How to find the angle between two points on the surface of earth with the center?

Question

What's the formula to finding the angle? assuming it is the angle of two lines both reaching the center of the earth from the two cities.

Answer 1

We can make up a formula that works for this situation. If you imagine the earth as a perfect circle, and the cities on the circle itself. We have to assume the earth is a perfect circle so that if we draw a line from the center to each city, the distance would be the same.

The circumference of the earth (or of any circle) would be 2*pi*r. This distance is good for the entire circle of 360 degrees. For part of the circle, then, it would depend on the angle that the arc covers. So if the arc (distance between cities) and the angle (that's what you're looking for) are set up in a ratio and compared to the entire circle, we can say the following:

pi*r/180 = arc/theta

Now this shows us that we need two pieces of information - the radius of the earth (you can Google that) and the distance between cities (again, Google that too). Assuming we knew those two values, you can then solve the equation for the angle theta:

theta = (180*arc) / (pi*r)