Mr Optimistic
The problem with the poor professor's paper is that it is quite simply unintelligent to include the range variation of gravity as its very small perturbing effect relative to a constant model is less than trivial when compared to the other forces acting and the inherent limitations of the model.
As this is a technical forum I was hoping you would flesh this out by showing the calculations. I really don't think it is fair comment to label the guy as unintelligent and expect forum users to simply take your word for it. Has he done something to your sister or do you have another reason for the ad-homs approach?
As neither yourself or awblain have shown any inclination to do the sums I thought I'd do them myself:
According to his paper
g is adjusted by the following equation:
gₐ =
gₑ x (rₑ ÷ rₐ)²
It is obvious that at low altitudes this is going to make no difference. But what is the upper limit where a tool such as this would be used? A case study would be the Columbia disaster.
The altitude of that break-up was ≈ 64km. The Earth radius is ≈ 6380km at the equator (WGS84). So, rₑ is 6380km and rₐ is 6444km. Using 9.81 for
gₑ in the above equation and evaluating for
gₐ results in 9.62ms⁻².
By using the equation:
R = V₀ x √(2h ÷
g)
..we can get a feel for how much difference this would make to horizontal range, using the velocity at break-up ≈ 6000ms⁻¹ and evaluating R when
g = 9.81 and then again when
g = 9.62
This would not include drag. The answers are
685.4km and
692.1km
So, up to about 7km would be the maximum difference this technique would make, before drag. Clearly, drag would reduce this.
Whether or not you think that is trivial depends on one's point of view. I think that if his model allows him to make such a correction he may as well have it. Even if it isn't necessary.