I am unable to reproduce correct calculation of angular distance of the globe.
I selected two point near my home on Google Earth:
and measured the distance between them by the ruler tool.
Distance in meters is approximately
100 and distance in arcseconds is reported by program as
I have calculated this formula
and found it equals to
3.23 which is close to the value, reported by Google Earth and the difference is probably caused by geoid shape.
Now I tried to calculate the same value trough vectors on the computer and encountered much bigger error
As you see, first I converted geographic coordinates to 3D cartesian ones and then calculate an angle between two vectors by normalizing inner product. Unfortunately, the result is
2.18, which is much more wrong.
Intermediate value also presented.
Looks like the main problem is calculating inverse cosine for the value, close to
1. Is this true?
How to overcome this problem?