Flybyknight is only partially correct. You are measuring a difference of one minute of longitude, that's true, and that is not generally equal to one minute of arc. However you are doing it at the equator, and as a simple approximation, one minute of longitude at the equator is indeed one nautical mile.
Without knowing more about what exactly you're doing, it's hard to say.
One thing I can say is that "calculated distance" and "assumed distance" are not terms I know of in celestial navigation. You have an "assumed position", and from this position, you calculate an altitude and azimuth of the body you're observing. I don't know of any easy way to check these values with Google Earth.
Furthermore, if you assume a position somewhere on the equator and then actually measure altitude in Hinton, Alberta, of course your results will be way off.
Finally, computing distance between two points is done by a simple formula, and is not really something you frequently do in celestial navigation. If that's all you're trying to do, Wikipedia has a few formulas, some quite simple, some quite complex. For me, the Spherical Law of Cosines suffices. Google Earth probably uses something much more complex, so don't expect the values to match exactly, though on the equator the approximation should be quite good.
Sounds like a lot is missing from your story. Please explain exactly what you're trying to do and what procedure you're using so we can help.
1972 Catalina 27