A small rectangle on a large ball - distortion?

[gerbil]

Hi

Let's assume we have a, say, 10 cm * 20 cm, not very thick, rectangular object. We also have a huge ball, with a known radius of about 1 m. Now be put that rectangle onto the ball surface. What happens to the rectangle?

I know that a 2D-object doesn't fit very well onto a spherical surface, of course. Just wondering, does anyone know a way to get some numerical information about the distortion? I have googled A LOT but haven't really found anything.

I guess that a few great mathematicians have already solved this problem..?

 

[mgb_phys]

The topic is called spherical trigonometry -it's widely used in navaigation ( we live on a ball) and astronomy. The wiki article on spherical trig is a good intro.