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 3-d distance formula; for points (x1, y1, z1) and (x2, y2, z2), the distance will be sqrt( (x2-x1)^2 + (y2-y1)^2 + (z2-z1)^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 Joe-Speedy 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/Great-circle_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/Great-circle_distance

Copyright 2020, Wired Ivy, LLC