I do not interpret it, or any of your other responses, as hostility. (I've been upvoting your responses. I requested feedback, and you've provided it.)

I did indicate the integral would be more accurate; I can run a summation in a few seconds, however, where an integral requires breaking out a pencil and paper and skills I haven't touched since college. It was a rough estimate, which I used strictly to show what it was such a test should be looking for. Since we aren't running the test itself, accuracy didn't seem particularly important, since the purpose was strictly demonstrative.

(Neither formula is actually correct for the idea, however. The constant would be be wrong, and would need to be adjusted so the gravitational force would be equivalent to the existing formula for an object at rest.)

Thank you for your time!