If you would go straightlined to the other corner, digging earth, the distance would be:

2 * R * sin(100/(2D)) = 2D/2pi . sin(2pi * 100/2D)

you can simplify sin(x) to x as the other terms are powers of x,

so:

= 100 m

joop_eggena at 2007-7-13 11:25:20 >