geodetic2aer elevation and range calculation

Hi,

I'd like to calculate an elevation and a range from a known point on earth to a plane flying at distanse 200Km.

Our calculation using following formulas:

% p1.alt, p2.alt - highth above earth + earth radius (6378138 m)
% assumtoin is that earth is sphere with same radius.

alpha=acos(sin(p1.lat)*sin(p2.lat)+cos(p1.lat)*cos(p2.lat)*cos(p2.long-p1.long))  % Earth Central Angle
SlantRange=sqrt(p1.alt.^2 + p2.alt.^2-2*p1.alt*p2.alt*cos(alpha))  %cosine law.
elevation=acos(p1.alt.^2 + SlantRange.^2 -p2.alt.^2)/(2*SlantRange*p1.alt)

Plotting the 2 graphs I can see that the results are same more or less, but when doing the zoom-in, while a plane is at 120Km distanse (for example), I can see that there is diffrenece between my code and result of geodetic2aer by ~500m and elevation of 1 degree!

Digging into the code of geodetic2aer, I can see that some part of the geodetic2aer is using a Pythagorean theorem, but it is also uses semimahor axis and semiminor axis valeus.

So my question is - is there some assumtions which are taken into account for the geodetic2aer?

Which is more correct? (Myabe none of the 2 is correct and needs to use other formula to get the exact value).