Earlier quoted context omitted.
>> Starlink satellites are in orbit 550km high. So any journey would add at least 1100km Might want to check with Pythagoras on that one..
Meh, he said at least. There could be cases where you beam up then down nearly vertically (same city).
Consider a right-angled triangle with base length d and height 550, corresponding to transmission from a base-station to a satellite. The hypotenuse has length sqrt(d^2 + 550^2), so the difference in length between the hypotenuse and base is sqrt(d^2 + 550^2) - d.
This has a maximum of 550 when d=0 (i.e., shooting straight up), and decreases as d increases: https://www.wolframalpha.com/input/?i=plot+sqrt%28d%5E2+%2B+...
Alternatively, consider the triangle inequality: the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side. This directly implies that the difference in length between the hypotenuse and base is less than or equal the height [base + height >= hypotenuse implies height >= hypotenuse - base].