<< Another solution: just make a line between the two points and use the project curve command to project the line to the sphere. For the direction clic the center of the sphere and then center of the line you just created and thats it!>>

That is actually how I did it (before I even opened up this thread), but I thought that there must be an easier way to do it with the ARC command! But it doesn't seem that there is.

Thanks to everyone for all of their help.