ANSWERS: 3

The shortest distance between two points is a straight line. On a spehre, the shortest distance would be through the center. At the equator, the distance would be the equal to the diameter. As one of the points moves, the distance gets smaller. I am not sure how to calculate the distance along the base of an arc but the distance along the surface is L = m/360 degrees * circumference, where m is the measure of the central angle.

Your question is ambiguous.  The shortest distance between two points which happen to lie on a sphere is the general 3d distance formula; for points (x1, y1, z1) and (x2, y2, z2), the distance will be sqrt( (x2x1)^2 + (y2y1)^2 + (z2z1)^2 ) This will be along a chord of the great circle including the two points.  The shortest distance on the surface of a sphere between two points on the sphere is, as JoeSpeedy alludes, the distance on the great circle including the two points along the arc subtended by the smaller central angle defined. See the wikipedia entry ( http://en.wikipedia.org/wiki/Greatcircle_distance ) for examples in terms of latitude and longitude.

A simple formula, is K arccos{sin(lat1) sin(lat2) + cos(lat1) cos(lat2) cos(lon2  lon1)) where K is a constant equal to the circumference of the sphere divided by the number of angular units in a circle (i.e. 360 if you're using degrees or two pi if using radians). On a scientific calculator arccos(x) is obtained typically by entering x and pressing Inv then Cos or "2nd" then Cos. For more info: http://en.wikipedia.org/wiki/Greatcircle_distance
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